{"title":"Differential calculus and equations Books","description":"","products":[{"product_id":"mathematical-physics-with-differential-equations-9780192872623","title":"Mathematical Physics with Differential Equations","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis textbook uses insight from differential equations to analyse fundamental subjects of modern theoretical physics, including classical and quantum mechanics, thermodynamics, electromagnetism, superconductivity, gravitational physics, and quantum field theories.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface Notation and Convention 1: Hamiltonian Systems and Applications 2: Schrödinger Equation and Quantum Mechanics 3: Maxwell Equations, Dirac Monopole, and Gauge Fields 4: Special Relativity 5: Abelian Gauge Field Equations 6: Dirac Equations 7: GinzburgDSLandau Equations for Superconductivity 8: Magnetic Vortices in Abelian Higgs Theory 9: Non-Abelian Gauge Field Equations 10: Einstein Equations and Related Topics 11: Charged Vortices and ChernDSSimons Equations 12: Skyrme Model and Related Topics 13: Strings and Branes 14: BornDSInfeld Theory of Electromagnetism 15: Canonical Quantization of Fields Appendices Bibliography Index","brand":"Oxford University Press","offers":[{"title":"Default Title","offer_id":48732608463191,"sku":"9780192872623","price":38.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780192872623.jpg?v=1719997631"},{"product_id":"a-first-course-in-finite-elements-9780470035801","title":"A First Course in Finite Elements","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThe text material evolved from over 50 years of combined teaching experience it deals with a formulation and application of the finite element method. A meaningful course can be constructed from a subset of the chapters in this book for a quarter course; instructions for such use are given in the preface.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"Recommended for upper division undergraduates and above.\" (\u003ci\u003eCHOICE\u003c\/i\u003e, February 2008)\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003ePreface xi\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Introduction 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Background 1\u003c\/p\u003e \u003cp\u003e1.2 Applications of Finite elements 7\u003c\/p\u003e \u003cp\u003eReferences 9\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Direct Approach for Discrete Systems 11\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Describing the Behavior of a Single Bar Element 11\u003c\/p\u003e \u003cp\u003e2.2 Equations for a System 15\u003c\/p\u003e \u003cp\u003e2.2.1 Equations for Assembly 18\u003c\/p\u003e \u003cp\u003e2.2.2 Boundary Conditions and System Solution 20\u003c\/p\u003e \u003cp\u003e2.3 Applications to Other Linear Systems 24\u003c\/p\u003e \u003cp\u003e2.4 Two-Dimensional Truss Systems 27\u003c\/p\u003e \u003cp\u003e2.5 Transformation Law 30\u003c\/p\u003e \u003cp\u003e2.6 Three-Dimensional Truss Systems 35\u003c\/p\u003e \u003cp\u003eReferences 36\u003c\/p\u003e \u003cp\u003eProblems 37\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Strong andWeak Forms for One-Dimensional Problems 41\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 The Strong Form in One-Dimensional Problems 42\u003c\/p\u003e \u003cp\u003e3.1.1 The Strong Form for an Axially Loaded Elastic Bar 42\u003c\/p\u003e \u003cp\u003e3.1.2 The Strong Form for Heat Conduction in One Dimension 44\u003c\/p\u003e \u003cp\u003e3.1.3 Diffusion in One Dimension 46\u003c\/p\u003e \u003cp\u003e3.2 TheWeak Form in One Dimension 47\u003c\/p\u003e \u003cp\u003e3.3 Continuity 50\u003c\/p\u003e \u003cp\u003e3.4 The Equivalence Between theWeak and Strong Forms 51\u003c\/p\u003e \u003cp\u003e3.5 One-Dimensional Stress Analysis with Arbitrary Boundary Conditions 58\u003c\/p\u003e \u003cp\u003e3.5.1 Strong Form for One-Dimensional Stress Analysis 58\u003c\/p\u003e \u003cp\u003e3.5.2 Weak Form for One-Dimensional Stress Analysis 59\u003c\/p\u003e \u003cp\u003e3.6 One-Dimensional Heat Conduction with Arbitrary Boundary Conditions 60\u003c\/p\u003e \u003cp\u003e3.6.1 Strong Form for Heat Conduction in One Dimension with Arbitrary Boundary Conditions 60\u003c\/p\u003e \u003cp\u003e3.6.2 Weak Form for Heat Conduction in One Dimension with Arbitrary Boundary Conditions 61\u003c\/p\u003e \u003cp\u003e3.7 Two-Point Boundary Value Problem with Generalized Boundary Conditions 62\u003c\/p\u003e \u003cp\u003e3.7.1 Strong Form for Two-Point Boundary Value Problems with Generalized Boundary Conditions 62\u003c\/p\u003e \u003cp\u003e3.7.2 Weak Form for Two-Point Boundary Value Problems with Generalized Boundary Conditions 63\u003c\/p\u003e \u003cp\u003e3.8 Advection–Diffusion 64\u003c\/p\u003e \u003cp\u003e3.8.1 Strong Form of Advection–Diffusion Equation 65\u003c\/p\u003e \u003cp\u003e3.8.2 Weak Form of Advection–Diffusion Equation 66\u003c\/p\u003e \u003cp\u003e3.9 Minimum Potential Energy 67\u003c\/p\u003e \u003cp\u003e3.10 Integrability 71\u003c\/p\u003e \u003cp\u003eReferences 72\u003c\/p\u003e \u003cp\u003eProblems 72\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Approximation of Trial Solutions,Weight Functions and Gauss Quadrature for One-Dimensional Problems 77\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Two-Node Linear Element 79\u003c\/p\u003e \u003cp\u003e4.2 Quadratic One-Dimensional Element 81\u003c\/p\u003e \u003cp\u003e4.3 Direct Construction of Shape Functions in One Dimension 82\u003c\/p\u003e \u003cp\u003e4.4 Approximation of theWeight Functions 84\u003c\/p\u003e \u003cp\u003e4.5 Global Approximation and Continuity 84\u003c\/p\u003e \u003cp\u003e4.6 Gauss Quadrature 85\u003c\/p\u003e \u003cp\u003eReference 90\u003c\/p\u003e \u003cp\u003eProblems 90\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Finite Element Formulation for One-Dimensional Problems 93\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Development of Discrete Equation: Simple Case 93\u003c\/p\u003e \u003cp\u003e5.2 Element Matrices for Two-Node Element 97\u003c\/p\u003e \u003cp\u003e5.3 Application to Heat Conduction and Diffusion Problems 99\u003c\/p\u003e \u003cp\u003e5.4 Development of Discrete Equations for Arbitrary Boundary Conditions 105\u003c\/p\u003e \u003cp\u003e5.5 Two-Point Boundary Value Problem with Generalized Boundary Conditions 111\u003c\/p\u003e \u003cp\u003e5.6 Convergence of the FEM 113\u003c\/p\u003e \u003cp\u003e5.6.1 Convergence by Numerical Experiments 115\u003c\/p\u003e \u003cp\u003e5.6.2 Convergence by Analysis 118\u003c\/p\u003e \u003cp\u003e5.7 FEM for Advection–Diffusion Equation 120\u003c\/p\u003e \u003cp\u003eReferences 122\u003c\/p\u003e \u003cp\u003eProblems 123\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Strong andWeak Forms for Multidimensional Scalar Field Problems 131\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Divergence Theorem and Green’s Formula 133\u003c\/p\u003e \u003cp\u003e6.2 Strong Form 139\u003c\/p\u003e \u003cp\u003e6.3 Weak Form 142\u003c\/p\u003e \u003cp\u003e6.4 The Equivalence BetweenWeak and Strong Forms 144\u003c\/p\u003e \u003cp\u003e6.5 Generalization to Three-Dimensional Problems 145\u003c\/p\u003e \u003cp\u003e6.6 Strong andWeak Forms of Scalar Steady-State Advection–Diffusion in Two Dimensions 146\u003c\/p\u003e \u003cp\u003eReferences 148\u003c\/p\u003e \u003cp\u003eProblems 148\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Approximations of Trial Solutions,Weight Functions and Gauss Quadrature for Multidimensional Problems 151\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Completeness and Continuity 152\u003c\/p\u003e \u003cp\u003e7.2 Three-Node Triangular Element 154\u003c\/p\u003e \u003cp\u003e7.2.1 Global Approximation and Continuity 157\u003c\/p\u003e \u003cp\u003e7.2.2 Higher Order Triangular Elements 159\u003c\/p\u003e \u003cp\u003e7.2.3 Derivatives of Shape Functions for the Three-Node Triangular Element 160\u003c\/p\u003e \u003cp\u003e7.3 Four-Node Rectangular Elements 161\u003c\/p\u003e \u003cp\u003e7.4 Four-Node Quadrilateral Element 164\u003c\/p\u003e \u003cp\u003e7.4.1 Continuity of Isoparametric Elements 166\u003c\/p\u003e \u003cp\u003e7.4.2 Derivatives of Isoparametric Shape Functions 166\u003c\/p\u003e \u003cp\u003e7.5 Higher Order Quadrilateral Elements 168\u003c\/p\u003e \u003cp\u003e7.6 Triangular Coordinates 172\u003c\/p\u003e \u003cp\u003e7.6.1 Linear Triangular Element 172\u003c\/p\u003e \u003cp\u003e7.6.2 Isoparametric Triangular Elements 174\u003c\/p\u003e \u003cp\u003e7.6.3 Cubic Element 175\u003c\/p\u003e \u003cp\u003e7.6.4 Triangular Elements by Collapsing Quadrilateral Elements 176\u003c\/p\u003e \u003cp\u003e7.7 Completeness of Isoparametric Elements 177\u003c\/p\u003e \u003cp\u003e7.8 Gauss Quadrature in Two Dimensions 178\u003c\/p\u003e \u003cp\u003e7.8.1 Integration Over Quadrilateral Elements 179\u003c\/p\u003e \u003cp\u003e7.8.2 Integration Over Triangular Elements 180\u003c\/p\u003e \u003cp\u003e7.9 Three-Dimensional Elements 181\u003c\/p\u003e \u003cp\u003e7.9.1 Hexahedral Elements 181\u003c\/p\u003e \u003cp\u003e7.9.2 Tetrahedral Elements 183\u003c\/p\u003e \u003cp\u003eReferences 185\u003c\/p\u003e \u003cp\u003eProblems 186\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Finite Element Formulation for Multidimensional Scalar Field Problems 189\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Finite Element Formulation for Two-Dimensional Heat Conduction Problems 189\u003c\/p\u003e \u003cp\u003e8.2 Verification and Validation 201\u003c\/p\u003e \u003cp\u003e8.3 Advection–Diffusion Equation 207\u003c\/p\u003e \u003cp\u003eReferences 209\u003c\/p\u003e \u003cp\u003eProblems 209\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Finite Element Formulation for Vector Field Problems – Linear Elasticity 215\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Linear Elasticity 215\u003c\/p\u003e \u003cp\u003e9.1.1 Kinematics 217\u003c\/p\u003e \u003cp\u003e9.1.2 Stress and Traction 219\u003c\/p\u003e \u003cp\u003e9.1.3 Equilibrium 220\u003c\/p\u003e \u003cp\u003e9.1.4 Constitutive Equation 222\u003c\/p\u003e \u003cp\u003e9.2 Strong andWeak Forms 223\u003c\/p\u003e \u003cp\u003e9.3 Finite Element Discretization 225\u003c\/p\u003e \u003cp\u003e9.4 Three-Node Triangular Element 228\u003c\/p\u003e \u003cp\u003e9.4.1 Element Body Force Matrix 229\u003c\/p\u003e \u003cp\u003e9.4.2 Boundary Force Matrix 230\u003c\/p\u003e \u003cp\u003e9.5 Generalization of Boundary Conditions 231\u003c\/p\u003e \u003cp\u003e9.6 Discussion 239\u003c\/p\u003e \u003cp\u003e9.7 Linear Elasticity Equations in Three Dimensions 240\u003c\/p\u003e \u003cp\u003eProblems 241\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Finite Element Formulation for Beams 249\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Governing Equations of the Beam 249\u003c\/p\u003e \u003cp\u003e10.1.1 Kinematics of Beam 249\u003c\/p\u003e \u003cp\u003e10.1.2 Stress–Strain Law 252\u003c\/p\u003e \u003cp\u003e10.1.3 Equilibrium 253\u003c\/p\u003e \u003cp\u003e10.1.4 Boundary Conditions 254\u003c\/p\u003e \u003cp\u003e10.2 Strong Form toWeak Form 255\u003c\/p\u003e \u003cp\u003e10.2.1 Weak Form to Strong Form 257\u003c\/p\u003e \u003cp\u003e10.3 Finite Element Discretization 258\u003c\/p\u003e \u003cp\u003e10.3.1 Trial Solution andWeight Function Approximations 258\u003c\/p\u003e \u003cp\u003e10.3.2 Discrete Equations 260\u003c\/p\u003e \u003cp\u003e10.4 Theorem of Minimum Potential Energy 261\u003c\/p\u003e \u003cp\u003e10.5 Remarks on Shell Elements 265\u003c\/p\u003e \u003cp\u003eReference 269\u003c\/p\u003e \u003cp\u003eProblems 269\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Commercial Finite Element Program ABAQUS Tutorials 275\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 Introduction 275\u003c\/p\u003e \u003cp\u003e11.1.1 Steady-State Heat Flow Example 275\u003c\/p\u003e \u003cp\u003e11.2 Preliminaries 275\u003c\/p\u003e \u003cp\u003e11.3 Creating a Part 276\u003c\/p\u003e \u003cp\u003e11.4 Creating a Material Definition 278\u003c\/p\u003e \u003cp\u003e11.5 Defining and Assigning Section Properties 279\u003c\/p\u003e \u003cp\u003e11.6 Assembling the Model 280\u003c\/p\u003e \u003cp\u003e11.7 Configuring the Analysis 280\u003c\/p\u003e \u003cp\u003e11.8 Applying a Boundary Condition and a Load to the Model 280\u003c\/p\u003e \u003cp\u003e11.9 Meshing the Model 282\u003c\/p\u003e \u003cp\u003e11.10 Creating and Submitting an Analysis Job 284\u003c\/p\u003e \u003cp\u003e11.11 Viewing the Analysis Results 284\u003c\/p\u003e \u003cp\u003e11.12 Solving the Problem Using Quadrilaterals 284\u003c\/p\u003e \u003cp\u003e11.13 Refining the Mesh 285\u003c\/p\u003e \u003cp\u003e11.13.1 Bending of a Short Cantilever Beam 287\u003c\/p\u003e \u003cp\u003e11.14 Copying the Model 287\u003c\/p\u003e \u003cp\u003e11.15 Modifying the Material Definition 287\u003c\/p\u003e \u003cp\u003e11.16 Configuring the Analysis 287\u003c\/p\u003e \u003cp\u003e11.17 Applying a Boundary Condition and a Load to the Model 288\u003c\/p\u003e \u003cp\u003e11.18 Meshing the Model 289\u003c\/p\u003e \u003cp\u003e11.19 Creating and Submitting an Analysis Job 290\u003c\/p\u003e \u003cp\u003e11.20 Viewing the Analysis Results 290\u003c\/p\u003e \u003cp\u003e11.20.1 Plate with a Hole in Tension 290\u003c\/p\u003e \u003cp\u003e11.21 Creating a New Model 292\u003c\/p\u003e \u003cp\u003e11.22 Creating a Part 292\u003c\/p\u003e \u003cp\u003e11.23 Creating a Material Definition 293\u003c\/p\u003e \u003cp\u003e11.24 Defining and Assigning Section Properties 294\u003c\/p\u003e \u003cp\u003e11.25 Assembling the Model 295\u003c\/p\u003e \u003cp\u003e11.26 Configuring the Analysis 295\u003c\/p\u003e \u003cp\u003e11.27 Applying a Boundary Condition and a Load to the Model 295\u003c\/p\u003e \u003cp\u003e11.28 Meshing the Model 297\u003c\/p\u003e \u003cp\u003e11.29 Creating and Submitting an Analysis Job 298\u003c\/p\u003e \u003cp\u003e11.30 Viewing the Analysis Results 299\u003c\/p\u003e \u003cp\u003e11.31 Refining the Mesh 299\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAppendix 303\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eA.1 Rotation of Coordinate System in Three Dimensions 303\u003c\/p\u003e \u003cp\u003eA.2 Scalar Product Theorem 304\u003c\/p\u003e \u003cp\u003eA.3 Taylor’s Formula with Remainder and the Mean Value Theorem 304\u003c\/p\u003e \u003cp\u003eA.4 Green’s Theorem 305\u003c\/p\u003e \u003cp\u003eA.5 Point Force (Source) 307\u003c\/p\u003e \u003cp\u003eA.6 Static Condensation 308\u003c\/p\u003e \u003cp\u003eA.7 Solution Methods 309\u003c\/p\u003e \u003cp\u003eDirect Solvers 310\u003c\/p\u003e \u003cp\u003eIterative Solvers 310\u003c\/p\u003e \u003cp\u003eConditioning 311\u003c\/p\u003e \u003cp\u003eReferences 312\u003c\/p\u003e \u003cp\u003eProblem 312\u003c\/p\u003e \u003cp\u003eIndex 313\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":48733786177879,"sku":"9780470035801","price":50.3,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780470035801.jpg?v=1720001680"},{"product_id":"fractal-geometry-complex-dimensions-and-zeta-functions-9781461421757","title":"Fractal Geometry Complex Dimensions and Zeta","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eIn its Second Edition, this in-depth study of the vibrations of fractal strings interlinks number theory, spectral geometry and fractal geometry. Includes a geometric reformulation of the Riemann hypothesis and a new final chapter on recent topics and results.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e“This interesting volume gives a thorough introduction to an active field of research and will be very valuable to graduate students and researchers alike.” (C. Baxa, Monatshefte für Mathematik, Vol. 180, 2016)\u003c\/p\u003e\u003cp\u003e“In this research monograph the authors provide a mathematical theory of complex dimensions of fractal strings and its many applications. … The book is written in a self-contained manner the results … are completely proved. I appreciate that the book is useful for mathematicians, students, researchers, postgraduates, physicians and other specialists which are interested in studying the fractals and dimension theory.” (Philosophy, Religion and Science Book Reviews, bookinspections.wordpress.com, April, 2013)\u003cbr\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e“The authors provide a mathematical theory of complex dimensions of fractal strings and its many applications. … The book is written in a self-contained manner, the results (including some fundamental ones) are completely proved. … the book will be useful to mathematicians, students, researchers, postgraduates, physicians and other specialists which are interested in studying fractals and dimension theory.” (Nicolae-Adrian Secelean, Zentralblatt MATH, Vol. 1261, 2013)\u003c\/p\u003e\u003cp\u003e\"In this book the author encompasses a broad range of topics that connect many areas of mathematics, including fractal geometry, number theory, spectral geometry, dynamical systems, complex analysis, distribution theory and mathematical physics. The book is self containing, the material organized in chapters preceding by an introduction and finally there are some interesting applications of the theory presented. ...The book is very well written and organized and the subject is very interesting and actual and has many applications.\" -- Nicolae-Adrian Secelean for Zentralblatt MATH\u003c\/p\u003e\u003cp\u003e\"This highly original self-contained book will appeal to geometers, fractalists, mathematical physicists and number theorists, as well as to graduate students in these fields and others interested in gaining insight into these rich areas either for its own sake or with a view to applications. They will find it a stimulating guide, well written in a clear and pleasant style.\" -- Mathematical Reviews (Review of previous book by authors)\u003c\/p\u003e\u003cp\u003e\"It is the reviewera (TM)s opinion that the authors have succeeded in showing that the complex dimensions provide a very natural and unifying mathematical framework for investigating the oscillations in the geometry and the spectrum of a fractal string. The book is well written. The exposition is self-contained, intelligent and well paced.\" -- Bulletin of the London Mathematical Society (Review of previous book by authors)\u003c\/p\u003e\u003cp\u003e\"The new approach and results on the important problems illuminated in this work will appeal to researchers and graduate students in number theory, fractal geometry, dynamical systems, spectral geometry, and mathematical physics.\" -- Simulation News Europe (Review of previous book by authors)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003ePreface.- Overview.- Introduction.- 1. Complex Dimensions of Ordinary Fractal Strings.- 2. Complex Dimensions of Self-Similar Fractal Strings.- 3. Complex Dimensions of Nonlattice Self-Similar Strings.- 4. Generalized Fractal Strings Viewed as Measures.- 5. Explicit Formulas for Generalized Fractal Strings.- 6. The Geometry and the Spectrum of Fractal Strings.- 7. Periodic Orbits of Self-Similar Flows.- 8. Fractal Tube Formulas.- 9. Riemann Hypothesis and Inverse Spectral Problems.- 10. Generalized Cantor Strings and their Oscillations.- 11. Critical Zero of Zeta Functions.- 12 Fractality and Complex Dimensions.- 13. Recent Results and Perspectives.- Appendix A. Zeta Functions in Number Theory.- Appendix B. Zeta Functions of Laplacians and Spectral Asymptotics.- Appendix C. An Application of Nevanlinna Theory.- Bibliography.- Author Index.- Subject Index.- Index of Symbols.- Conventions.- Acknowledgements.\u003c\/p\u003e","brand":"Springer-Verlag New York Inc.","offers":[{"title":"Default Title","offer_id":48739348971863,"sku":"9781461421757","price":107.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781461421757.jpg?v=1720051981"},{"product_id":"formal-and-analytic-solutions-of-differential-equations-9781800611351","title":"Formal And Analytic Solutions Of Differential","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThe book provides the reader with an overview of the actual state of research in ordinary and partial differential equations in the complex domain. Topics include summability and asymptotic study of both ordinary and partial differential equations, and also q-difference and differential-difference equations. This book will be of interest to researchers and students who wish to expand their knowledge of these fields.With the latest results and research developments and contributions from experts in their field, Formal and Analytic Solutions of Differential Equations provides a valuable contribution to methods, techniques, different mathematical tools, and study calculations.","brand":"World Scientific Europe Ltd","offers":[{"title":"Default Title","offer_id":48741753749847,"sku":"9781800611351","price":121.5,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781800611351.jpg?v=1720058693"},{"product_id":"wave-phenomena-mathematical-analysis-and-numerical-approximation-9783031057922","title":"Wave Phenomena: Mathematical Analysis and","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis book presents the notes from the seminar on wave phenomena given in 2019 at the Mathematical Research Center in Oberwolfach.\u003cbr\u003eThe research on wave-type problems is a fascinating and emerging field in mathematical research with many challenging applications in sciences and engineering. Profound investigations on waves require a strong interaction of several mathematical disciplines including functional analysis, partial differential equations, mathematical modeling, mathematical physics, numerical analysis, and scientific computing.\u003cbr\u003eThe goal of this book is to present a comprehensive introduction to the research on wave phenomena. Starting with basic models for acoustic, elastic, and electro-magnetic waves, topics such as the existence of solutions for linear and some nonlinear material laws, efficient discretizations and solution methods in space and time, and the application to inverse parameter identification problems are covered. The aim of this book is to intertwine analysis and numerical mathematics for wave-type problems promoting thus cooperative research projects in this field.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eSpace-time approximations for linear acoustic, elastic, and electro-magnetic wave equations.- Local wellposedness and long-time behavior of quasilinear Maxwell equations.- Error analysis of second-order time integration methods for discontinuous Galerkin discretizations of Friedrichs’ systems.- An abstract framework for inverse wave problems with applications.","brand":"Birkhauser Verlag AG","offers":[{"title":"Default Title","offer_id":48743066632535,"sku":"9783031057922","price":41.24,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783031057922.jpg?v=1720063962"},{"product_id":"difference-matrices-for-ode-and-pde-a-matlab-r-companion-9783031119996","title":"Difference Matrices for ODE and PDE: A MATLAB®","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThe use of difference matrices and high-level MATLAB® commands to implement finite difference algorithms is pedagogically novel. This unique and concise textbook gives the reader easy access and a general ability to use first and second difference matrices to set up and solve linear and nonlinear systems in MATLAB which approximate ordinary and partial differential equations. Prerequisites include a knowledge of basic calculus, linear algebra, and ordinary differential equations. Some knowledge of partial differential equations is a plus though the text may easily serve as a supplement for the student currently working through an introductory PDEs course.  Familiarity with MATLAB is not required though a little prior experience with programming would be helpful.\u003c\/p\u003e  In addition to its special focus on solving in MATLAB, the abundance of examples and exercises make this text versatile in use. It would serve well in a graduate course in introductory scientific computing for partial differential equations. With prerequisites mentioned above plus some elementary numerical analysis, most of the material can be covered and many of the exercises assigned in a single semester course. Some of the more challenging exercises make substantial projects and relate to topics from other typical graduate mathematics courses, e.g., linear algebra, differential equations, or topics in nonlinear functional analysis. A selection of the exercises may be assigned as projects throughout the semester. The student will develop the skills to run simulations corresponding to the primarily theoretical course material covered by the instructor. The book can serve as a supplement for the instructor teaching any course in differential equations. Many of the examples can be easily implemented and the resulting simulation demonstrated by the instructor. If the course has a numerical component, a few of the more difficult exercises may be assigned as student projects.\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e  Established researchers in theoretical partial differential equations may find this book useful as well, particularly as an introductory guide for their research students. Those unfamiliar with MATLAB can use the material as a reference to quickly develop their own applications in that language. Practical assistance in implementing algorithms in MATLAB can be found in these pages. A mathematician who is new to the practical implementation of methods for scientific computation in general can learn how to implement and execute numerical simulations of differential equations in MATLAB with relative ease by working through a selection of exercises. Additionally, the book can serve as a practical guide in independent study, undergraduate or graduate research experiences, or for reference in simulating solutions to specific thesis or dissertation-related experiments.\u003cp\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e1. Introduction.- 2. Review of elementary numerical methods and MATLAB(R).- 3. Ordinary Differential Equations.- 4. Partial Differential Equations.- 5. Advanced topics in semilinear elliptic BVP.- References.","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":48743070859607,"sku":"9783031119996","price":999.99,"currency_code":"GBP","in_stock":false}]},{"product_id":"input-to-state-stability-theory-and-applications-9783031146732","title":"Input-to-State Stability: Theory and Applications","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003ci\u003eInput-to-State Stability\u003c\/i\u003e presents the dominating stability paradigm in nonlinear control theory that revolutionized our view on stabilization of nonlinear systems, design of robust nonlinear observers, and stability of nonlinear interconnected control systems.\u003c\/p\u003e  The applications of input-to-state stability (ISS) are manifold and include mechatronics, aerospace engineering, and systems biology. Although the book concentrates on the ISS theory of finite-dimensional systems, it emphasizes the importance of a more general view of infinite-dimensional ISS theory. This permits the analysis of more general system classes and provides new perspectives on and a better understanding of the classical ISS theory for ordinary differential equations (ODEs).\u003cp\u003e\u003c\/p\u003e  Features of the book include:\u003cbr\u003e • a comprehensive overview of the theoretical basis of ISS;\u003cbr\u003e • a description of the central applications of ISS in nonlinear control theory;\u003cbr\u003e • a detailed discussion of the role of small-gain methods in the stability of nonlinear networks; and\u003cbr\u003e • an in-depth comparison of ISS for finite- and infinite-dimensional systems.\u003cp\u003e\u003c\/p\u003e  \u003cp\u003eThe book also provides a short overview of the ISS theory for other systems classes (partial differential equations, hybrid, impulsive, and time-delay systems) and surveys the available results for the important stability properties that are related to ISS.\u003c\/p\u003e  \u003cp\u003eThe reader should have a basic knowledge of analysis, Lebesgue integration theory, linear algebra, and the theory of ODEs but requires no prior knowledge of dynamical systems or stability theory. The author introduces all the necessary ideas within the book.\u003ci\u003e\u003c\/i\u003e\u003c\/p\u003e  \u003cp\u003e\u003ci\u003eInput-to-State Stability\u003c\/i\u003e will interest researchers and graduate students studying nonlinear control from either a mathematical or engineering background. It is intended for active readers and contains numerous exercises of varying difficulty, which are integral to the text, complementing and widening the material developed in the monograph.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e \u003cbr\u003e","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":48743073022295,"sku":"9783031146732","price":123.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783031146732.jpg?v=1720063990"},{"product_id":"model-order-reduction-and-applications-cetraro-italy-2021-9783031295621","title":"Model Order Reduction and Applications: Cetraro,","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis book addresses the state of the art of reduced order methods for modelling and computational reduction of complex parametrised systems, governed by ordinary and\/or partial differential equations, with a special emphasis on real time computing techniques and applications in various fields.\u003cp\u003eConsisting of  four contributions presented at the CIME summer school, the book presents several points of view and techniques to solve demanding problems of increasing complexity. The focus is on theoretical investigation and applicative algorithm development for reduction in the complexity – the dimension, the degrees of freedom, the data – arising in these models.\u003c\/p\u003eThe book is addressed to graduate students, young researchers and people interested in the field. It is a good companion for graduate\/doctoral classes.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e- 1. The Reduced Basis Method in Space and Time: Challenges, Limits and Perspectives. - 2. Inverse Problems: A Deterministic Approach Using Physics-Based Reduced Models. - 3. Model Order Reduction for Optimal Control Problems. - 4. Machine Learning Methods for Reduced Order Modeling.","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":48743079739735,"sku":"9783031295621","price":42.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783031295621.jpg?v=1720064021"},{"product_id":"the-big-book-of-real-analysis-from-numbers-to-measures-9783031308314","title":"The Big Book of Real Analysis: From Numbers to","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis book provides an introduction to real analysis, a fundamental topic that is an essential requirement in the study of mathematics. It deals with the concepts of infinity and limits, which are the cornerstones in the development of calculus.\u003c\/p\u003e  \u003cp\u003eBeginning with some basic proof techniques and the notions of sets and functions, the book rigorously constructs the real numbers and their related structures from the natural numbers. During this construction, the readers will encounter the notions of infinity, limits, real sequences, and real series. These concepts are then formalised and focused on as stand-alone objects. Finally, they are expanded to limits, sequences, and series of more general objects such as real-valued functions. Once the fundamental tools of the trade have been established, the readers are led into the classical study of calculus (continuity, differentiation, and Riemann integration) from first principles. The book concludes with an introduction to the study of measures and how one can construct the Lebesgue integral as an extension of the Riemann integral.\u003c\/p\u003e  \u003cp\u003eThis textbook is aimed at undergraduate students in mathematics. As its title suggests, it covers a large amount of material, which can be taught in around three semesters. Many remarks and examples help to motivate and provide intuition for the abstract theoretical concepts discussed. In addition, more than 600 exercises are included in the book, some of which will lead the readers to more advanced topics and could be suitable for independent study projects. Since the book is fully self-contained, it is also ideal for self-study.\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003ePreface.- 1. Logic and Sets.- 2. Integers.- 3. Construction of the Real Numbers.- 4. The Real Numbers.- 5. Real Sequences.- 6. Some Applications of Real Sequences.- 7. Real Series.- 8. Additional Topics in Real Series.- 9. Functions and Limits.- 10. Continuity.- 11. Function Sequences and Series.- 12. Power Series.- 13. Differentiation.- 14. Some Applications of Differentiation.- 15. Riemann and Darboux Integration.- 16. The Fundamental Theorem of Calculus.- 17. Taylor and MacLaurin Series.- 18. Introduction to Measure Theory.- 19. Lebesgue Integration.- 20. Double Integrals.- Solutions to the Exercises.- Bibliography.- Index. \u003c\/p\u003e","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":48743080165719,"sku":"9783031308314","price":80.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783031308314.jpg?v=1720064022"},{"product_id":"partial-differential-equations-ii-qualitative-studies-of-linear-equations-9783031336997","title":"Partial Differential Equations II: Qualitative","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis second in the series of three volumes builds upon the basic theory of linear PDE given in volume 1, and pursues more advanced topics. Analytical tools introduced here include pseudodifferential operators, the functional analysis of self-adjoint operators, and Wiener measure. The book also develops basic differential geometrical concepts, centered about curvature. Topics covered include spectral theory of elliptic differential operators, the theory of scattering of waves by obstacles, index theory for Dirac operators, and Brownian motion and diffusion. The book is targeted at graduate students in mathematics and at professional mathematicians with an interest in partial differential equations, mathematical physics, differential geometry, harmonic analysis, and complex analysis.\u003cbr\u003eThe third edition further expands the material by incorporating new theorems and applications throughout the book, and by deepening connections and relating concepts across chapters.  It includes new sections on rigid body motion, on probabilistic results related to random walks, on aspects of operator theory related to quantum mechanics, on overdetermined systems, and on the Euler equation for incompressible fluids.  The appendices have also been updated with additional results, ranging from weak convergence of measures to the curvature of Kahler manifolds.\u003cbr\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eMichael E. Taylor is a Professor of Mathematics at the University of North Carolina, Chapel Hill, NC.\u003c\/p\u003e\u003cp\u003eReview of first edition: “These volumes will be read by several generations of readers eager to learn the modern theory of partial differential equations of mathematical physics and the analysis in which this theory is rooted.”\u003c\/p\u003e\u003cp\u003e(Peter Lax, SIAM review, June 1998)\u003cbr\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003ePreface.- 7 Pseudodifferential Operators.- 8 Spectral Theory.- 9 Scattering by Obstacles.- 10 Dirac Operators and Index Theory.- 11 Brownian Motion and Potential Theory.- 12 The ∂-Neumann Problem.- C Connections and Curvature.- Index.\u003c\/p\u003e","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":48743082197335,"sku":"9783031336997","price":58.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783031336997.jpg?v=1720064031"},{"product_id":"partial-differential-equations-iii-nonlinear-equations-9783031339271","title":"Partial Differential Equations III: Nonlinear","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThe third of three volumes on partial differential equations, this is devoted to nonlinear PDE. It treats a number of equations of classical continuum mechanics, including relativistic versions, as well as various equations arising in differential geometry, such as in the study of minimal surfaces, isometric imbedding, conformal deformation, harmonic maps, and prescribed Gauss curvature. In addition, some nonlinear diffusion problems are studied. It also introduces such analytical tools as the theory of L^p Sobolev spaces, Holder spaces, Hardy spaces, and Morrey spaces, and also a development of Calderon-Zygmund theory and paradifferential operator calculus. The book is targeted at graduate students in mathematics and at professional mathematicians with an interest in partial differential equations, mathematical physics, differential geometry, harmonic analysis, and complex analysis. \u003cbr\u003eThe third edition further expands the material by incorporating new theorems and applications throughout the book, and by deepening connections and relating concepts across chapters.  It includes new sections on rigid body motion, on probabilistic results related to random walks, on aspects of operator theory related to quantum mechanics, on overdetermined systems, and on the Euler equation for incompressible fluids.  The appendices have also been updated with additional results, ranging from weak convergence of measures to the curvature of Kahler manifolds.\u003cbr\u003e\u003cp\u003eMichael E. Taylor is a Professor of Mathematics at the University of North Carolina, Chapel Hill, NC.\u003c\/p\u003e\u003cp\u003eReview of first edition: “These volumes will be read by several generations of readers eager to learn the modern theory of partial differential equations of mathematical physics and the analysis in which this theory is rooted.”\u003c\/p\u003e\u003cp\u003e(Peter Lax, SIAM review, June 1998)\u003cbr\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eContents of Volumes I and II.- Preface.- 13 Function Space and Operator Theory for Nonlinear Analysis.- 14 Nonlinear Elliptic Equations.- 15 Nonlinear Parabolic Equations.- 16 Nonlinear Hyperbolic Equations.- 17 Euler and Navier–Stokes Equations for Incompressible Fluids.- 18 Einstein’s Equations.- Index.","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":48743082393943,"sku":"9783031339271","price":999.99,"currency_code":"GBP","in_stock":false}]},{"product_id":"inverse-problems-in-ordinary-differential-equations-and-applications-9783319263373","title":"Inverse Problems in Ordinary Differential","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis book is dedicated to study the inverse problem of ordinary differential equations, that is it focuses in finding all ordinary differential equations that satisfy a given set of properties. The Nambu bracket is the central tool in developing this approach. The authors start characterizing the ordinary differential equations in R^N which have a given set of partial integrals or first integrals. The results obtained are applied first to planar polynomial differential systems with a given set of such integrals, second to solve the 16th Hilbert problem restricted to generic algebraic limit cycles, third for solving the inverse problem for constrained Lagrangian and Hamiltonian mechanical systems, fourth for studying the integrability of a constrained rigid body. Finally the authors conclude with an analysis on nonholonomic mechanics, a generalization of the Hamiltonian principle, and the statement an solution of the inverse problem in vakonomic mechanics.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e“The book presents a new approach to … inverse problems, where the authors mainly use as an essential tool the Nambu bracket. They deduce new properties of this bracket, which plays a fundamental role in the proof of all the results and in their applications throughout the book. … The book is well written and contains new and valuable results in the development of the inverse problem in ordinary differential equations and its applications.” (Leonardo Colombo, Mathematical Reviews, January, 2017)\u003cp\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003ePreface.- 1.Differential Equations with Given Partial and First Integrals.- 2.Polynomial Vector Fields with Given Partial and First Integrals.- 3.16th Hilbert Problem for Algebraic Limit Cycles.- 4.Inverse Problem for Constrained Lagrangian Systems.- 5.Inverse Problem for Constrained Hamiltonian Systems.- 6.Integrability of the Constrained Rigid Body.- 7.Inverse Problem in the Vakonomic Mechanics.- Index.- Bibliography.\u003c\/p\u003e","brand":"Birkhauser Verlag AG","offers":[{"title":"Default Title","offer_id":48743093403991,"sku":"9783319263373","price":82.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783319263373.jpg?v=1720064082"},{"product_id":"differential-equations-a-primer-for-scientists-and-engineers-9783319502236","title":"Differential Equations: A Primer for Scientists","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis textbook is designed with the needs of today’s student in mind. It is the ideal textbook for a first course in elementary differential equations for future engineers and scientists, including mathematicians. This book is accessible to anyone who has a basic knowledge of precalculus algebra and differential and integral calculus. Its carefully crafted text adopts a concise, simple, no-frills approach to differential equations, which helps students acquire a solid experience in many classical solution techniques. With a lighter accent on the physical interpretation of the results, a more manageable page count than comparable texts, a highly readable style, and over 1000 exercises designed to be solved without a calculating device, this book emphasizes the understanding and practice of essential topics in a succinct yet fully rigorous fashion. Apart from several other enhancements, the second edition contains one new chapter on numerical methods of solution.\u003cp\u003eThe book formally splits the \"pure\" and \"applied\" parts of the contents by placing the discussion of selected mathematical models in separate chapters. At the end of most of the 246 worked examples, the author provides the commands in \u003ci\u003eMathematica\u003c\/i\u003e® for verifying the results. The book can be used independently by the average student to learn the fundamentals of the subject, while those interested in pursuing more advanced material can regard it as an easily taken first step on the way to the next level. Additionally, practitioners who encounter differential equations in their professional work will find this text to be a convenient source of reference.\u003c\/p\u003e\u003cp\u003e\u003cbr\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e1. Introduction.- 2. First Order Equations.- 3. Mathematical Models with First-Order Equations.- 4. Linear Second-Order Equations.- 4. Higher-Order Equations.- 5. Mathematical Models with Second-Order Equations.- 6. Higher-Order Linear Equations.- 7. Systems of Differential Equations.- 8. The Laplace Transformation.- 9. Series Solutions.- 10. Numerical Methods.- A. Algebra Techniques.- B. Calculus Techniques.- C. Table of Laplace Transforms.- D. The Greek Alphabet.- Further Reading.- Answers to Odd-Numbered Exercises.- Index.\u003c\/p\u003e","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":48743096910167,"sku":"9783319502236","price":49.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783319502236.jpg?v=1720064096"},{"product_id":"optimization-and-approximation-9783319648422","title":"Optimization and Approximation","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis book provides a basic, initial resource, introducing science and engineering students to the field of optimization. It covers three main areas: mathematical programming, calculus of variations and optimal control, highlighting the ideas and concepts and offering insights into the importance of optimality conditions in each area. It also systematically presents affordable approximation methods. Exercises at various levels have been included to support the learning process.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e“This book, consisting of eight chapters, provides an introduction to optimization aimed at engineering and science students. ... This book is equally suitable to those without prior knowledge in the field as well as those already familiar with the key concepts as a useful reference. The book concludes with a very useful appendix containing hints or full solutions to the exercises presented throughout the book.” (Efstratios Rappos, zbMATH 1375.90002, 2018)\u003cp\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e1 Overview. Part I Mathematical Programming. - 2 Linear Programming.- 3 Nonlinear programming.- 4 Numerical approximation.- Part II Variational problems.- 5 Basic theory for variational problems 6 Numerical approximation of variational problems.- Part III Optimal Control.- 7 Basic facts about optimal control . 8 Numerical approximation of basic optimal control problems, and dynamic programming. Part IV Appendix.- 9 Hints and solutions to exercises. \u003cp\u003e\u003c\/p\u003e","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":48743100809559,"sku":"9783319648422","price":999.99,"currency_code":"GBP","in_stock":false}]},{"product_id":"grundlagen-der-differenzialgleichungen-fur-dummies-9783527715572","title":"Grundlagen der Differenzialgleichungen für","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eDifferenzialgleichungen sind Ihnen ein Buch mit sieben Siegeln? Kein Problem! Im ersten Teil liefert Ihnen dieses Buch wirklich alles, was Sie an Handwerkszeug zum Lösen von Differenzialgleichungen benötigen. Anschließend erfahren Sie, was Differenzialgleichungen überhaupt sind und mit welchen Methoden man sie lösen kann. Im dritten Teil wird es ernst: Sie werden einfache Differenzialgleichungen rechnerisch lösen. Aber keine Sorge: Vielfältige Beispiele geben Ihnen die Gelegenheit, die Verfahren gründlich zu üben. Und damit Sie wissen, warum Sie sich all diesen Mühen unterziehen, werden Sie zuletzt auf berühmte Differenzialgleichungen aus Biologie, Chemie, Physik und Ökonomie treffen.","brand":"Wiley-VCH Verlag GmbH","offers":[{"title":"Default Title","offer_id":48743128498519,"sku":"9783527715572","price":16.14,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783527715572.jpg?v=1720064234"},{"product_id":"the-analysis-of-linear-partial-differential-operators-ii-differential-operators-with-constant-coefficients-9783540225164","title":"The Analysis of Linear Partial Differential","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eAuthor received the 1962 Fields Medal\u003c\/p\u003e \u003cp\u003eAuthor received the 1988 Wolf Prize (honoring achievemnets of a lifetime)\u003c\/p\u003e \u003cp\u003eAuthor is leading expert in partial differential equations\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eFrom the reviews: \u003c\/p\u003e\u003cp\u003e\"...these volumes are excellently written and make for greatly profitable reading. For years to come they will surely be a main reference for anyone wishing to study partial differential operators.\"-- MATHEMATICAL REVIEWS \u003c\/p\u003e\u003cp\u003e\"This volume focuses on linear partial differential operators with constant coefficients … . Each chapter ends with notes on the literature, and there is a large bibliography. … The binding of this softcover reprint seems quite good … . Overall, it is great to have this book back at an affordable price. It really does deserve to be described as a classic.\" (Fernando Q. Gouvêa, MathDL, January, 2005)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eExistence and Approximation of Solutions of Differential Equations.- Interior Regularity of Solutions of Differential Equations.- The Cauchy and Mixed Problems.- Differential Operators of Constant Strength.- Scattering Theory.- Analytic Function Theory and Differential Equations.- Convolution Equations.","brand":"Springer-Verlag Berlin and Heidelberg GmbH \u0026 Co. KG","offers":[{"title":"Default Title","offer_id":48743129940311,"sku":"9783540225164","price":49.99,"currency_code":"GBP","in_stock":true}]},{"product_id":"elliptic-partial-differential-equations-of-second-order-9783540411604","title":"Elliptic Partial Differential Equations of Second","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eFrom the reviews: \"This is a book of interest to any having to work with differential equations, either as a reference or as a book to learn from. The authors have taken trouble to make the treatment self-contained. It (is) suitable required reading for a PhD student.\" --New Zealand Mathematical Society, 1985\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e“This book is a bibliographical monument to the theory of both theoretical and applied PDEs that has not acquired any flaws due to its age. On the contrary, it remains a crucial and essential tool for the active research in the field.” (Francesco Petitta, SIAM Review, Vol. 61 (4), December, 2019)\u003cb\u003e\u003cbr\u003e\u003c\/b\u003e\u003cb\u003eFrom the reviews:\u003c\/b\u003e\u003cbr\u003e\"The aim of the book is to present \"the systematic development of the general theory of second order quasilinear elliptic equations and of the linear theory required in the process\". The book is divided into two parts. The first (Chapters 2-8) is devoted to the linear theory, the second (Chapters 9-15) to the theory of quasilinear partial differential equations. These 14 chapters are preceded by an Introduction (Chapter 1) which expounds the main ideas and can serve as a guide to the book. ...The authors have succeeded admirably in their aims; the book is a real pleasure to read\".\u003cbr\u003e\u003ci\u003eMathematical Reviews,1986\u003c\/i\u003e \u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\"Advanced students and professionals are snapping up this paperback text on linear and quasilinear partial differential equations. Whether you use their book as textbook or reference, the authors give you plenty to think about and work on, including an epilogue summarizing the latest research.\"\u003cbr\u003e\u003ci\u003eAmazon.com delivers Mathematics and Statistics e-bulletin, \u003c\/i\u003e \u003ci\u003eJuly 2001\u003c\/i\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eChapter 1. Introduction Part I: Linear Equations Chapter 2. Laplace's Equation 2.1 The Mean Value Inequalities 2.2 Maximum and Minimum Principle 2.3 The Harnack Inequality 2.4 Green's Representation 2.5 The Poisson Integral 2.6 Convergence Theorems 2.7 Interior Estimates of Derivatives 2.8 The Dirichlet Problem; the Method of Subharmonic Functions 2.9 Capacity Problems Chapter 3. The Classical Maximum Principle 3.1 The Weak Maximum Principle 3.2 The Strong Maximum Principle 3.3 Apriori Bounds 3.4 Gradient Estimates for Poisson's Equation 3.5 A Harnack Inequality 3.6 Operators in Divergence Form Notes Problems Chapter 4. Poisson's Equation and Newtonian Potential 4.1 Hölder Continuity 4.2 The Dirichlet Problem for Poisson's Equation 4.3 Hölder Estimates for the Second Derivatives 4.4 Estimates at the Boundary 4.5 Hölder Estimates for the First Derivatives Notes  Problems Chapter 5. Banach and Hilbert Spaces 5.1 The Contraction Mapping 5.2 The Method of Cintinuity 5.3 The Fredholm Alternative 5.4 Dual Spaces and Adjoints 5.5 Hilbert Spaces 5.6 The Projection Theorem 5.7 The Riesz Representation Theorem 5.8 The Lax-Milgram Theorem 5.9 The Fredholm Alternative in Hilbert Spaces 5.10 Weak Compactness Notes Problems Chapter 6. Classical Solutions; the Schauder Approach 6.1 The Schauder Interior Estimates 6.2 Boundary and Global Estimates 6.3 The Dirichlet Problem 6.4 Interior and Boundary Regularity 6.5 An Alternative Approach 6.6 Non-Uniformly Elliptic Equations 6.7 Other Boundary Conditions; the Obliue Derivative Problem 6.8 Appendix 1: Interpolation Inequalities 6.9 Appendix 2: Extension Lemmas Notes Problems Chapter 7. Sobolev Spaces 7.1 L^p spaces 7.2 Regularization and Approximation by Smooth Functions 7.3 Weak Derivatives 7.4 The Chain Rule 7.5 The W^(k,p) Spaces 7.6 DensityTheorems 7.7 Imbedding Theorems 7.8 Potential Estimates and Imbedding Theorems 7.9 The Morrey and John-Nirenberg Estimes 7.10 Compactness Results 7.11 Difference Quotients 7.12 Extension and Interpolation Notes Problems Chapter 8 Generalized Solutions and Regularity 8.1 The Weak Maximum Principle 8.2 Solvability of the Dirichlet Problem 8.3 Diferentiability of Weak Solutions 8.4 Global Regularity 8.5 Global Boundedness of Weak Solutions 8.6 Local Properties of Weak Solutions 8.7 The Strong Maximum Principle 8.8 The Harnack Inequality 8.9 Hölder Continuity 8.10 Local Estimates at the Boundary 8.11 Hölder Estimates for the First Derivatives 8.12 The Eigenvalue Problem Notes Problems Chapter 9. Strong Solutions 9.1 Maximum Princiles for Strong Solutions 9.2 L^p Estimates: Preliminary Analysis 9.3 The Marcinkiewicz Interpolation Theorem 9.4 The Calderon-Zygmund Inequality 9.5 L^p Estimates 9.6 The Dirichlet Problem 9.7 A Local Maximum Principle 9.8 Hölder and Harnack Estimates 9.9 Local Estimates at the Boundary Notes Problems Part II: Quasilinear Equations Chapter 10. Maximum and Comparison Principles 10.1 The Comparison Principle 10.2 Maximum Principles 10.3 A Counterexample 10.4 Comparison Principles for Divergence Form Operators 10.5 Maximum Principles for Divergence Form Operators Notes  Problems Chapter 11. Topological Fixed Point Theorems and Their Application 11.1 The Schauder Fixes Point Theorem 11.2 The Leray-Schauder Theorem: a Special Case 11.3 An Application 11.4 The Leray-Schauder Fixed Point Theorem 11.5 Variational Problems Notes Chapter 12. Equations in Two Variables 12.1 Quasiconformal Mappings 12.2 hölder Gradient Estimates for Linear Equations 12.3 The Dirichlet Problem for Uniformly Elliptic Equations 12.4 Non-Uniformly Elliptic Equations Notes Problems Chapter 13. Hölder Estimates for","brand":"Springer-Verlag Berlin and Heidelberg GmbH \u0026 Co. KG","offers":[{"title":"Default Title","offer_id":48743130464599,"sku":"9783540411604","price":49.99,"currency_code":"GBP","in_stock":true}]},{"product_id":"perturbation-theory-for-linear-operators-9783540586616","title":"Perturbation Theory for Linear Operators","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eFrom the reviews: \"[…] An excellent textbook in the theory of linear operators in Banach and Hilbert spaces. It is a thoroughly worthwhile reference work both for graduate students in functional analysis as well as for researchers in perturbation, spectral, and scattering theory. […] I can recommend it for any mathematician or physicist interested in this field.\" Zentralblatt MATH\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"The monograph by T. Kato is an excellent textbook in the theory of linear operators in Banach and Hilbert spaces. It is a thoroughly worthwhile reference work both for graduate students in functional analysis as well as for researchers in perturbation, spectral, and scattering theory.\u003cbr\u003eIn chapters 1, 3, 5 operators in finite-dimensional vector spaces, Banach spaces and Hilbert spaces are introduced. Stability and perturbation theory are studied in finite-dimensional spaces (chapter 2) and in Banach spaces (chapter 4). Sesquilinear forms in Hilbert spaces are considered in detail (chapter 6), analytic and asymptotic perturbation theory is described (chapter 7 and 8). The fundamentals of semigroup theory are given in chapter 9. The supplementary notes appearing in the second edition of the book gave mainly additional information concerning scattering theory described in chapter 10.\u003cbr\u003eThe first edition is now 30 years old. The revised edition is 20 years old. Nevertheless it is a standard textbook for the theory of linear operators. It is user-friendly in the sense that any sought after definitions, theorems or proofs may be easily located. In the last two decades much progress has been made in understanding some of the topics dealt with in the book, for instance in semigroup and scattering theory. However the book has such a high didactical and scientific standard that I can recomment it for any mathematician or physicist interested in this field.\u003cbr\u003e\u003ci\u003eZentralblatt MATH, 836\u003c\/i\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eOne Operator theory in finite-dimensional vector spaces.- § 1. Vector spaces and normed vector spaces.- 1. Basic notions.- 2. Bases.- 3. Linear manifolds.- 4. Convergence and norms.- 5. Topological notions in a normed space.- 6. Infinite series of vectors.- 7. Vector-valued functions.- § 2. Linear forms and the adjoint space.- 1. Linear forms.- 2. The adjoint space.- 3. The adjoint basis.- 4. The adjoint space of a normed space.- 5. The convexity of balls.- 6. The second adjoint space.- § 3. Linear operators.- 1. Definitions. Matrix representations.- 2. Linear operations on operators.- 3. The algebra of linear operators.- 4. Projections. Nilpotents.- 5. Invariance. Decomposition.- 6. The adjoint operator.- § 4. Analysis with operators.- 1. Convergence and norms for operators.- 2. The norm of Tn.- 3. Examples of norms.- 4. Infinite series of operators.- 5. Operator-valued functions.- 6. Pairs of projections.- § 5. The eigenvalue problem.- 1. Definitions.- 2. The resolvent.- 3. Singularities of the resolvent.- 4. The canonical form of an operator.- 5. The adjoint problem.- 6. Functions of an operator.- 7. Similarity transformations.- § 6. Operators in unitary spaces.- 1. Unitary spaces.- 2. The adjoint space.- 3. Orthonormal families.- 4. Linear operators.- 5. Symmetric forms and symmetric operators.- 6. Unitary, isometric and normal operators.- 7. Projections.- 8. Pairs of projections.- 9. The eigenvalue problem.- 10. The minimax principle.- Two Perturbation theory in a finite-dimensional space.- § 1. Analytic perturbation of eigenvalues.- 1. The problem.- 2. Singularities of the eigenvalues.- 3. Perturbation of the resolvent.- 4. Perturbation of the eigenprojections.- 5. Singularities of the eigenprojections.- 6. Remarks and examples.- 7. The case of T(x) linear in x.- 8. Summary.- § 2. Perturbation series.- 1. The total projection for the ?-group.- 2. The weighted mean of eigenvalues.- 3. The reduction process.- 4. Formulas for higher approximations.- 5. A theorem of Motzkin-Taussky.- 6. The ranks of the coefficients of the perturbation series.- § 3. Convergence radii and error estimates.- 1. Simple estimates.- 2. The method of majorizing series.- 3. Estimates on eigenvectors.- 4. Further error estimates.- 5. The special case of a normal unperturbed operator.- 6. The enumerative method.- § . Similarity transformations of the eigenspaces and eigenvectors.- 1. Eigenvectors.- 2. Transformation functions.- 3. Solution of the differential equation.- 4. The transformation function and the reduction process.- 5. Simultaneous transformation for several projections.- 6. Diagonalization of a holomorphic matrix function.- § 5. Non-analytic perturbations.- 1. Continuity of the eigenvalues and the total projection.- 2. The numbering of the eigenvalues.- 3. Continuity of the eigenspaces and eigenvectors.- 4. Differentiability at a point.- 5. Differentiability in an interval.- 6. Asymptotic expansion of the eigenvalues and eigenvectors.- 7. Operators depending on several parameters.- 8. The eigenvalues as functions of the operator.- § 6. Perturbation of symmetric operators.- 1. Analytic perturbation of symmetric operators.- 2. Orthonormal families of eigenvectors.- 3. Continuity and differentiability.- 4. The eigenvalues as functions of the symmetric operator.- 5. Applications. A theorem of Lidskii.- Three Introduction to the theory of operators in Banach spaces.- § 1. Banach spaces.- 1. Normed spaces.- 2. Banach spaces.- 3. Linear forms.- 4. The adjoint space.- 5. The principle of uniform boundedness.- 6. Weak convergence.- 7. Weak* convergence.- 8. The quotient space.- § 2. Linear operators in Banach spaces.- 1. Linear operators. The domain and range.- 2. Continuity and boundedness.- 3. Ordinary differential operators of second order.- § 3. Bounded operators.- 1. The space of bounded operators.- 2. The operator algebra ?(X).- 3. The adjoint operator.- 4. Projections.- § 4. Compact operators.- 1. Definition.- 2. The space of compact operators.- 3. Degenerate operators. The trace and determinant.- § 5. Closed operators.- 1. Remarks on unbounded operators.- 2. Closed operators.- 3. Closable operators.- 4. The closed graph theorem.- 5. The adjoint operator.- 6. Commutativity and decomposition.- § 6. Resolvents and spectra.- 1. Definitions.- 2. The spectra of bounded operators.- 3. The point at infinity.- 4. Separation of the spectrum.- 5. Isolated eigenvalues.- 6. The resolvent of the adjoint.- 7. The spectra of compact operators.- 8. Operators with compact resolvent.- Four Stability theorems.- §1. Stability of closedness and bounded invertibility.- 1. Stability of closedness under relatively bounded perturbation.- 2. Examples of relative boundedness.- 3. Relative compactness and a stability theorem.- 4. Stability of bounded in vertibility.- § 2. Generalized convergence of closed operators.- 1. The gap between subspaces.- 2. The gap and the dimension.- 3. Duality.- 4. The gap between closed operators.- 5. Further results on the stability of bounded in vertibility.- 6. Generalized convergence.- § 3. Perturbation of the spectrum.- 1. Upper semicontinuity of the spectrum.- 2. Lower semi-discontinuity of the spectrum.- 3. Continuity and analyticity of the resolvent.- 4. Semicontinuity of separated parts of the spectrum.- 5. Continuity of a finite system of eigenvalues.- 6. Change of the spectrum under relatively bounded perturbation.- 7. Simultaneous consideration of an infinite number of eigenvalues.- 8. An application to Banach algebras. Wiener’s theorem.- § 4. Pairs of closed linear manifolds.- 1. Definitions.- 2. Duality.- 3. Regular pairs of closed linear manifolds.- 4. The approximate nullity and deficiency.- 5. Stability theorems.- § 5. Stability theorems for semi-Fredholm operators.- 1. The nullity, deficiency and index of an operator.- 2. The general stability theorem.- 3. Other stability theorems.- 4. Isolated eigenvalues.- 5. Another form of the stability theorem.- 6. Structure of the spectrum of a closed operator.- § 6. Degenerate perturbations.- 1. The Weinstein-Aronszajn determinants.- 2. The W-A formulas.- 3. Proof of the W-A formulas.- 4. Conditions excluding the singular case.- Five Operators in Hilbert spaces.- § 1. Hilbert space.- 1. Basic notions.- 2. Complete orthonormal families.- § 2. Bounded operators in Hilbert spaces.- 1. Bounded operators and their adjoints.- 2. Unitary and isometric operators.- 3. Compact operators.- 4. The Schmidt class.- 5. Perturbation of orthonormal families.- § 3. Unbounded operators in Hilbert spaces.- 1. General remarks.- 2. The numerical range.- 3. Symmetric operators.- 4. The spectra of symmetric operators.- 5. The resolvents and spectra of selfadjoint operators.- 6. Second-order ordinary differential operators.- 7. The operators T*T.- 8. Normal operators.- 9. Reduction of symmetric operators.- 10. Semibounded and accretive operators.- 11. The square root of an m-accretive operator.- § 4. Perturbation of self adjoint operators.- 1. Stability of selfadjointness.- 2. The case of relative bound 1.- 3. Perturbation of the spectrum.- 4. Semibounded operators.- 5. Completeness of the eigenprojections of slightly non-selfadjoint operators.- § 5. The Schrödinger and Dirac operators.- 1. Partial differential operators.- 2. The Laplacian in the whole space.- 3. The Schrödinger operator with a static potential.- 4. The Dirac operator.- Six Sesquilinear forms in Hilbert spaces and associated operators.- § 1. Sesquilinear and quadratic forms.- 1. Definitions.- 2. Semiboundedness.- 3. Closed forms.- 4. Closable forms.- 5. Forms constructed from sectorial operators.- 6. Sums of forms.- 7. Relative boundedness for forms and operators.- § 2. The representation theorems.- 1. The first representation theorem.- 2. Proof of the first representation theorem.- 3. The Friedrichs extension.- 4. Other examples for the representation theorem.- 5. Supplementary remarks.- 6. The second representation theorem.- 7. The polar decomposition of a closed operator.- § 3. Perturbation of sesquilinear forms and the associated operators.- 1. The real part of an m-sectorial operator.- 2. Perturbation of an m-sectorial operator and its resolvent.- 3. Symmetric unperturbed operators.- 4. Pseudo-Friedrichs extensions.- § 4. Quadratic forms and the Schrödinger operators.- 1. Ordinary differential operators.- 2. The Dirichlet form and the Laplace operator.- 3. The Schrödinger operators in R3.- 4. Bounded regions.- § 5. The spectral theorem and perturbation of spectral families.- 1. Spectral families.- 2. The selfadjoint operator associated with a spectral family.- 3. The spectral theorem.- 4. Stability theorems for the spectral family.- Seven Analytic perturbation theory.- § 1. Analytic families of operators.- 1. Analyticity of vector- and operator-valued functions.- 2. Analyticity of a family of unbounded operators.- 3. Separation of the spectrum and finite systems of eigenvalues.- 4. Remarks on infinite systems of eigenvalues.- 5. Perturbation series.- 6. A holomorphic family related to a degenerate perturbation.- § 2. Holomorphic families of type (A).- 1. Definition.- 2. A criterion for type (A).- 3. Remarks on holomorphic families of type (A).- 4. Convergence radii and error estimates.- 5. Normal unperturbed operators.- § 3. Selfadjoint holomorphic families.- 1. General remarks.- 2. Continuation of the eigenvalues.- 3. The Mathieu, Schrödinger, and Dirac equations.- 4. Growth rate of the eigenvalues.- 5. Total eigenvalues considered simultaneously.- § 4. Holomorphic families of type (B).- 1. Bounded-holomorphic families of sesquilinear forms.- 2. Holomorphic families of forms of type (a) and holomorphic families of operators of type (B).- 3. A criterion for type (B).- 4. Holomorphic families of type (B0).- 5. The relationship between holomorphic families of types (A) and (B).- 6. Perturbation series for eigenvalues and eigenprojections.- 7. Growth rate of eigenvalues and the total system of eigenvalues.- 8. Application to differential operators.- 9. The two-electron problem.- § 5. Further problems of analytic perturbation theory.- 1. Holomorphic families of type (C).- 2. Analytic perturbation of the spectral family.- 3. Analyticity of |H(x)| and |H(x)|?.- § 6. Eigenvalue problems in the generalized form.- 1. General considerations.- 2. Perturbation theory.- 3. Holomorphic families of type (A).- 4. Holomorphic families of type (B).- 5. Boundary perturbation.- Eight Asymptotic perturbation theory.- § 1. Strong convergence in the generalized sense.- 1. Strong convergence of the resolvent.- 2. Generalized strong convergence and spectra.- 3. Perturbation of eigenvalues and eigenvectors.- 4. Stable eigenvalues.- § 2. Asymptotic expansions.- 1. Asymptotic expansion of the resolvent.- 2. Remarks on asymptotic expansions.- 3. Asymptotic expansions of isolated eigenvalues and eigenvectors.- 4. Further asymptotic expansions.- § 3. Generalized strong convergence of sectorial operators.- 1. Convergence of a sequence of bounded forms.- 2. Convergence of sectorial forms “from above”.- 3. Nonincreasing sequences of symmetric forms.- 4. Convergence from below.- 5. Spectra of converging operators.- § 4. Asymptotic expansions for sectorial operators.- 1. The problem. The zeroth approximation for the resolvent.- 2. The 1\/2-order approximation for the resolvent.- 3. The first and higher order approximations for the resolvent.- 4. Asymptotic expansions for eigenvalues and eigenvectors.- § 5. Spectral concentration.- 1. Unstable eigenvalues.- 2. Spectral concentration.- 3. Pseudo-eigenvectors and spectral concentration.- 4. Asymptotic expansions.- Nine Perturbation theory for semigroups of operators.- § 1. One-parameter semigroups and groups of operators.- 1. The problem.- 2. Definition of the exponential function.- 3. Properties of the exponential function.- 4. Bounded and quasi-bounded semigroups.- 5. Solution of the inhomogeneous differential equation.- 6. Holomorphic semigroups.- 7. The inhomogeneous differential equation for a holomorphic semigroup.- 8. Applications to the heat and Schrödinger equations.- § 2. Perturbation of semigroups.- 1. Analytic perturbation of quasi-bounded semigroups.- 2. Analytic perturbation of holomorphic semigroups.- 3. Perturbation of contraction semigroups.- 4. Convergence of quasi-bounded semigroups in a restricted sense.- 5. Strong convergence of quasi-bounded semigroups.- 6. Asymptotic perturbation of semigroups.- § 3. Approximation by discrete semigroups.- 1. Discrete semigroups.- 2. Approximation of a continuous semigroup by discrete semigroups.- 3. Approximation theorems.- 4. Variation of the space.- Ten Perturbation of continuous spectra and unitary equivalence.- §1. The continuous spectrum of a selfadjoint operator.- 1. The point and continuous spectra.- 2. The absolutely continuous and singular spectra.- 3. The trace class.- 4. The trace and determinant.- § 2. Perturbation of continuous spectra.- 1. A theorem of Weyl-von Neumann.- 2. A generalization.- § 3. Wave operators and the stability of absolutely continuous spectra.- 1. Introduction.- 2. Generalized wave operators.- 3. A sufficient condition for the existence of the wave operator.- 4. An application to potential scattering.- § 4. Existence and completeness of wave operators.- 1. Perturbations of rank one (special case).- 2. Perturbations of rank one (general case).- 3. Perturbations of the trace class.- 4. Wave operators for functions of operators.- 5. Strengthening of the existence theorems.- 6. Dependence of W± (H2, H1) on H1 and H2.- § 5. A stationary method.- 1. Introduction.- 2. The ? operations.- 3. Equivalence with the time-dependent theory.- 4. The ? operations on degenerate operators.- 5. Solution of the integral equation for rank A = 1.- 6. Solution of the integral equation for a degenerate A.- 7. Application to differential operators.- Supplementary Notes.- Supplementary Bibliography.- Notation index.- Author index.","brand":"Springer-Verlag Berlin and Heidelberg GmbH \u0026 Co. KG","offers":[{"title":"Default Title","offer_id":48743131251031,"sku":"9783540586616","price":49.99,"currency_code":"GBP","in_stock":true}]},{"product_id":"optimal-transport-old-and-new-9783540710493","title":"Optimal Transport: Old and New","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eAt the close of the 1980s, the independent contributions of Yann Brenier, Mike Cullen and John Mather launched a revolution in the venerable field of optimal transport founded by G. Monge in the 18th century, which has made breathtaking forays into various other domains of mathematics ever since. The author presents a broad overview of this area, supplying complete and self-contained proofs of all the fundamental results of the theory of optimal transport at the appropriate level of generality. Thus, the book encompasses the broad spectrum ranging from basic theory to the most recent research results. \u003c\/p\u003e \u003cp\u003e\u003c\/p\u003e \u003cp\u003ePhD students or researchers can read the entire book without any prior knowledge of the field. A comprehensive bibliography with notes that extensively discuss the existing literature underlines the book’s value as a most welcome reference text on this subject. \u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eFrom the reviews:\u003c\/p\u003e\u003cp\u003e\"The book is aimed to old and new problems of optimal transport. … This meticulous work is based on very large bibliography … that is converted into a very valuable monograph that presents many statements and theorems written specifically for this approach, complete and self-contained proofs of the most important results, and extensive bibliographical notes.\" (Mihail Voicu, Zentralblatt MATH, Vol. 1156, 2009)\u003c\/p\u003e\u003cp\u003e“This book wins the challenge to give a new and broad perspective on the multifacet topic of the optimal mass transport. … Besides extensive and accurate references therein the reader will find comments on related questions barely touched upon in the main text as well as lively presentations on how ideas and results have developed. This book should prove useful both to the expert and to the beginner looking for a reference text on the subject.” (Dario Cordero Erausquin, Mathematical Reviews, Issue 2010 f)\u003c\/p\u003e\u003cp\u003e“The book is an in-depth, modern, clear exposition of the advanced theory of optimal transport, and it tries to put together in a unified way almost all the recent developments of the theory. … the book is extremely well written and very pleasant to read. … I strongly recommend this excellent book to every researcher or graduate student in the field of optimal transport. … of interest to many mathematicians in different areas, who are simply interested in having an overview of the subject.” (Alessio Figalli, Bulletin of the American Mathematical Society, Vol. 47 (4), February, 2010)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eCouplings and changes of variables.- Three examples of coupling techniques.- The founding fathers of optimal transport.- Qualitative description of optimal transport.- Basic properties.- Cyclical monotonicity and Kantorovich duality.- The Wasserstein distances.- Displacement interpolation.- The Monge—Mather shortening principle.- Solution of the Monge problem I: global approach.- Solution of the Monge problem II: Local approach.- The Jacobian equation.- Smoothness.- Qualitative picture.- Optimal transport and Riemannian geometry.- Ricci curvature.- Otto calculus.- Displacement convexity I.- Displacement convexity II.- Volume control.- Density control and local regularity.- Infinitesimal displacement convexity.- Isoperimetric-type inequalities.- Concentration inequalities.- Gradient flows I.- Gradient flows II: Qualitative properties.- Gradient flows III: Functional inequalities.- Synthetic treatment of Ricci curvature.- Analytic and synthetic points of view.- Convergence of metric-measure spaces.- Stability of optimal transport.- Weak Ricci curvature bounds I: Definition and Stability.- Weak Ricci curvature bounds II: Geometric and analytic properties.","brand":"Springer-Verlag Berlin and Heidelberg GmbH \u0026 Co. KG","offers":[{"title":"Default Title","offer_id":48743131283799,"sku":"9783540710493","price":113.99,"currency_code":"GBP","in_stock":true}]},{"product_id":"solving-nonlinear-partial-differential-equations-with-maple-and-mathematica-9783709105160","title":"Solving Nonlinear Partial Differential Equations","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThe emphasis of the book is given in how to construct different types of solutions (exact, approximate analytical, numerical, graphical) of numerous nonlinear PDEs correctly, easily, and quickly. The reader can learn a wide variety of techniques and solve numerous nonlinear PDEs included and many other differential equations, simplifying and transforming the equations and solutions, arbitrary functions and parameters, presented in the book). Numerous comparisons and relationships between various types of solutions, different methods and approaches are provided, the results obtained in Maple and Mathematica, facilitates a deeper understanding of the subject. Among a big number of CAS, we choose the two systems, Maple and Mathematica, that are used worldwide by students, research mathematicians, scientists, and engineers. As in the our previous books, we propose the idea to use in parallel both systems, Maple and Mathematica, since in many research problems frequently it is required to compare independent results obtained by using different computer algebra systems, Maple and\/or Mathematica, at all stages of the solution process. One of the main points (related to CAS) is based on the implementation of a whole solution method (e.g. starting from an analytical derivation of exact governing equations, constructing discretizations and analytical formulas of a numerical method, performing numerical procedure, obtaining various visualizations, and comparing the numerical solution obtained with other types of solutions considered in the book, e.g. with asymptotic solution).\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eFrom the reviews:\u003c\/p\u003e\u003cp\u003e“The authors consider the problem of constructing closed-form and approximate solutions to nonlinear partial differential equations with the help of computer algebra systems. … The book will be useful for readers who want to try modern methods for solving nonlinear partial differential equations on concrete examples without bothering too much about the mathematics behind the methods. Thus it is mainly of interest for applied scientists. Mathematicians may use it in connection with more theoretical works; some references are given throughout the book.” (Werner M. Seiler, Zentralblatt MATH, Vol. 1233, 2012)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e1 Introduction 1.1 Basic Concepts 2 Algebraic Approach 2.1 Point Transformations 2.2 Contact Transformations 2.3 Transformations Relating Differential Equations 2.4 Linearizing and Bilinearizing Transformations 2.5 Reductions of Nonlinear PDEs 2.6 Separation of Variables 2.7 Transformation Groups 2.8 Nonlinear Systems 3 Geometric-Qualitative Approach 3.1 Method of Characteristics 3.2 Generalized Method of Characteristics 3.3 Qualitative Analysis 4 General Analytical Approach. Integrability 4.1 Painlevé Test and Integrability 4.2 Complete Integrability. Evolution Equations 4.3 Nonlinear Systems. Integrability Conditions 5 Approximate Analytical Approach 5.1 Adomian Decomposition Method 5.2 Asymptotic Expansions. Perturbation Methods 6 Numerical Approach 6.1 Embedded Numerical Methods 6.2 Finite DifferenceMethods 7 Analytical-Numerical Approach 7.1 Method of Lines 7.2 Spectral Collocation Method;  A Brief Description of Maple A.1 Introduction A.2 Basic Concepts A.3 Maple Language B Brief Description of Mathematica B.1 Introduction B.2 Basic Concepts B.3 Mathematica Language; References, Index\u003c\/p\u003e","brand":"Springer Verlag GmbH","offers":[{"title":"Default Title","offer_id":48743145079127,"sku":"9783709105160","price":82.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783709105160.jpg?v=1720064307"},{"product_id":"spectral-theory-of-dynamical-systems-9789386279811","title":"Spectral Theory of Dynamical Systems","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis book treats some basic topics in the spectral theory of dynamical systems. The treatment is at a general level, but two more advanced theorems, one by H. Helson and W. Parry and the other by B. Host, are presented. Moreover, Ornstein's family of mixing rank one automorphisms is described with construction and proof. Systems of imprimitivity and their relevance to ergodic theory are discussed, and Baire category theorems of ergodic theory, scattered in the literature, are derived in a unified way. Riesz products are considered and they are used to describe the spectral types and eigenvalues of rank one automorphisms.\u003cbr\u003e\u003cbr\u003eThe major change in this edition is that a new chapter titled Calculus of Generalized Riesz Products has been added. This is based on some recent work of the author with El Houcein El Abdalaoui and supplements the material presented elsewhere in the book.","brand":"Jainendra K Jain","offers":[{"title":"Default Title","offer_id":48743250919767,"sku":"9789386279811","price":54.9,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9789386279811.jpg?v=1720064779"},{"product_id":"ordinary-differential-equations-with-applications-third-edition-9789811250743","title":"Ordinary Differential Equations With Applications","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eWritten in a straightforward and easily accessible style, this volume is suitable as a textbook for advanced undergraduate or first-year graduate students in mathematics, physical sciences, and engineering. The aim is to provide students with a strong background in the theories of Ordinary Differential Equations, Dynamical Systems and Boundary Value Problems, including regular and singular perturbations. It is also a valuable resource for researchers.This volume presents an abundance of examples in physical and biological sciences, and engineering to illustrate the applications of the theorems in the text. Readers are introduced to some important theorems in Nonlinear Analysis, for example, Brouwer fixed point theorem and fundamental theorem of algebras.  A chapter on Monotone Dynamical Systems takes care of the new developments in Ordinary Differential Equations and Dynamical Systems.In this third edition, an introduction to Hamiltonian Systems is included to enhance and complete its coverage on Ordinary Differential Equations with applications in Mathematical Biology and Classical Mechanics.","brand":"World Scientific Publishing Co Pte Ltd","offers":[{"title":"Default Title","offer_id":48743283884375,"sku":"9789811250743","price":58.5,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9789811250743.jpg?v=1720064919"},{"product_id":"an-introduction-to-fractional-differential-equations-9789819960798","title":"An Introduction to Fractional Differential","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis is an introductory-level text on fractional calculus and fractional differential equations. Targeted to graduate students of mathematics and researchers, it contains several new definitions of fractional integrals and fractional derivatives. With interesting applications of the subject in several areas of physical sciences, life sciences, engineering, and technology, the book helps the students understand the importance and developments of this topic. The book is enriched with a list of useful references to published literature, and the presentation of the book is entirely new and easily comprehensible to the students. Some of the topics are refined, and new examples are included to supplement theories to help students understand the concepts easily and clearly.\u003cp\u003e \u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eChapter 1 Introduction.- Chapter 2 Fractional Calculus.- Chapter 3 Fractional Differential Equations.- Chapter 4 Applications.- Chapter 5 Fractional Partial Differential Equations.","brand":"Springer Verlag, Singapore","offers":[{"title":"Default Title","offer_id":48743302627671,"sku":"9789819960798","price":38.24,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9789819960798.jpg?v=1720065002"},{"product_id":"differential-equations-for-dummies-9780470178140","title":"Differential Equations For Dummies","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eA differential equation involves an unknown function and its derivative. It is an important subject that lies in the heart of understanding calculus or analysis.   Differential Equations For Dummies takes readers step-by-step through this intimidating subject.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cb\u003eIntroduction.\u003c\/b\u003e  \u003cp\u003e\u003cb\u003ePart I: Focusing on First Order Differential Equations.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eChapter 1: Welcome to the World of Differential Equations.\u003c\/p\u003e \u003cp\u003eChapter 2: Looking at Linear First Order Differential Equations.\u003c\/p\u003e \u003cp\u003eChapter 3: Sorting Out Separable First Order Differential Equations.\u003c\/p\u003e \u003cp\u003eChapter 4: Exploring Exact First Order Differential Equations and Euler’s Method.\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart II: Surveying Second and Higher Order Differential Equations.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eChapter 5: Examining Second Order Linear Homogeneous Differential Equations.\u003c\/p\u003e \u003cp\u003eChapter 6: Studying Second Order Linear Nonhomogeneous Differential Equations.\u003c\/p\u003e \u003cp\u003eChapter 7: Handling Higher Order Linear Homogeneous Differential Equations.\u003c\/p\u003e \u003cp\u003eChapter 8: Taking On Higher Order Linear Nonhomogeneous Differential Equations.\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart III: The Power Stuff: Advanced Techniques.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eChapter 9: Getting Serious with Power Series and Ordinary Points.\u003c\/p\u003e \u003cp\u003eChapter 10: Powering through Singular Points.\u003c\/p\u003e \u003cp\u003eChapter 11: Working with Laplace Transforms.\u003c\/p\u003e \u003cp\u003eChapter 12: Tackling Systems of First Order Linear Differential Equations.\u003c\/p\u003e \u003cp\u003eChapter 13: Discovering Three Fail-Proof Numerical Methods.\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart IV: The Part of Tens.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eChapter 14: Ten Super-Helpful Online Differential Equation Tutorials.\u003c\/p\u003e \u003cp\u003eChapter 15: Ten Really Cool Online Differential Equation Solving Tools.\u003c\/p\u003e \u003cp\u003e\u003cb\u003eIndex.\u003c\/b\u003e\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":48864624509271,"sku":"9780470178140","price":17.09,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780470178140.jpg?v=1722272781"},{"product_id":"differential-equations-workbook-for-dummies-9780470472019","title":"Differential Equations Workbook For Dummies","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eDifferential Equations Workbook For Dummies  is a course supplement and practice guide for students taking a course that involves the use of differential equations. This book takes readers step-by-step through this intimidating subject and features numerous practice exercises and clear, concise examples to improve problem-solving skills.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eIntroduction 1\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart I: Tackling First Order Differential Equations 5\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eChapter 1: Looking Closely at Linear First Order Differential Equations 7\u003c\/p\u003e \u003cp\u003eChapter 2: Surveying Separable First Order Differential Equations 29\u003c\/p\u003e \u003cp\u003eChapter 3: Examining Exact First Order Differential Equations 59\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart II: Finding Solutions to Second and Higher Order Differential Equations 79\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eChapter 4: Working with Linear Second Order Differential Equations 81\u003c\/p\u003e \u003cp\u003eChapter 5: Tackling Nonhomogeneous Linear Second Order Differential Equations 105\u003c\/p\u003e \u003cp\u003eChapter 6: Handling Homogeneous Linear Higher Order Differential Equations 129\u003c\/p\u003e \u003cp\u003eChapter 7: Taking On Nonhomogeneous Linear Higher Order Differential Equations 153\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart III: The Power Stuff: Advanced Techniques 175\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eChapter 8: Using Power Series to Solve Ordinary Differential Equations 177\u003c\/p\u003e \u003cp\u003eChapter 9: Solving Differential Equations with Series Solutions Near Singular Points 199\u003c\/p\u003e \u003cp\u003eChapter 10: Using Laplace Transforms to Solve Differential Equations 225\u003c\/p\u003e \u003cp\u003eChapter 11: Solving Systems of Linear First Order Differential Equations 249\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart IV: The Part of Tens 273\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eChapter 12: Ten Common Ways of Solving Differential Equations 275\u003c\/p\u003e \u003cp\u003eChapter 13: Ten Real-World Applications of Differential Equations 279\u003c\/p\u003e \u003cp\u003eIndex 283\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":48864629031255,"sku":"9780470472019","price":14.24,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780470472019.jpg?v=1722272805"},{"product_id":"spatial-ecology-via-reactiondiffusion-equations-9780471493013","title":"Spatial Ecology Via ReactionDiffusion Equations","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eMany ecological phenomena may be modelled using apparently random processes involving space (and possibly time). Such phenomena are classified as spatial in their nature and include all aspects of pollution. This book addresses the problem of modelling spatial effects in ecology and population dynamics using reaction-diffusion models.\u003cbr\u003e * Rapidly expanding area of research for biologists and applied mathematicians\u003cbr\u003e * Provides a unified and coherent account of methods developed to study spatial ecology via reaction-diffusion models\u003cbr\u003e * Provides the reader with the tools needed to construct and interpret models\u003cbr\u003e * Offers specific applications of both the models and the methods\u003cbr\u003e * Authors have played a dominant role in the field for years\u003cbr\u003e Essential reading for graduate students and researchers working with spatial modelling from mathematics, statistics, ecology, geography and biology.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"…particularly attractive and useful for graduate students and other researchers who are interested in studying applications of reaction-diffusion theory to spatial ecology.\" (\u003ci\u003eMathematical Reviews\u003c\/i\u003e, Issue 2007a)  \u003cp\u003e\"…I would recommend this book to anyone who wants a well supported journey into the modern theory of partial differential equations and dynamic systems…\" (\u003ci\u003eThe Mathematical Gazette\u003c\/i\u003e, March 2005)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface.\u003cbr\u003e \u003cbr\u003e Series Preface.\u003cbr\u003e \u003cbr\u003e 1 Introduction.\u003cbr\u003e \u003cbr\u003e 1.1 Introductory Remarks.\u003cbr\u003e \u003cbr\u003e 1.2 Nonspatial Models for a Single Species.\u003cbr\u003e \u003cbr\u003e 1.3 Nonspatial Models For Interacting Species.\u003cbr\u003e \u003cbr\u003e 1.4 Spatial Models: A General Overview.\u003cbr\u003e \u003cbr\u003e 1.5 Reaction-Diffusion Models.\u003cbr\u003e \u003cbr\u003e 1.6 Mathematical Background.\u003cbr\u003e \u003cbr\u003e 2 Linear Growth Models for a Single Species: Averaging Spatial Effects Via Eigenvalues.\u003cbr\u003e \u003cbr\u003e 2.1 Eigenvalues, Persistence, and Scaling in Simple Models.\u003cbr\u003e \u003cbr\u003e 2.2 Variational Formulations of Eigenvalues: Accounting for Heterogeneity.\u003cbr\u003e \u003cbr\u003e 2.3 Effects of Fragmentation and Advection\/Taxis in Simple Linear Models.\u003cbr\u003e \u003cbr\u003e 2.4 Graphical Analysis in One Space Dimension.\u003cbr\u003e \u003cbr\u003e 2.5 Eigenvalues and Positivity.\u003cbr\u003e \u003cbr\u003e 2.6 Connections with Other Topics and Models.\u003cbr\u003e \u003cbr\u003e Appendix.\u003cbr\u003e \u003cbr\u003e 3 Density Dependent Single-Species Models.\u003cbr\u003e \u003cbr\u003e 3.1 The Importance of Equilibria in Single Species Models.\u003cbr\u003e \u003cbr\u003e 3.2 Equilibria and Stability: Sub- and Supersolutions.\u003cbr\u003e \u003cbr\u003e 3.3 Equilibria and Scaling: One Space Dimension.\u003cbr\u003e \u003cbr\u003e 3.4 Continuation and Bifurcation of Equilibria.\u003cbr\u003e \u003cbr\u003e 3.5 Applications and Properties of Single Species Models.\u003cbr\u003e \u003cbr\u003e 3.6 More General Single Species Models.\u003cbr\u003e \u003cbr\u003e Appendix.\u003cbr\u003e \u003cbr\u003e 4 Permanence.\u003cbr\u003e \u003cbr\u003e 4.1 Introduction.\u003cbr\u003e \u003cbr\u003e 4.2 Definition of Permanence.\u003cbr\u003e \u003cbr\u003e 4.3 Techniques for Establishing Permanence.\u003cbr\u003e \u003cbr\u003e 4.4 Invasibility Implies Coexistence.\u003cbr\u003e \u003cbr\u003e 4.5 Permanence in Reaction-Diffusion Models for Predation.\u003cbr\u003e \u003cbr\u003e 4.6 Ecological Permanence and Equilibria.\u003cbr\u003e \u003cbr\u003e Appendix.\u003cbr\u003e \u003cbr\u003e 5 Beyond Permanence: More Persistence Theory.\u003cbr\u003e \u003cbr\u003e 5.1 Introduction.\u003cbr\u003e \u003cbr\u003e 5.2 Compressivity.\u003cbr\u003e \u003cbr\u003e 5.3 Practical Persistence.\u003cbr\u003e \u003cbr\u003e 5.4 Bounding Transient Orbits.\u003cbr\u003e \u003cbr\u003e 5.5 Persistence in Nonautonomous Systems.\u003cbr\u003e \u003cbr\u003e 5.6 Conditional Persistence.\u003cbr\u003e \u003cbr\u003e 5.7 Extinction Results.\u003cbr\u003e \u003cbr\u003e Appendix.\u003cbr\u003e \u003cbr\u003e 6 Spatial Heterogeneity in Reaction-Diffusion Models.\u003cbr\u003e \u003cbr\u003e 6.1 Introduction.\u003cbr\u003e \u003cbr\u003e 6.2 Spatial Heterogeneity within the Habitat Patch.\u003cbr\u003e \u003cbr\u003e 6.3 Edge Mediated Effects.\u003cbr\u003e \u003cbr\u003e 6.4 Estimates and Consequences.\u003cbr\u003e \u003cbr\u003e Appendix.\u003cbr\u003e \u003cbr\u003e 7 Nonmonotone Systems.\u003cbr\u003e \u003cbr\u003e 7.1 Introduction.\u003cbr\u003e \u003cbr\u003e 7.2 Predator Mediated Coexistence.\u003cbr\u003e \u003cbr\u003e 7.3 Three Species Competition.\u003cbr\u003e \u003cbr\u003e 7.4 Three Trophic Level Models.\u003cbr\u003e \u003cbr\u003e Appendix.\u003cbr\u003e \u003cbr\u003e References.\u003cbr\u003e \u003cbr\u003e Index.","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":48864649609559,"sku":"9780471493013","price":159.26,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780471493013.jpg?v=1722272893"},{"product_id":"numerical-solution-of-partial-differential-equations-by-the-finite-element-method-9780486469003","title":"Numerical Solution of Partial Differential","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e","brand":"Dover Publications Inc.","offers":[{"title":"Default Title","offer_id":48864735494487,"sku":"9780486469003","price":14.39,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780486469003.jpg?v=1722273003"},{"product_id":"ordinary-differential-equations-9780486649405","title":"Ordinary Differential Equations","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e","brand":"Dover Publications Inc.","offers":[{"title":"Default Title","offer_id":48864739656023,"sku":"9780486649405","price":26.19,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780486649405.jpg?v=1722273020"},{"product_id":"introduction-to-partial-differential-equations-9780691043616","title":"Introduction to Partial Differential Equations","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eServes as a text for mathematics students at the intermediate graduate level. This book aims to acquaint readers with the fundamental classical results of partial differential equations and to guide them into some aspects of the modern theory to the point where they will be equipped to read advanced treatises and research papers.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"The first edition of Folland's text on PDEs used to be my favorite source for a course on DPEs. The new edition includes many more exercises and offers a new chapter on pseudodifferential operators. ... This text book is a pleasant compromise between the modern abstract theory and the concrete classical examples and applications.\"--Monatshefte fur Mathematik\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e* Local Existence Theory * The Laplace Operator * Layer Potentials * The Heat Operator * The Wave Operator * The L2 Theory of Derivatives * Elliptic Boundary Value Problems * Pseudodifferential Operators","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":48865516192087,"sku":"9780691043616","price":92.65,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691043616.jpg?v=1722274344"},{"product_id":"the-essential-john-nash-9780691096100","title":"The Essential John Nash","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eWhen John Nash won the Nobel prize in economics in 1994, many people were surprised to learn that he was alive. This book presents Nash's contributions not only to game theory, for which he received the Nobel, but to mathematics - from Riemannian geometry and partial differential equations - in which he commands greater acclaim among academics.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"If you want to see a sugary Hollywood depiction of John Nash's life, go to the cinema. Afterwards, if you are curious about his insights, pick up a new book that explains his work and reprints his most famous papers. It is just as amazing as his personal story.\"--Chris Giles, Financial Times \"One of the most beautifully designed economics books I have ever seen and at a low price... Why are we so intrigued by the story of John Nash? We are curious to understand a person who proves theorems we are unable to fathom. We imagine the voices from another world he has heard. We ask where he was for 30 years during which he walked among us but wasn't here. We are frightened and we are attracted by this combination of 'crazy' and 'genius', an invitation for visiting the edge of our own minds.\"--Ariel Rubinstein, The Times Higher Education Supplement \"Any mathematician who read A Beautiful Mind ... had to be looking for the appendices--the ones explaining what Nash actually did to earn his formidable reputation within the mathematical community. Well, here they are, in a beautifully produced volume... Kuhn, Nasar, and the other contributors have performed a most welcome service by collaborating to bring together the pieces missing from A Beautiful Mind... The mathematical community is eternally in their debt.\"--SIAM News \"The book is written in a pleasant and informal style, addressed to a large audience.\"--P.T. Moranu, Mathematica\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePREFACE by Harold W. Kuhn vii  INTRODUCTION by Sylvia Nasar xi  Chapter 1: Press Release--The Royal Swedish Academy of Sciences 1  Chapter 2: Autobiography 5  Photo Essay 13  Editor's introduction to Chapter 3 29  Chapter 3: The Game of Hex by John Milnor 31  Editor's Introduction to Chapter 4 35  Chapter 4: The bargaining problem 37  Editor's Introduction to Chapters 5, 6, and 7 47  Chapter 5: Equilibrium Points in n-Person games 49  Chapter 6: Non-Cooperative Games Facsimile of Ph.D. Thesis 51  Chapter 7: Non-Cooperative Games 85  Chapter 8: Two-Person Coooperative Games 99  Editor's Introduction to Chapter 9 115  Chapter 9: Parallel Control 117  Chapter 10: real Algebraic Manifolds 127  Chapter 11: The Imbedding problem for Riemannian Manifolds 151  Chapter 12: Continuity of Solutions of Parabolic and Elliptic Equations 211  AFTERWORD 241  SOURCES 243","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":48865517764951,"sku":"9780691096100","price":31.5,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691096100.jpg?v=1722274352"},{"product_id":"linear-systems-theory-9780691179575","title":"Linear Systems Theory","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"Praise for the previous edition: \"\u003ci\u003eLinear Systems Theory\u003c\/i\u003e gives a good presentation of the main topics on linear systems as well as more advanced topics related to controller design. The scholarship is sound and the book is very well written and readable.\"\"\u003cb\u003e---Ian Petersen, University of New South Wales\u003c\/b\u003e\u003cbr\u003e\"Praise for the previous edition: \"This book provides a sound basis for an excellent course on linear systems theory. It covers a breadth of material in a fast-paced and mathematically focused way. It can be used by students wishing to specialize in this subject, as well as by those interested in this topic generally.\"\"\u003cb\u003e---Geir E. Dullerud, University of Illinois, Urbana-Champaign\u003c\/b\u003e","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":48865539588439,"sku":"9780691179575","price":71.4,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691179575.jpg?v=1722274460"},{"product_id":"filtering-and-system-identification-a-least-squares-approach-9781107405028","title":"Filtering and System Identification A Least","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis 2007 book discusses the design of reliable numerical methods to retrieve missing information in models of complex systems.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface; 1. Introduction; 2. Linear algebra; 3. Discrete-time signals and systems; 4. Random variables and signals; 5. Kalman filtering; 6. Estimation of spectra and frequency response functions; 7. Output-error parametric model estimation; 8. Prediction-error parametric model estimation; 9. Subspace model identification; 10. The system identification cycle; Notation and symbols; List of abbreviations; References; Index.","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":48866340143447,"sku":"9781107405028","price":49.39,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781107405028.jpg?v=1722278207"},{"product_id":"a-first-course-in-differential-equations-with-modeling-applications-international-metric-edition-9781337556644","title":"A First Course in Differential Equations with","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eStraightforward and easy to read, A FIRST COURSE IN DIFFERENTIAL EQUATIONS WITH MODELING APPLICATIONS, 11E, INTERNATIONAL METRIC EDITION, gives you a thorough overview of the topics typically taught in a first course in differential equations. Your study of differential equations and its applications will be supported by a bounty of pedagogical aids, including an abundance of examples, explanations, \"Remarks\" boxes, definitions, and more.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e1. INTRODUCTION TO DIFFERENTIAL EQUATIONS. Definitions and Terminology. Initial-Value Problems. Differential Equations as Mathematical Models. Chapter 1 in Review. 2. FIRST-ORDER DIFFERENTIAL EQUATIONS. Solution Curves Without a Solution. Separable Variables. Linear Equations. Exact Equations and Integrating Factors. Solutions by Substitutions. A Numerical Method. Chapter 2 in Review. 3. MODELING WITH FIRST-ORDER DIFFERENTIAL EQUATIONS. Linear Models. Nonlinear Models. Modeling with Systems of First-Order Differential Equations. Chapter 3 in Review. 4. HIGHER-ORDER DIFFERENTIAL EQUATIONS. Preliminary Theory-Linear Equations. Reduction of Order. Homogeneous Linear Equations with Constant Coefficients. Undetermined Coefficients-Superposition Approach. Undetermined Coefficients-Annihilator Approach. Variation of Parameters. Cauchy-Euler Equation. Solving Systems of Linear Differential Equations by Elimination. Nonlinear Differential Equations. Chapter 4 in Review. 5. MODELING WITH HIGHER-ORDER DIFFERENTIAL EQUATIONS. Linear Models: Initial-Value Problems. Linear Models: Boundary-Value Problems. Nonlinear Models. Chapter 5 in Review. 6. SERIES SOLUTIONS OF LINEAR EQUATIONS. Review of Power Series Solutions About Ordinary Points. Solutions About Singular Points. Special Functions. Chapter 6 in Review. 7. LAPLACE TRANSFORM. Definition of the Laplace Transform. Inverse Transform and Transforms of Derivatives. Operational Properties I. Operational Properties II. Dirac Delta Function. Systems of Linear Differential Equations. Chapter 7 in Review. 8. SYSTEMS OF LINEAR FIRST-ORDER DIFFERENTIAL EQUATIONS. Preliminary Theory. Homogeneous Linear Systems. Nonhomogeneous Linear Systems. Matrix Exponential. Chapter 8 in Review. 9. NUMERICAL SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS. Euler Methods. Runge-Kutta Methods. Multistep Methods. Higher-Order Equations and Systems. Second-Order Boundary-Value Problems. Chapter 9 in Review. Appendix I. Gamma Function. Appendix II. Matrices. Appendix III. Laplace Transforms. Answers for Selected Odd-Numbered Problems.","brand":"Cengage Learning, Inc","offers":[{"title":"Default Title","offer_id":48866572009815,"sku":"9781337556644","price":79.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781337556644.jpg?v=1722279272"},{"product_id":"a-closer-look-at-boundary-value-problems-9781536178579","title":"A Closer Look at Boundary Value Problems","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eMany problems encountered in applied mathematics or mathematical physics can be modelled by using differential equations under different boundary conditions. In this regard, linear and nonlinear partial differential equations are often used because of their strong capacity to describe and formulate many real-world problems governed by dynamical phenomena. There are many different methods to solve linear and nonlinear problems arising from different studies in various disciplines. However, due to lack of general existence theorems for establishing solutions, scientists have to seek alternative approaches and methods. In this context, the present work demonstrates different methods and approaches to obtain solutions to some class of differential equations given under different boundary conditions. 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This is a contributed book of seventh chapters encompassing local and no-local diffusion phenomena modelled with integer-order (local) and non-local operators. This book collates research results developed by scientists from different countries but with common research interest in modelling of diffusion problems. The results reported encompass diffusion problems related to efficient numerical modelling, hypersonic flows, approximate analytical solutions of solvent diffusion in polymers and wetting of soils. Some chapters are devoted to fractional diffusion problem with operators with singular and non-singular memory kernels. The book content cannot present the entire rich area of problems related to modelling of diffusion phenomena but allow seeing some new trends and approaches in the modelling technologies. In this context, the fractional models with singular and non-singular kernels the numerical methods and the development of the integration techniques related to the integral-balance approach form fresh fluxes of ideas to this classical engineering area of research. 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The authors study the existence and regularity of solutions for some nonlinear second order differential equations, showing the existence of mild solutions and giving sufficient conditions ensuring the existence of strict solutions. Sufficient conditions for the oscillation of solutions of neutral impulsive differential equations are also presented. In the penultimate study, the oscillatory behaviour of the solutions of a class of nonlinear first-order neutral differential equations with several delays of one form are studied. 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This book also covers degenerate parabolic equations, abstract differential equations, comments on the Schrodinger equation, solutions in banach spaces, periodic and quasi-periodic solutions, concave Lagragian systems and integral equations.","brand":"Nova Science Publishers Inc","offers":[{"title":"Default Title","offer_id":48886592700759,"sku":"9781600213427","price":67.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781600213427.jpg?v=1722540772"},{"product_id":"differential-equations-application-systems-functions-9781613240915","title":"Differential Equations: Application Systems \u0026","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e","brand":"Nova Science Publishers Inc","offers":[{"title":"Default Title","offer_id":48886832529751,"sku":"9781613240915","price":106.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781613240915.jpg?v=1722541782"},{"product_id":"partial-differential-equations-classification-properties-applications-9781634826433","title":"Partial Differential Equations: Classification,","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis book includes research on the Lax-Milgram theorem, which can be used to prove existence and uniqueness of weak solutions to partial differential equations and several examples of its application to relevant boundary value problems are presented. 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Therefore, these equations arise as models in virtually all branches of science and technology. Our goal in this book is to help you to understand what this vast subject is about. The book is an introduction to the field suitable for senior undergraduate and junior graduate students. Introductory courses in partial differential equations (PDEs) are given all over the world in various forms. The traditional approach to the subject is to introduce a number of analytical techniques, enabling the student to derive exact solutions of some simplified problems. Students who learn about computational techniques in other courses subsequently realize the scope of partial differential equations beyond paper and pencil. Our book is significantly different from the existing ones. We introduce both analytical theory, including the theory of classical solutions and that of weak solutions, and introductory techniques of ill-posed problems with reference to weak solutions. 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