Differential calculus and equations Books
Dover Publications Inc. Ordinary Differential Equations
Book Synopsis
£26.14
Wellesley-Cambridge Press,U.S. Differential Equations and Linear Algebra
Book SynopsisDifferential equations and linear algebra are two central topics in the undergraduate mathematics curriculum. This innovative textbook allows the two subjects to be developed either separately or together, illuminating the connections between two fundamental topics, and giving increased flexibility to instructors. It can be used either as a semester-long course in differential equations, or as a one-year course in differential equations, linear algebra, and applications. Beginning with the basics of differential equations, it covers first and second order equations, graphical and numerical methods, and matrix equations. The book goes on to present the fundamentals of vector spaces, followed by eigenvalues and eigenvectors, positive definiteness, integral transform methods and applications to PDEs. The exposition illuminates the natural correspondence between solution methods for systems of equations in discrete and continuous settings. The topics draw on the physical sciences, engineer
£54.14
Princeton University Press Linear Systems Theory
Book SynopsisTrade Review"Praise for the previous edition: "Linear Systems Theory 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.""---Ian Petersen, University of New South Wales"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.""---Geir E. Dullerud, University of Illinois, Urbana-Champaign
£71.40
World Scientific Europe Ltd Geometric Mechanics Part Iii Broken Symmetry And
Book Synopsis
£33.25
Springer-Verlag New York Inc. Stochastic Calculus and Applications
Book SynopsisCompletely revised and greatly expanded, the new edition of this text takes readers who have been exposed to only basic courses in analysis through the modern general theory of random processes and stochastic integrals as used by systems theorists, electronic engineers and, more recently, those working in quantitative and mathematical finance.Trade Review“As supplementary reading for a second course or as s comprehensive (!) resource for the general theory of processes aimed at Ph. D. students and scholars, this second edition will stay a valuable resource.” (René L. Schilling, Mathematical Reviews, October, 2016)“This is a fundamental book in modern stochastic calculus and its applications: rich contents, well structured material, comprehensive coverage of all significant results given with complete proofs and well illustrated by examples, carefully written text. Hence, there are more than enough reasons to strongly recommend the book to a wide audience. Among them, there are good and motivated graduate university students. … Also, the book is an excellent reference book.” (Jordan M. Stoyanov, zbMATH 1338.60001, 2016)Table of ContentsPart I: Measure Theoretic Probability.- Measure Integral.- Probabilities and Expectation.- Part II: Stochastic Processes.- Filtrations, Stopping Times and Stochastic Processes.- Martingales in Discrete Time.- Martingales in Continuous Time.- The Classification of Stopping Times.- The Progressive, Optional and Predicable -Algebras.- Part III: Stochastic Integration.- Processes of Finite Variation.- The Doob-Meyer Decomposition.- The Structure of Square Integrable Martingales.- Quadratic Variation and Semimartingales.- The Stochastic Integral.- Random Measures.- Part IV: Stochastic Differential Equations.- Ito's Differential Rule.- The Exponential Formula and Girsanov's Theorem.- Lipschitz Stochastic Differential Equations.- Markov Properties of SDEs.- Weak Solutions of SDEs.- Backward Stochastic Differential Equations.- Part V: Applications.- Control of a Single Jump.- Optimal Control of Drifts and Jump Rates.- Filtering. Part VI: Appendices.
£52.49
Cengage Learning, Inc Differential Equations with BoundaryValue
Book SynopsisTable of Contents1. 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. 10. PLANE AUTONOMOUS SYSTEMS. Autonomous Systems. Stability of Linear Systems. Linearization and Local Stability. Autonomous Systems as Mathematical Models. Chapter 10 in Review. 11. ORTHOGONAL FUNCTIONS AND FOURIER SERIES. Orthogonal Functions. Fourier Series and Orthogonal Functions. Fourier Cosine and Sine Series. Sturm-Liouville Problem. Bessel and Legendre Series. Chapter 11 in Review. 12. BOUNDARY-VALUE PROBLEMS IN RECTANGULAR COORDINATES. Separable Partial Differential Equations. Classical PDE's and Boundary-Value Problems. Heat Equation. Wave Equation. Laplace's Equation. Nonhomogeneous Boundary-Value Problems. Orthogonal Series Expansions. Higher-Dimensional Problems. Chapter 12 in Review. 13. BOUNDARY-VALUE PROBLEMS IN OTHER COORDINATE SYSTEMS. Polar Coordinates. Polar and Cylindrical Coordinates. Spherical Coordinates. Chapter 13 in Review. 14. INTEGRAL TRANSFORM METHOD. Error Function. Laplace Transform. Fourier Integral. Fourier Transforms. Chapter 14 in Review. 15. NUMERICAL SOLUTIONS OF PARTIAL DIFFERENTIAL EQUATIONS. Laplace's Equation. Heat Equation. Wave Equation. Chapter 15 in Review. Appendix I: Gamma Function. Appendix II: Matrices. Appendix III: Laplace Transforms. Answers for Selected Odd-Numbered Problems.
£72.99
Dover Publications Inc. Numerical Solution of Partial Differential
Book Synopsis
£14.39
Elsevier Science Differential Equations Dynamical Systems and an
Book SynopsisSuitable for students in the fields of mathematics, science, and engineering, this title provides a theoretical approach to dynamical systems and chaos. It helps them to analyze the types of differential equations that arise in their area of study.Table of Contents1. First-Order Equations 2. Planar Linear Systems 3. Phase Portraits 4. Classification of Planar Systems 5. Higher Dimension Linear Algebra 6. Higher Dimension Linear Systems 7. Nonlinear Systems 8. Equilibria in Nonlinear Systems 9. Global Nonlinear Techniques 10. Closed Orbits and Limit Sets 11. Applications in Biology 12. Applications in Circuit Theory 13. Applications in Mechanics 14. The Lorenz System 15. Discrete Dynamical Systems 16. Homoclinic Phenomena 17. Existence and Uniqueness Revisited
£75.04
Cambridge University Press Filtering and System Identification A Least
Book SynopsisThis 2007 book discusses the design of reliable numerical methods to retrieve missing information in models of complex systems.Table of ContentsPreface; 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.
£51.99
Elsevier Science Fractional Differential Equations
Book SynopsisIntended for readers who are new to the fields of fractional derivatives and fractional-order mathematical models, this covers the topics necessary for initial study and immediate application of fractional derivatives fractional differential equations. It also includes tables of fractional derivatives.Trade Review"...This is by no means the first (or the last) book on the subject of fractional calculus, but indeed it is one that wouldundoubtedly attract the attention (and successfully serve the needs) of mathematical, physical, and engineering scientists looking for applications of fractional calculus. I, therefore, recommend this well-written book to all users of fractional calculus." --H. M. Srivastava, Zentralblatt MATHTable of ContentsPreface. Acknowledgments. Special Functions Of Preface. Acknowledgements. Special Functions of the Fractional Calculus. Gamma Function. Mittag-Leffler Function. Wright Function. Fractional Derivatives and Integrals. The Name of the Game. Grünwald-Letnikov Fractional Derivatives. Riemann-Liouville Fractional Derivatives. Some Other Approaches. Sequential Fractional Derivatives. Left and Right Fractional Derivatives. Properties of Fractional Derivatives. Laplace Transforms of Fractional Derivatives. Fourier Transforms of Fractional Derivatives. Mellin Transforms of Fractional Derivatives. Existence and Uniqueness Theorems. Linear Fractional Differential Equations. Fractional Differential Equation of a General Form. Existence and Uniqueness Theorem as a Method of Solution. Dependence of a Solution on Initial Conditions. The Laplace Transform Method. Standard Fractional Differential Equations. Sequential Fractional Differential Equations. Fractional Green's Function. Definition and Some Properties. One-Term Equation. Two-Term Equation. Three-Term Equation. Four-Term Equation. Calculation of Heat Load Intensity Change in Blast Furnace Walls. Finite-Part Integrals and Fractional Derivatives. General Case: n-term Equation. Other Methods for the Solution of Fractional-order Equations. The Mellin Transform Method. Power Series Method. Babenko's Symbolic Calculus Method. Method of Orthogonal Polynomials. Numerical Evaluation of Fractional Derivatives. Approximation of Fractional Derivatives. The "Short-Memory" Principle. Order of Approximation. Computation of Coefficients. Higher-order Approximations. Numerical Solution of Fractional Differential Equations. Initial Conditions: Which Problem to Solve? Numerical Solution. Examples of Numerical Solutions. The "Short-Memory" Principle in Initial Value Problems for Fractional Differential Equations. Fractional-Order Systems and Controllers. Fractional-Order Systems and Fractional-Order Controllers. Example. On Viscoelasticity. Bode's Analysis of Feedback Amplifiers. Fractional Capacitor Theory. Electrical Circuits. Electroanalytical Chemistry. Electrode-Electrolyte Interface. Fractional Multipoles. Biology. Fractional Diffusion Equations. Control Theory. Fitting of Experimental Data. The "Fractional-Order" Physics? Bibliography. Tables of Fractional Derivatives. Index.
£88.19
Princeton University Press Introduction to Differential Equations with
Book SynopsisDiscusses about differential equations. This book presents elementary dynamical systems. It is suitable for undergraduate mathematics, engineering, and science students.Trade Review"These two experienced applied mathematicians have sought to provide an easy-to-read introduction to differential equations for typical students... The writing is clear and well illustrated."--Robert E. O'Mally, Jr., SIAM Review "Introduction to Differential Equations with Dynamical Systems is directed towards students. This concise and up-to-date textbook addresses the challenges that undergraduate mathematics, engineering and science students experience during a first course on differential equations."--L'Enseignement MathematiqueTable of ContentsPreface ix CHAPTER 1: First-Order Differential Equations and Their Applications 1 1.1 Introduction to Ordinary Differential Equations 1 1.2 The Definite Integral and the Initial Value Problem 4 1.2.1 The Initial Value Problem and the Indefinite Integral 5 1.2.2 The Initial Value Problem and the Definite Integral 6 1.2.3 Mechanics I: Elementary Motion of a Particle with Gravity Only 8 1.3 First-Order Separable Differential Equations 13 1.3.1 Using Definite Integrals for Separable Differential Equations 16 1.4 Direction Fields 19 1.4.1 Existence and Uniqueness 25 1.5 Euler's Numerical Method (optional) 31 1.6 First-Order Linear Differential Equations 37 1.6.1 Form of the General Solution 37 1.6.2 Solutions of Homogeneous First-Order Linear Differential Equations 39 1.6.3 Integrating Factors for First-Order Linear Differential Equations 42 1.7 Linear First-Order Differential Equations with Constant Coefficients and Constant Input 48 1.7.1 Homogeneous Linear Differential Equations with Constant Coefficients 48 1.7.2 Constant Coefficient Linear Differential Equations with Constant Input 50 1.7.3 Constant Coefficient Differential Equations with Exponential Input 52 1.7.4 Constant Coefficient Differential Equations with Discontinuous Input 52 1.8 Growth and Decay Problems 59 1.8.1 A First Model of Population Growth 59 1.8.2 Radioactive Decay 65 1.8.3 Thermal Cooling 68 1.9 Mixture Problems 74 1.9.1 Mixture Problems with a Fixed Volume 74 1.9.2 Mixture Problems with Variable Volumes 77 1.10 Electronic Circuits 82 1.11 Mechanics II: Including Air Resistance 88 1.12 Orthogonal Trajectories (optional) 92 CHAPTER 2: Linear Second- and Higher-Order Differential Equations 96 2.1 General Solution of Second-Order Linear Differential Equations 96 2.2 Initial Value Problem (for Homogeneous Equations) 100 2.3 Reduction of Order 107 2.4 Homogeneous Linear Constant Coefficient Differential Equations (Second Order) 112 2.4.1 Homogeneous Linear Constant Coefficient Differential Equations (nth-Order) 122 2.5 Mechanical Vibrations I: Formulation and Free Response 124 2.5.1 Formulation of Equations 124 2.5.2 Simple Harmonic Motion (No Damping, delta =0) 128 2.5.3 Free Response with Friction (delta > 0) 135 2.6 The Method of Undetermined Coefficients 142 2.7 Mechanical Vibrations II: Forced Response 159 2.7.1 Friction is Absent (delta = 0) 159 2.7.2 Friction is Present (delta > 0) (Damped Forced Oscillations) 168 2.8 Linear Electric Circuits 174 2.9 Euler Equation 179 2.10 Variation of Parameters (Second-Order) 185 2.11 Variation of Parameters (nth-Order) 193 CHAPTER 3: The Laplace Transform 197 3.1 Definition and Basic Properties 197 3.1.1 The Shifting Theorem (Multiplying by an Exponential) 205 3.1.2 Derivative Theorem (Multiplying by t ) 210 3.2 Inverse Laplace Transforms (Roots, Quadratics, and Partial Fractions) 213 3.3 Initial Value Problems for Differential Equations 225 3.4 Discontinuous Forcing Functions 234 3.4.1 Solution of Differential Equations 239 3.5 Periodic Functions 248 3.6 Integrals and the Convolution Theorem 253 3.6.1 Derivation of the Convolution Theorem (optional) 256 3.7 Impulses and Distributions 260 CHAPTER 4: An Introduction to Linear Systems of Differential Equations and Their Phase Plane 265 4.1 Introduction 265 4.2 Introduction to Linear Systems of Differential Equations 268 4.2.1 Solving Linear Systems Using Eigenvalues and Eigenvectors of the Matrix 269 4.2.2 Solving Linear Systems if the Eigenvalues are Real and Unequal 272 4.2.3 Finding General Solutions of Linear Systems in the Case of Complex Eigenvalues 276 4.2.4 Special Systems with Complex Eigenvalues (optional) 279 4.2.5 General Solution of a Linear System if the Two Real Eigenvalues are Equal (Repeated) Roots 281 4.2.6 Eigenvalues and Trace and Determinant (optional) 283 4.3 The Phase Plane for Linear Systems of Differential Equations 287 4.3.1 Introduction to the Phase Plane for Linear Systems of Differential Equations 287 4.3.2 Phase Plane for Linear Systems of Differential Equations 295 4.3.3 Real Eigenvalues 296 4.3.4 Complex Eigenvalues 304 4.3.5 General Theorems 310 CHAPTER 5: Mostly Nonlinear First-Order Differential Equations 315 5.1 First-Order Differential Equations 315 5.2 Equilibria and Stability 316 5.2.1 Equilibrium 316 5.2.2 Stability 317 5.2.3 Review of Linearization 318 5.2.4 Linear Stability Analysis 318 5.3 One-Dimensional Phase Lines 322 5.4 Application to Population Dynamics: The Logistic Equation 327 CHAPTER 6: Nonlinear Systems of Differential Equations in the Plane 332 6.1 Introduction 332 6.2 Equilibria of Nonlinear Systems, Linear Stability Analysis of Equilibrium, and the Phase Plane 335 6.2.1 Linear Stability Analysis and the Phase Plane 336 6.2.2 Nonlinear Systems: Summary, Philosophy, Phase Plane, Direction Field, Nullclines 341 6.3 Population Models 349 6.3.1 Two Competing Species 350 6.3.2 Predator-Prey Population Models 356 6.4 Mechanical Systems 363 6.4.1 Nonlinear Pendulum 363 6.4.2 Linearized Pendulum 364 6.4.3 Conservative Systems and the Energy Integral 364 6.4.4 The Phase Plane and the Potential 367 Answers to Odd-Numbered Exercises 379 Index 429
£84.00
MP-AMM American Mathematical An Introduction to Stochastic Differential
Book SynopsisProvides a quick, but very readable introduction to stochastic differential equations—that is, to differential equations subject to additive “white noise" and related random disturbances. The exposition is strongly focused upon the interplay between probabilistic intuition and mathematical rigour.Trade Review... [A]n interesting and unusual introduction to stochastic differential equations...topical and appealing to a wide audience. ... This is interesting stuff and, because of Evans' always clear explanations, it is fun too." - MAA ReviewsTable of Contents Preface Introduction A crash course in probability theory Brownian motion and “white noise” Stochastical integrals Stochastic differential equations Applications Appendix Exercises Notes and suggested reading Bibliography Index
£35.96
McGraw-Hill Education - Europe Schaums Outline of Lagrangian Dynamics
Book SynopsisIncludes 275 solved problems.Table of ContentsBackground Material.Lagrange's Equations of Motion of a Single Particle.Lagrange's Equations of Motion for a System of Particles.Conservative Systems.Dissipative Forces.General Treatment of Moments and Products of Inertia.Lagrangian Treatment of Rigid Body Dynamics.The Euler Method of Rigid Body Dynamics.Small Oscillations about Positions of Equilibrium.Small Oscillations about Steady Motion.Forces of Constraint.Driving Forces Required to Establish Known Motions.Effects of Earth's Figure and Daily Rotation on Dynamical Problems.Application of Lagrange's Equations to Electrical and Electromechanical Systems.Hamilton's Equations of Motion.Hamilton's Principle.Basic Equations of Dynamics in Vector and Tensor Notation.Appendix: Relations between Direction Cosines.
£26.99
John Wiley & Sons Inc Differential Equations For Dummies
Book SynopsisA 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.Table of ContentsIntroduction. Part I: Focusing on First Order Differential Equations. Chapter 1: Welcome to the World of Differential Equations. Chapter 2: Looking at Linear First Order Differential Equations. Chapter 3: Sorting Out Separable First Order Differential Equations. Chapter 4: Exploring Exact First Order Differential Equations and Euler’s Method. Part II: Surveying Second and Higher Order Differential Equations. Chapter 5: Examining Second Order Linear Homogeneous Differential Equations. Chapter 6: Studying Second Order Linear Nonhomogeneous Differential Equations. Chapter 7: Handling Higher Order Linear Homogeneous Differential Equations. Chapter 8: Taking On Higher Order Linear Nonhomogeneous Differential Equations. Part III: The Power Stuff: Advanced Techniques. Chapter 9: Getting Serious with Power Series and Ordinary Points. Chapter 10: Powering through Singular Points. Chapter 11: Working with Laplace Transforms. Chapter 12: Tackling Systems of First Order Linear Differential Equations. Chapter 13: Discovering Three Fail-Proof Numerical Methods. Part IV: The Part of Tens. Chapter 14: Ten Super-Helpful Online Differential Equation Tutorials. Chapter 15: Ten Really Cool Online Differential Equation Solving Tools. Index.
£16.14
Dover Publications Inc. Partial Differential Equations with Fourier
Book Synopsis
£43.59
Springer International Publishing AG Model Order Reduction and Applications: Cetraro,
Book SynopsisThis 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.Consisting 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.The book is addressed to graduate students, young researchers and people interested in the field. It is a good companion for graduate/doctoral classes.Table of Contents- 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.
£47.49
Elsevier - Health Sciences Division Advanced Mathematics for Engineering Students
Book SynopsisTrade Review"Overall, the reviewer considers this text to offer a good and useful coverage of advanced mathematics for engineers. It gives useful and succinct coverage of the topics included." --IEEE PulseTable of Contents1. Prologue 2. Ordinary Differential Equations 3. Laplace and Fourier Transform Methods 4. Matrices and Linear Systems of Equations 5. Analytical Methods for Solving Partial Differential Equations 6.Difference Numerical Methods for Differential Equations 7. Finite Element Technique 8. Treatment of Experimental Results 9. Numerical Analysis 10. Introduction to Complex Analysis 11. Nondimensionalisation 12. Nonlinear Differential Equations 13. Integral Equations 14. Calculus of Variations
£69.26
Pearson Education (US) Student Solutions Manual for Differential
Book SynopsisC. Henry Edwards is emeritus professor of mathematics at the University of Georgia. He earned his Ph.D. at the University of Tennessee in 1960, and recently retired after 40 years of classroom teaching (including calculus or differential equations almost every term) at the universities of Tennessee, Wisconsin, and Georgia, with a brief interlude at the Institute for Advanced Study (Princeton) as an Alfred P. Sloan Research Fellow. He has received numerous teaching awards, including the University of Georgia's honoratus medal in 1983 (for sustained excellence in honors teaching), its Josiah Meigs award in 1991 (the institution's highest award for teaching), and the 1997 statewide Georgia Regents award for research university faculty teaching excellence. His scholarly career has ranged from research and dissertation direction in topology to the history of mathematics to computing and technology in the teaching and applications of mathematics. In additioTable of ContentsTable of Contents First-Order Differential Equations 1.1 Differential Equations and Mathematical Models 1.2 Integrals as General and Particular Solutions 1.3 Slope Fields and Solution Curves 1.4 Separable Equations and Applications 1.5 Linear First-Order Equations 1.6 Substitution Methods and Exact Equations Mathematical Models and Numerical Methods 2.1 Population Models 2.2 Equilibrium Solutions and Stability 2.3 Acceleration–Velocity Models 2.4 Numerical Approximation: Euler's Method 2.5 A Closer Look at the Euler Method 2.6 The Runge–Kutta Method Linear Systems and Matrices 3.1 Introduction to Linear Systems 3.2 Matrices and Gaussian Elimination 3.3 Reduced Row-Echelon Matrices 3.4 Matrix Operations 3.5 Inverses of Matrices 3.6 Determinants 3.7 Linear Equations and Curve Fitting Vector Spaces 4.1 The Vector Space R3 4.2 The Vector Space Rn and Subspaces 4.3 Linear Combinations and Independence of Vectors 4.4 Bases and Dimension for Vector Spaces 4.5 Row and Column Spaces 4.6 Orthogonal Vectors in Rn 4.7 General Vector Spaces Higher-Order Linear Differential Equations 5.1 Introduction: Second-Order Linear Equations 5.2 General Solutions of Linear Equations 5.3 Homogeneous Equations with Constant Coefficients 5.4 Mechanical Vibrations 5.5 Nonhomogeneous Equations and Undetermined Coefficients 5.6 Forced Oscillations and Resonance Eigenvalues and Eigenvectors 6.1 Introduction to Eigenvalues 6.2 Diagonalization of Matrices 6.3 Applications Involving Powers of Matrices Linear Systems of Differential Equations 7.1 First-Order Systems and Applications 7.2 Matrices and Linear Systems 7.3 The Eigenvalue Method for Linear Systems 7.4 A Gallery of Solution Curves of Linear Systems 7.5 Second-Order Systems and Mechanical Applications 7.6 Multiple Eigenvalue Solutions 7.7 Numerical Methods for Systems Matrix Exponential Methods 8.1 Matrix Exponentials and Linear Systems 8.2 Nonhomogeneous Linear Systems 8.3 Spectral Decomposition Methods Nonlinear Systems and Phenomena 9.1 Stability and the Phase Plane 9.2 Linear and Almost Linear Systems 9.3 Ecological Models: Predators and Competitors 9.4 Nonlinear Mechanical Systems Laplace Transform Methods 10.1 Laplace Transforms and Inverse Transforms 10.2 Transformation of Initial Value Problems 10.3 Translation and Partial Fractions 10.4 Derivatives, Integrals, and Products of Transforms 10.5 Periodic and Piecewise Continuous Input Functions Power Series Methods 11.1 Introduction and Review of Power Series 11.2 Power Series Solutions 11.3 Frobenius Series Solutions 11.4 Bessel Functions Appendix A: Existence and Uniqueness of Solutions Appendix B: Theory of Determinants APPLICATION MODULES The modules listed below follow the indicated sections in the text. Most provide computing projects that illustrate the corresponding text sections. Many of these modules are enhanced by the supplementary material found at the new Expanded Applications website. 1.3 Computer-Generated Slope Fields and Solution Curves 1.4 The Logistic Equation 1.5 Indoor Temperature Oscillations 1.6 Computer Algebra Solutions 2.1 Logistic Modeling of Population Data 2.3 Rocket Propulsion 2.4 Implementing Euler's Method 2.5 Improved Euler Implementation 2.6 Runge-Kutta Implementation 3.2 Automated Row Operations 3.3 Automated Row Reduction 3.5 Automated Solution of Linear Systems 5.1 Plotting Second-Order Solution Families 5.2 Plotting Third-Order Solution Families 5.3 Approximate Solutions of Linear Equations 5.5 Automated Variation of Parameters 5.6 Forced Vibrations and Resonance 7.1 Gravitation and Kepler's Laws of Planetary Motion 7.3 Automatic Calculation of Eigenvalues and Eigenvectors 7.4 Dynamic Phase Plane Graphics 7.5 Earthquake-Induced Vibrations of Multistory Buildings 7.6 Defective Eigenvalues and Generalized Eigenvectors 7.7 Comets and Spacecraft 8.1 Automated Matrix Exponential Solutions 8.2 Automated Variation of Parameters 9.1 Phase Portraits and First-Order Equations 9.2 Phase Portraits of Almost Linear Systems 9.3 Your Own Wildlife Conservation Preserve 9.4 The Rayleigh and van der Pol Equations
£70.60
Pearson Education (US) Differential Equations Classic Version
Book SynopsisTable of ContentsChapter 1: Introduction to Differential Equations Differential Equation Models. The Derivative. Integration. Chapter 2: First-Order Equations Differential Equations and Solutions. Solutions to Separable Equations. Models of Motion. Linear Equations. Mixing Problems. Exact Differential Equations. Existence and Uniqueness of Solutions. Dependence of Solutions on Initial Conditions. Autonomous Equations and Stability. Project 2.10 The Daredevil Skydiver. Chapter 3: Modeling and Applications Modeling Population Growth. Models and the Real World. Personal Finance. Electrical Circuits. Project 3.5 The Spruce Budworm. Project 3.6 Social Security, Now or Later. Chapter 4: Second-Order Equations Definitions and Examples. Second-Order Equations and Systems. Linear, Homogeneous Equations with Constant Coefficients. Harmonic Motion. Inhomogeneous Equations; the Method of Undetermined Coefficients. Variation of Parameters. Forced Harmonic Motion. Project 4.8 Nonlinear Oscillators. Chapter 5: The Laplace Transform The Definition of the Laplace Transform. Basic Properties of the Laplace Transform 241. The Inverse Laplace Transform Using the Laplace Transform to Solve Differential Equations. Discontinuous Forcing Terms. The Delta Function. Convolutions. Summary. Project 5.9 Forced Harmonic Oscillators. Chapter 6: Numerical Methods Euler’s Method. Runge-Kutta Methods. Numerical Error Comparisons. Practical Use of Solvers. A Cautionary Tale. Project 6.6 Numerical Error Comparison. Chapter 7: Matrix Algebra Vectors and Matrices. Systems of Linear Equations with Two or Three Variables. Solving Systems of Equations. Homogeneous and Inhomogeneous Systems. Bases of a subspace. Square Matrices. Determinants. Chapter 8: An Introduction to Systems Definitions and Examples. Geometric Interpretation of Solutions. Qualitative Analysis. Linear Systems. Properties of Linear Systems. Project 8.6 Long-Term Behavior of Solutions. Chapter 9: Linear Systems with Constant Coefficients Overview of the Technique. Planar Systems. Phase Plane Portraits. The Trace-Determinant Plane. Higher Dimensional Systems. The Exponential of a Matrix. Qualitative Analysis of Linear Systems. Higher-Order Linear Equations. Inhomogeneous Linear Systems. Project 9.10 Phase Plane Portraits. Project 9.11 Oscillations of Linear Molecules. Chapter 10: Nonlinear Systems The Linearization of a Nonlinear System. Long-Term Behavior of Solutions. Invariant Sets and the Use of Nullclines. Long-Term Behavior of Solutions to Planar Systems. Conserved Quantities. Nonlinear Mechanics. The Method of Lyapunov. Predator—Prey Systems. Project 10.9 Human Immune Response to Infectious Disease. Project 10.10 Analysis of Competing Species. Chapter 11: Series Solutions to Differential Equations Review of Power Series. Series Solutions Near Ordinary Points. Legendre’s Equation. Types of Singular Points–Euler’s Equation. Series Solutions Near Regular Singular Points. Series Solutions Near Regular Singular Points – the General Case. Bessel’s Equation and Bessel Functions.
£114.10
Oxford University Press Mathematical Physics with Differential Equations
Book SynopsisThis 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.Table of ContentsPreface 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
£76.00
Oxford University Press Mathematical Physics with Differential Equations
Book SynopsisThis 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.Table of ContentsPreface 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
£38.00
Clarendon Press P And HP Finite Element Methods Theory and Applications to Solid and Fluid Mechanics Numerical Mathematics and Scientific Computation
Book SynopsisThis title is an introduction to the mathematical analysis of p- and hp-finite elements applied to elliptic problems in solid and fluid mechanics, and is suitable for graduate students and researchers who have had some prior exposure to finite element methods (FEM).Trade Review'Summarizing the book is the first theoretical book addressing the hp-version of the finite element method which is used today in practical computations. It is very well written and gives a very good review of the techniques and results in this relatively new direction in the FEM. It is highly recommended to anybody with mathematical interest for both learning and reference' ZAMMTable of ContentsVariational formulation of boundary value problems ; The Finite Element Method (FEM): definition, basic properties ; hp- Finite Elements in one dimension ; hp- Finite Elements in two dimensions ; Finite Element analysis of saddle point problems, mixed hp-FEM in incompressible fluid flow ; hp-FEM in the theory of elasticity
£153.00
Oxford University Press Hyperbolic Systems of Conservation Laws
Book SynopsisThis book provides a self-contained introduction to the mathematical theory of hyperbolic systems of conservation laws, with particular emphasis on the study of discontinuous solutions, characterized by the appearance of shock waves. This area has experienced substantial progress in very recent years thanks to the introduction of new techniques, in particular the front tracking algorithm and the semigroup approach. These techniques provide a solution to the long standing open problems of uniqueness and stability of entropy weak solutions. This monograph is the first to present a comprehensive account of these new, fundamental advances, mainly obtained by the author together with several collaborators. It also includes a detailed analysis of the stability and convergence of the front tracking algorithm. The book is addressed to graduate students as well as researchers. Both the elementary and the more advanced material are carefully explained, helping the reader''s visual intuition withTrade ReviewAn excellent and self-contained treatment of the mathematical theory of hyperbolic systems of conservation laws ... written in a clear and self-contained way and will be of great value for graduate students and specialists in the field. * EMS *
£132.75
Oxford University Press, USA Introduction to the Mathematical Theory of Compressible Flow 27 Oxford Lecture Series in Mathematics and Its Applications
Book SynopsisThis book provides a rapid introduction to the mathematical theory of compressible flow, giving a comprehensive account of the field and all important results up to the present day. The book is written in a clear, instructive and self-contained manner and will be accessible to a wide audience.Table of Contents1. Fundamental concepts and equations ; 2. Theoretical results for the Euler equations ; 3. Some mathematical tools for compressible flows ; 4. Weak solutions for steady compressible Navier-Stokes equations in barotropic regime ; 5. Strong solutions for steady compressible Navier-Stokes equations and small data ; 6. Some mathematical tools for non-steady equations ; 7. Weak solutions for non-stationary compressible Navier-Stokes equations ; 8. Global behavior of weak solutions ; 9. Strong solutions of non-steady compressible Navier-Stokes equations
£146.25
Oxford University Press, USA An Introduction to Homogenization 17 Oxford Lecture Series in Mathematics and Its Applications
Book SynopsisThe theory of homogenization replaces a real composite material with an imaginary homogeneous one, to describe the macroscopic properties of the composite using the properties of the microscopic structure. This work illustrates the relevant mathematics, logic and methodology with examples.Trade Review'serve as good textbook for a post-graduate course' ZAMMTable of Contents1. Weak and weak - convergence in Banach spaces ; 2. Rapidly oscillating periodic functions ; 3. Some classes of Sobolev spaces ; 4. Some variational elliptic problems ; 5. Examples of periodic composite materials ; 6. Homogenization of elliptic equations: the convergence result ; 7. The multiple-scale method ; 8. Tartar's method of oscillating test functions ; 9. The two-scale convergence method ; 10. Homogenization in linearized elasticity ; 11. Homogenization of the heat equation ; 12. Homogenization of the wave equation ; 13. General Approaches to the non-periodic case ; References
£139.50
Clarendon Press Heuns Differential Equations
Book SynopsisHeun''s equation is a second-order differential equation which crops up in a variety of forms in a wide range of problems in applied mathematics. These include integral equations of potential theory, wave propogation, electrostatic oscillation, and Schrodinger''s equation. This volume brings together important research work for the first time, providing an important resource for all those interested in this mathematical topic. Both the current theory and the main areas of application are surveyed, and includes contributions from authoritative researchers such as Felix Arscott (Canada), P. Maroni (France), and Gerhard Wolf (Germany).Trade ReviewThere is a wealth of important results and open problems and the book is a welcome addition to the literature on these important special functions and their applications. * B D Sleeman, Zbl. Math. 847/96. *Table of ContentsA. HEUN'S EQUATION ; I: GENERAL AND POWER SERIES ; II: HYPERGEOMETRIC FUNCTION SERIES ; B. CONFLUENT HEUN EQUATION ; C. DOUBLE CONFLUENT HEUN EQUATION ; D. BICONFLUENT HEUN EQUATION ; E. TRICONFLUENT HEUN EQUATION
£146.25
Oxford University Press Solitons Instantons and Twistors
Book SynopsisMost nonlinear differential equations arising in natural sciences admit chaotic behaviour and cannot be solved analytically. Integrable systems lie on the other extreme. They possess regular, stable, and well-behaved solutions known as solitons and instantons. These solutions play important roles in pure and applied mathematics as well as in theoretical physics where they describe configurations topologically different from vacuum. While integrable equations in lower space-time dimensions can be solved using the inverse scattering transform, the higher-dimensional examples of anti-self-dual Yang-Mills and Einstein equations require twistor theory. Both techniques rely on an ability to represent nonlinear equations as compatibility conditions for overdetermined systems of linear differential equations.The book provides a self-contained and accessible introduction to the subject. It starts with an introduction to integrability of ordinary and partial differential equations. Subsequent ch
£90.00
Oxford University Press Solitons Instantons and Twistors
Book Synopsis
£42.75
Oxford University Press, USA Smoothing and Decay Estimates for Nonlinear Diffusion Equations
Book SynopsisThis text is concerned with the quantitative aspects of the theory of nonlinear diffusion equations; equations which can be seen as nonlinear variations of the classical heat equation. They appear as mathematical models in different branches of Physics, Chemistry, Biology, and Engineering, and are also relevant in differential geometry and relativistic physics. Much of the modern theory of such equations is based on estimates and functional analysis.Concentrating on a class of equations with nonlinearities of power type that lead to degenerate or singular parabolicity (equations of porous medium type), the aim of this text is to obtain sharp a priori estimates and decay rates for general classes of solutions in terms of estimates of particular problems. These estimates are the building blocks in understanding the qualitative theory, and the decay rates pave the way to the fine study of asymptotics. Many technically relevant questions are presented and analyzed in detail. A systematic pTrade ReviewThis book is intended to introduce graduate students to the methods and results of nonlinear diffusion equations of porous medium type, as practised today. The present text, remarkable for generality and depth, is also notable for its author's concern, throughout, to keep the important issues about varieties clearly in the foreground ... [the book] succeeds admirably, in the reviewer's opinion, in introducing its difficult subject at a level appropriate for preparing future workers in the field. * Vicentiu Radulescu, Mathematical Reviews Issue 2007k *Table of ContentsPART I; PART II; PART III
£108.00
Oxford University Press A Posteriori Error Estimation Techniques for Finite Element Methods
Book SynopsisSelf-adaptive discretization methods are now an indispensable tool for the numerical solution of partial differential equations that arise from physical and technical applications. The aim is to obtain a numerical solution within a prescribed tolerance using a minimal amount of work. The main tools in achieving this goal are a posteriori error estimates which give global and local information on the error of the numerical solution and which can easily be computed from the given numerical solution and the data of the differential equation. This book reviews the most frequently used a posteriori error estimation techniques and applies them to a broad class of linear and nonlinear elliptic and parabolic equations. Although there are various approaches to adaptivity and a posteriori error estimation, they are all based on a few common principles. The main aim of the book is to elaborate these basic principles and to give guidelines for developing adaptive schemes for new problems. ChaptersTrade ReviewError control and adaptive solution algorithms for finite element approximation are a key concern of every practitioner. The present text, written by a leading authority in the field who has made many important contributions, will be valuable for theoreticians and practitioners alike. * Mark Ainsworth, Professor of Applied Mathematics, Brown University *Table of Contents1. A Simple Model Problem ; 2. Implementation ; 3. Auxiliary Results ; 4. Linear Elliptic Equations ; 5. Nonlinear Elliptic Equations ; 6. Parabolic Equations
£160.92
The University of Chicago Press Exterior Differential Systems and EulerLagrange
Book SynopsisThis study presents the results of the authors' development of a theory of the geometry of differential equations, focusing especially on Lagrangians and Poincare-Cartan forms.
£76.00
The University of Chicago Press Exterior Differential Systems and EulerLagrange
Book SynopsisThis study presents the results of the authors' development of a theory of the geometry of differential equations, focusing especially on Lagrangians and Poincare-Cartan forms.
£24.70
The University of Chicago Press Dimension Theory in Dynamical Systems
Book SynopsisThe principles of symmetry and self-symmetry are expressed in fractals, the subject of study in dimension theory. This book introduces an area of research which has recently appeared in the interface between dimension theory and the theory of dynamical systems, focusing on invariant fractals.
£30.40
Pearson Education (US) Student Solutions Manual for Differential
Book SynopsisC. Henry Edwards is emeritus professor of mathematics at the University of Georgia. He earned his Ph.D. at the University of Tennessee in 1960, and retired after 40 years of classroom teaching (including calculus or differential equations almost every term) at the universities of Tennessee, Wisconsin, and Georgia, with a brief interlude at the Institute for Advanced Study (Princeton) as an Alfred P. Sloan Research Fellow. He has received numerous teaching awards, including the University of Georgia's honoratus medal in 1983 (for sustained excellence in honors teaching), its Josiah Meigs award in 1991 (the institution's highest award for teaching), and the 1997 statewide Georgia Regents award for research university faculty teaching excellence. His scholarly career has ranged from research and dissertation direction in topology to the history of mathematics to computing and technology in the teaching and applications of mathematics. In addition to beinTable of Contents1. First-Order Differential Equations 1.1 Differential Equations and Mathematical Models 1.2 Integrals as General and Particular Solutions 1.3 Slope Fields and Solution Curves 1.4 Separable Equations and Applications 1.5 Linear First-Order Equations 1.6 Substitution Methods and Exact Equations 2. Mathematical Models and Numerical Methods 2.1 Population Models 2.2 Equilibrium Solutions and Stability 2.3 Acceleration—Velocity Models 2.4 Numerical Approximation: Euler’s Method 2.5 A Closer Look at the Euler Method 2.6 The Runge—Kutta Method 3. Linear Equations of Higher Order 3.1 Introduction: Second-Order Linear Equations 3.2 General Solutions of Linear Equations 3.3 Homogeneous Equations with Constant Coefficients 3.4 Mechanical Vibrations 3.5 Nonhomogeneous Equations and Undetermined Coefficients 3.6 Forced Oscillations and Resonance 3.7 Electrical Circuits 3.8 Endpoint Problems and Eigenvalues 4. Introduction to Systems of Differential Equations 4.1 First-Order Systems and Applications 4.2 The Method of Elimination 4.3 Numerical Methods for Systems 5. Linear Systems of Differential Equations 5.1 Matrices and Linear Systems 5.2 The Eigenvalue Method for Homogeneous Systems 5.3 A Gallery of Solution Curves of Linear Systems 5.4 Second-Order Systems and Mechanical Applications 5.5 Multiple Eigenvalue Solutions 5.6 Matrix Exponentials and Linear Systems 5.7 Nonhomogeneous Linear Systems 6. Nonlinear Systems and Phenomena 6.1 Stability and the Phase Plane 6.2 Linear and Almost Linear Systems 6.3 Ecological Models: Predators and Competitors 6.4 Nonlinear Mechanical Systems 6.5 Chaos in Dynamical Systems 7. Laplace Transform Methods 7.1 Laplace Transforms and Inverse Transforms 7.2 Transformation of Initial Value Problems 7.3 Translation and Partial Fractions 7.4 Derivatives, Integrals, and Products of Transforms 7.5 Periodic and Piecewise Continuous Input Functions 7.6 Impulses and Delta Functions
£65.32
Pearson Education (US) Fundamentals of Differential Equations
Book Synopsis R. Kent Nagle (deceased) taught at the University of South Florida. He was a research mathematician and an accomplished author. His legacy is honored in part by the Nagle Lecture Series which promotes mathematics education and the impact of mathematics on society. He was a member of the American Mathematical Society for 21 years. Throughout his life, he imparted his love for mathematics to everyone, from students to colleagues. Edward B. Saff received his B.S. in applied mathematics from Georgia Institute of Technology and his Ph.D. in Mathematics from the University of Maryland. After his tenure as Distinguished Research Professor at the University of South Florida, he joined the Vanderbilt University Mathematics Department faculty in 2001 as Professor and Director of the Center for Constructive ApproTable of Contents1. Introduction 1.1 Background 1.2 Solutions and Initial Value Problems 1.3 Direction Fields 1.4 The Approximation Method of Euler 2. First-Order Differential Equations 2.1 Introduction: Motion of a Falling Body 2.2 Separable Equations 2.3 Linear Equations 2.4 Exact Equations 2.5 Special Integrating Factors 2.6 Substitutions and Transformations 3. Mathematical Models and Numerical Methods Involving First Order Equations 3.1 Mathematical Modeling 3.2 Compartmental Analysis 3.3 Heating and Cooling of Buildings 3.4 Newtonian Mechanics 3.5 Electrical Circuits 3.6 Improved Euler's Method 3.7 Higher-Order Numerical Methods: Taylor and Runge-Kutta 4. Linear Second-Order Equations 4.1 Introduction: The Mass-Spring Oscillator 4.2 Homogeneous Linear Equations: The General Solution 4.3 Auxiliary Equations with Complex Roots 4.4 Nonhomogeneous Equations: The Method of Undetermined Coefficients 4.5 The Superposition Principle and Undetermined Coefficients Revisited 4.6 Variation of Parameters 4.7 Variable-Coefficient Equations 4.8 Qualitative Considerations for Variable-Coefficient and Nonlinear Equations 4.9 A Closer Look at Free Mechanical Vibrations 4.10 A Closer Look at Forced Mechanical Vibrations 5. Introduction to Systems and Phase Plane Analysis 5.1 Interconnected Fluid Tanks 5.2 Elimination Method for Systems with Constant Coefficients 5.3 Solving Systems and Higher-Order Equations Numerically 5.4 Introduction to the Phase Plane 5.5 Applications to Biomathematics: Epidemic and Tumor Growth Models 5.6 Coupled Mass-Spring Systems 5.7 Electrical Systems 5.8 Dynamical Systems, Poincaré Maps, and Chaos 6. Theory of Higher-Order Linear Differential Equations 6.1 Basic Theory of Linear Differential Equations 6.2 Homogeneous Linear Equations with Constant Coefficients 6.3 Undetermined Coefficients and the Annihilator Method 6.4 Method of Variation of Parameters 7. Laplace Transforms 7.1 Introduction: A Mixing Problem 7.2 Definition of the Laplace Transform 7.3 Properties of the Laplace Transform 7.4 Inverse Laplace Transform 7.5 Solving Initial Value Problems 7.6 Transforms of Discontinuous Functions 7.7 Transforms of Periodic and Power Functions 7.8 Convolution 7.9 Impulses and the Dirac Delta Function 7.10 Solving Linear Systems with Laplace Transforms 8. Series Solutions of Differential Equations 8.1 Introduction: The Taylor Polynomial Approximation 8.2 Power Series and Analytic Functions 8.3 Power Series Solutions to Linear Differential Equations 8.4 Equations with Analytic Coefficients 8.5 Cauchy-Euler (Equidimensional) Equations 8.6 Method of Frobenius 8.7 Finding a Second Linearly Independent Solution 8.8 Special Functions 9. Matrix Methods for Linear Systems 9.1 Introduction 9.2 Review 1: Linear Algebraic Equations 9.3 Review 2: Matrices and Vectors 9.4 Linear Systems in Normal Form 9.5 Homogeneous Linear Systems with Constant Coefficients 9.6 Complex Eigenvalues 9.7 Nonhomogeneous Linear Systems 9.8 The Matrix Exponential Function 10. Partial Differential Equations 10.1 Introduction: A Model for Heat Flow 10.2 Method of Separation of Variables 10.3 Fourier Series 10.4 Fourier Cosine and Sine Series 10.5 The Heat Equation 10.6 The Wave Equation 10.7 Laplace's Equation Appendix A. Newton's Method Appendix B. Simpson's Rule Appendix C. Cramer's Rule Appendix D. Method of Least Squares Appendix E. Runge-Kutta Procedure for n Equations
£173.56
Cengage Learning A First Course in Differential Equations with
Book Synopsis
£255.07
Taylor & Francis Ltd Student Solutions Manual for Non Linear Dynamics
Book SynopsisThis officialStudent Solutions Manualincludes solutions to the odd-numbered exercises featured in thethird edition of Steven Strogatz''s classic text Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering. The textbook and accompanyingStudent Solutions Manualare aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. Complete with graphs and worked-out solutions, this manual demonstrates techniques for students to analyze differential equations, bifurcations, chaos, fractals, and other subjects Strogatz explores in his popular book.
£26.59
Springer Functional Equations and How to Solve Them
Book SynopsisAn historical introduction.- Functional equations with two variables.- Functional equations with one variable.- Miscellaneous methods for functional equations.- Some closing heuristics.- Appendix: Hamel bases.- Hints and partial solutions to problems.Trade ReviewFrom the reviews: "This book is devoted to functional equations of a special type, namely to those appearing in competitions … . The book contains many solved examples and problems at the end of each chapter. … The book has 130 pages, 5 chapters and an appendix, a Hints/Solutions section, a short bibliography and an index. … The book will be valuable for instructors working with young gifted students in problem solving seminars." (EMS Newsletter, June, 2008)Table of ContentsAn historical introduction.- Functional equations with two variables.- Functional equations with one variable.- Miscellaneous methods for functional equations.- Some closing heuristics.- Appendix: Hamel bases.- Hints and partial solutions to problems.
£52.24
Springer-Verlag New York Inc. Nodal Discontinuous Galerkin Methods
Book SynopsisThis book offers an introduction to the key ideas, basic analysis, and efficient implementation of discontinuous Galerkin finite element methods (DG-FEM) for the solution of partial differential equations.Trade ReviewFrom the reviews: "This book provides comprehensive coverage of the major aspects of the DG-FEM, from derivation, analysis and implementation of the method to simulation of application problems. It is a highly valuable volume in the literature on the DG-FEM. It is also suitable as a textbook for a graduate-level course for students in computational and applied mathematics, physics and engineering." -Mathematical Reviews "The book under review presents basic ideas, theoretical analysis, MATLAB implementation and applications of the DG-FEM. … The representative references quoted are useful for any reader interested in applying the method in a particular area. … This book provides comprehensive coverage of the major aspects of the DG-FEM … . It is a highly valuable volume in the literature on the DG-FEM. It is also suitable as a textbook for a graduate-level course for students in computational and applied mathematics, physics, and engineering." (Weimin Han, Mathematical Reviews, Issue 2008 k) "This book is intended to offer a comprehensive introduction to, and an efficient implementation of discontinuous Galerkin finite element methods … . Each chapter of the book is largely self-contained and is complemented by adequate exercises. … The style of writing is clear and concise … . is an exceptionally complete and accessible reference for graduate students, researchers, and professionals in applied mathematics, physics, and engineering. It may be used in graduate-level courses, as a self-study resource, or as a research reference." (Marius Ghergu, Zentralblatt MATH, Vol. 1134 (12), 2008)Table of ContentsThe key ideas.- Making it work in one dimension.- Insight through theory.- Nonlinear problems.- Beyond one dimension.- Higher-order equations.- Spectral properties of discontinuous Galerkin operators.- Curvilinear elements and nonconforming discretizations.- Into the third dimension.
£71.99
Springer New York Distributions and Operators
Book SynopsisThis book gives an introduction to distribution theory, based on the work of Schwartz and of many other people. It is the first book to present distribution theory as a standard text. Each chapter has been enhanced with many exercises and examples.Trade ReviewFrom the reviews:"The book is directed at graduate students and ‘researchers interested in its special topics’ … . Distribution and Operators is split into five parts … . Well-written and scholarly, and equipped with many exercises of considerable pedagogical importance … Grubb’s book is a fine contribution to the literature and should soon occupy a solid place among graduate texts for aspiring hard analysts specializing, e.g., in PDE." (Michael Berg, MAA Online, December, 2008)“This textbook gives a very clear introduction to distribution theory with emphasis on applications using functional analysis. In more advanced parts of the book, pseudodifferential methods are introduced, specially tailored for the study of boundary value problems. … The whole book is carefully and nicely written and each chapter ends with a number of exercises … . perfect for a Ph.D. course … . most of the material has been used frequently at the University of Copenhagen for several graduate courses.” (Fabio Nicola, Mathematical Reviews, Issue 2010 b)“The book under review is a complete self-contained introduction to classical distribution theory with applications to the study of linear partial differential operators and, in particular, of (elliptic) boundary value problems, an area where the author has much experience … . very clear and precise. Almost all the results given in the book are proved, and the proofs give plenty of details and are easy to follow. There are a lot of examples and exercises … .” (David Jornet, Zentralblatt MATH, Vol. 1171, 2009)Table of ContentsDistributions and derivatives.- Motivation and overview.- Function spaces and approximation.- Distributions. Examples and rules of calculus.- Extensions and applications.- Realizations and Sobolev spaces.- Fourier transformation of distributions.- Applications to differential operators. The Sobolev theorem.- Pseudodifferential operators.- Pseudodifferential operators on open sets.- Pseudodifferential operators on manifolds, index of elliptic operators.- Boundary value problems.- Boundary value problems in a constant-coefficient case.- Pseudodifferential boundary operators.- Pseudodifferential methods for boundary value problems.- Topics on Hilbert space operators.- Unbounded linear operators.- Families of extensions.- Semigroups of operators.
£79.99
Copernicus Hilbert Diseases
Book SynopsisI Youth.- II Friends and Teachers.- III Doctor of Philosophy.- IV Paris.- V Gordan's Problem.- VI Changes.- VII Only Number Fields.- VIII Tables, Chairs, and Beer Mugs.- IX Problems.- X The Future of Mathematics.- XI The New Century.- XII Second Youth.- XIII The Passionate Scientific Life.- XIV Space, Time and Number.- XV Friends and Students.- XVI Physics.- XVII War.- XVIII The Foundations of Mathematics.- XIX The New Order.- XX The Infinite!.- XXI Borrowed Time.- XXII Logic and the Understanding of Nature.- XXIII Exodus.- XXIV Age.- XXV The Last Word.Trade ReviewFrom the reviews: THE BULLETIN OF MATHEMATICS BOOKS "Originally published to great acclaim, both books explore the dramatic scientific history expressed in the lives of these two great scientists and described in the lively, nontechnical writing style of Constance Reid."Table of ContentsI Youth.- II Friends and Teachers.- III Doctor of Philosophy.- IV Paris.- V Gordan’s Problem.- VI Changes.- VII Only Number Fields.- VIII Tables, Chairs, and Beer Mugs.- IX Problems.- X The Future of Mathematics.- XI The New Century.- XII Second Youth.- XIII The Passionate Scientific Life.- XIV Space, Time and Number.- XV Friends and Students.- XVI Physics.- XVII War.- XVIII The Foundations of Mathematics.- XIX The New Order.- XX The Infinite!.- XXI Borrowed Time.- XXII Logic and the Understanding of Nature.- XXIII Exodus.- XXIV Age.- XXV The Last Word.
£28.49
Taylor & Francis Ltd Dichotomies and Stability in Nonautonomous Linear
Book SynopsisLinear non-autonomous equations arise as mathematical models in mechanics, chemistry, and biology. This book explores the preservation of invariant tori of dynamic systems under perturbation. It is a useful contribution to the literature on stability theory and provides a source of reference for postgraduates and researchers.Trade Review"This volume will be of great interest to researchers and students dealing with nonautonomous systems." - Zentralblatt fur Mathematik, Vol. 1026Table of ContentsExponentially Dichotomous Linear Systems of Differential Equations and Lyapunov Functions of Variable Sign. Exponential Dichotomy Criterion for Linear Systems in Terms of Quadratic Forms. Decomposition Over the Whole R Axis of Linear Systems of Differential Equations Exponentially Dichotomous on Semiaxes R+ and R_. Degeneracy of the Quadratic Form Possessing a Definite-Sign Derivative Along the Solutions of the System (1.1.1). Integral Representation of Weakly Regular Systems Bounded on the Whole R Axis. Complement to the Exponentially Dichotomous of Weakly Regular on R Linear Systems. Regularity of Linear Systems of the Block-Triangular Form. Perturbation of the Block-Triangular Form Linear Systems which are Regular and Weakly Regular on the Whole R Axis. Exponentially Dichotomous Linear Systems with Parameters. Comments and References. Linear Extension of Dynamical Systems on a Torus. Necessary Existence Conditions for Invariant Tori. The Green Function. Sufficient Existence Conditions for an Invariant Torus. Existence Conditions for an Exponentially Stable Invariant Torus. Uniqueness Conditions for the Green Function and its Properties. Sufficient Conditions for Exponential Dichotomy of the Invariant Torus. Necessary Conditions for Exponential Dichotomy of the Invariant Torus. Existence Criterion for the Green Function. The Non-Unique Green Function and the Properties of the System Implied by its Existence. Invariant Tori of Linear Extensions with Slowly Changing Phase. Preserving the Green Function Under Small Perturbations of Linear Expansions on a Torus. On the Smoothness of an Exponentially Stable Invariant Torus. On the Dependence of Green Functions on Parameters. Continuity and Differentiability of the Green Function. Invariant Tori of Linear Extensions with a Degenerate Matrix at the Derivatives. Bounded Invariant Manifolds of Dynamical Systems and their Smoothness. Comments and References. Splitability of Linear Extensions of Dynamical Systems on a Torus. Sufficient Conditions for Splitability of Linear Extensions of Dynamical Systems on a Torus. Reversibility of the Theorem on Splitability. On Triangulation and the Relationship of C'-Block Splitability of a Linear System with the Problem on r-frame Complementability up to the Periodic Basis in R^Tn. Reducing on Linearized Systems to a Diagonal Form. On the Relationship of Exponentially Dichotomous Linear Expansions with the Algebraic System Solvability. Three Block Divisibility of Linear Extensions and Lyapunov Functions of Variable Sign. Algebraic Problems of the K-Blocked Divisibility of Linear Extensions on a Torus. Comments and References. Problems of Perturbation Theory of Smooth Invariant Tori of Dynamical Systems. Solution Variations on the Manifold M. Exponential Stability and Dichotomy Conditions for Linear Extensions of Dynamical Systems on a Torus. Roughness Conditions for the Green Function of the Linear Extension of a Dynamical System on a Torus with the Index of Smoothness. A Theorem of Perturbation Theory of an Invariant Torus of a Dynamical System. Green Function for a Linear Matrix Equation. On the Problem of Structure of Some Regular Linear Extensions of Dynamical Systems on a Torus. Invariant Manifolds of Autonomous Differential Equations and Lyapunov Functions with Alternating Signs. Comments and References. Index.
£209.00
Taylor & Francis Ltd Stability and Stabilization of Nonlinear Systems
Book SynopsisNonlinear systems with random structures arise quite frequently as mathematical models in diverse disciplines. This monograph presents a systematic treatment of stability theory and the theory of stabilization of nonlinear systems with random structure in terms of new developments in the direct Lyapunov's method. The analysis focuses on dynamic systems with random Markov parameters. This high-level research text is recommended for all those researching or studying in the fields of applied mathematics, applied engineering, and physics-particularly in the areas of stochastic differential equations, dynamical systems, stability, and control theory.Trade Review"This volume will be of interest to researchers and students in stochastic stability theory." - Zentralblatt fur Mathematik, Vol. 1026Table of ContentsIntroductory Remarks. Random Variables and Probability Distributions. Probability Processes and their Mathematical Description. Random Differential Equations. System with Random Structure. Stability Analysis Using Scalar Lyapunov Functions. Stability Concepts for Stochastic Systems. Random Scalar Lyapunov Functions. Conditions of Stability in Probability. Converse Theorems. Stability in Mean Square. Stability in Mean Square of Linear Systems. Stability Analysis Using Multi-component Lyapunov Functions. Vector Lyapunov Functions. Stochastic Matrix-Valued Lyapunov Functions. Stability Analysis in General. Stability Analysis of Systems in Ito's Form. Stochastic Singularly Perturbed Systems. Large-Scale Singularly Perturbed Systems. Stability Analysis by the First-Order Approximation. Stability Criterion by the First-Order Approximation. Stability with Respect to the First-Order Approximation. Stability by First-Order Approximation of Systems with Random Delay. Convergence of Stochastic Approximation Procedure. Stabilization of Controlled Systems with Random Structure. Problems of Stabilization. Optimal Stabilization. Linear-Quadratic Optimal Stabilization. Sufficient Stabilization Conditions for Linear Systems. Optimal Solution Existence. The Small Parameter Method Algorithm. Applications. A Stochastic Version of the Lefschetz Problem. Stability in Probability of Oscillating Systems. Stability in Probability of Regulation Systems. Price Stability in a Stochastic Market Model. References. Index. Lyapunov Functions. Stability Analysis Using Multicomponent Lyapunov Functions. Stability Analysis by the First-order Approximation. Stabilization of Controlled Systems with Random Structure. Applications; References; Index.
£199.50
Taylor & Francis Ltd Quantization Methods in the Theory of
Book SynopsisThis volume presents a systematic and mathematically rigorous exposition of methods for studying linear partial differential equations. It focuses on quantization of the corresponding objects (states, observables and canonical transformations) in the phase space. The quantization of all three types of classical objects is carried out in a unified way with the use of a special integral transform. This book covers recent as well as established results, treated within the framework of a universal approach. It also includes applications and provides a useful reference text for graduate and research-level readers.Table of ContentsSemiclassical Quantization. Quantization and Microlocalization. Quantization by the Wave Packet Transform. Maslov's Canonical Operator and Hormander's Oscillatory Integrals. Topological Aspects of Quantization Conditions. The Schrodinger Equation. The Maxwell Equations. Equations with Trapping Hamiltonians. Quantization by the Method of Ordered Operators (Noncommutative Analysis). Noncommutative Analysis: Main Ideas, Definitions, and Theorems. Exactly Soluble Commutation Relations. Operator Algebras on Singular Manifolds. The High-Frequency Asymptotics in the Problem of Wave Propagation in Plasma. Appendices.
£199.50
Taylor & Francis Ltd Stability Domains
Book SynopsisStability Domains is an up-to-date account of stability theory with particular emphasis on stability domains. Beyond the fundamental basis of the theory of dynamical systems, it includes recent developments in the classical Lyapunov stability concept, practical stabiliy properties, and a new Lyapunov methodology for nonlinear systems. It also introduces classical Lyapunov and practical stability theory for time-invariant nonlinear systems in general and for complex (interconnected, large scale) nonlinear dynamical systems in particular. This is a complete treatment of the theory of stability domains useful for postgraduates and researchers working in this area of applied mathematics and engineering.Table of ContentsStability Domains is an up-to-date account of stability theory with particular emphasis on stability domains. Beyond the fundamental basis of the theory of dynamical systems, it includes a recent developments in the classical Lyapunov stability concept, practical stabiliy properties, and new Lyapunov methodology for nonlinear systems. It also introduces classical Lyapunov and practical stability theory for time-invariant nonlinear systems in general, and for complex (interconnected, large scale) nonlinear dynamical systems in particular. This is a complete treatment of the theory of stability domains useful for postgraduates and researchers working in this area of applied mathematics and engineering.
£142.50
Taylor & Francis Ltd Equations of Mathematical Diffraction Theory 06
Book SynopsisEquations of Mathematical Diffraction Theory focuses on the comparative analysis and development of efficient analytical methods for solving equations of mathematical diffraction theory. Following an overview of some general properties of integral and differential operators in the context of the linear theory of diffraction processes, the authors provide estimates of the operator norms for various ranges of the wave number variation, and then examine the spectral properties of these operators. They also present a new analytical method for constructing asymptotic solutions of boundary integral equations in mathematical diffraction theory for the high-frequency case.Clearly demonstrating the close connection between heuristic and rigorous methods in mathematical diffraction theory, this valuable book provides you with the differential and integral equations that can easily be used in practical applications.Table of ContentsSome Preliminaries from Analysis and the Theory of Wave Processes. Integral Equations of Diffraction Theory for Obstacles in Unbounded Medium. Wave Fields in a Layer of Constant Thickness. Analytical Methods for Simply Connected Bounded Domains. Integral Equations in Diffraction by Linear Obstacles. Short-Wave Asymptotic Methods on the Basis of Multiple Integrals. Inverse Problems of the Short-Wave Diffraction. Ill-Posed Equations of Inverse Diffraction Problems for Arbitrary Boundary. Numerical Methods for Irregular Operator Equations.
£147.25
Taylor & Francis Ltd Nonlinear Random Vibration
Book SynopsisThis second edition of the book, Nonlinear Random Vibration: Analytical Techniques and Applications, expands on the original edition with additional detailed steps in various places in the text. It is a first systematic presentation on the subject. Its features include:â a concise treatment of Markovian and non- Markovian solutions of nonlinear stochastic differential equations,â exact solutions of Fokker-Planck-Kolmogorov equations,â methods of statistical linearization,â statistical nonlinearization techniques,â methods of stochastic averaging,â truncated hierarchy techniques, andâ an appendix on probability theory.A special feature is its incorporation of detailed steps in many examples of engineering applications.Targeted audience: Graduates, research scientists and engineers in mechanical, aerospace, civil and environmental (earthquake, wind and transportation), automobile, naval, architectural, and mining engineering.Trade ReviewIn summary, the technical material in Prof. To’s 2012 second edition of Nonlinear Random Vibration: Analytical Techniques and Applications is well presented, of sufficient depth, detail, and quality, and supported by a good number of solved example problems.Robert M. KochNaval Undersea Warfare Center, Newport, RI, USAIn: Noise Control Engr. J. 61 (2), March-April 2013, pp 251-252Table of ContentsIntroduction. Markovian and Non-Markovian Solutions of Stochastic Nonlinear Differential Equations. Exact Solution of the Fokker-Planck-Kolmogorov Equation. Methods of Statistical Linearization. Statistical Nonlinearization Techniques. Methods of Stochastic Averaging. Truncated Hierarchy and other Techniques.
£137.75
Elsevier Science Data Analysis in Pavement Engineering
Book SynopsisTable of ContentsPreface Chapter 1 Pavement Performance Data Chapter 2 Fundamentals of statistics Chapter 3 Design of experiments Chapter 4 Regression Chapter 5 Logistic regression Chapter 6 Count data models Chapter 7 Survival analysis Chapter 8 Time series Chapter 9 Stochastic process Chapter 10 Decision trees and ensemble learning Chapter 11 Neural networks Chapter 12 Support vector machine and k-nearest neighbors Chapter 13 Principal component analysis Chapter 14 Factor analysis Chapter 15 Cluster analysis Chapter 16 Discriminant analysis Chapter 17 Structural equation model Chapter 18 Markov chain Monte Carlo
£127.80
