Calculus and mathematical analysis Books
Springer New York Introduction to Hyperbolic Geometry Universitext
Book SynopsisThis book is an introduction to hyperbolic and differential geometry that provides material in the early chapters that can serve as a textbook for a standard upper division course on hyperbolic geometry. The book goes well beyond the standard course in later chapters, and there is enough material for an honors course, or for supplementary reading.Trade Review"The book is well laid out with no shortage of diagrams and with each chapter prefaced with its own useful introduction...Also well written, it makes pleasurable reading." Proceedings of the Edinburgh Mathematical SocietyTable of ContentsPreface; Introduction; 1. Axioms for Plane Geometry; 2. Some Neutral Theorems of Plane Geometry; 3. Qualitative Description of the Hyperbolic Plane; 4. H3 and Euclidean Approximations in H2; 5. Differential Geometry of Surface; 6. Quantitative Considerations; 7. Consistency and Categoricalness of the Hyperbolic Axioms- the Classical Models; 8. Matrix Representation of the Isometry Group; 9. Differential and Hyperbolic Geometry in More Dimensions; 10. Connections with the Lorentz Group of Special Relativity; 11. Constructions by Straightedge and Compass in the Hyperbolic Plane; Index
£62.99
Springer Understanding Nonlinear Dynamics
a huge range and FREE tracked UK delivery on ALL orders.
£44.99
Springer New York An Introduction to InfiniteDimensional Linear Systems Theory
Book SynopsisInfinite dimensional systems is now an established area of research. Given the recent trend in systems theory and in applications towards a synthesis of time- and frequency-domain methods, there is a need for an introductory text which treats both state-space and frequency-domain aspects in an integrated fashion.Table of Contents1 Introduction.- 1.1 Motivation.- 1.2 Systems theory concepts in finite dimensions.- 1.3 Aims of this book.- 2 Semigroup Theory.- 2.1 Strongly continuous semigroups.- 2.2 Contraction and dual semigroups.- 2.3 Riesz-spectral operators.- 2.4 Delay equations.- 2.5 Invariant subspaces.- 2.6 Exercises.- 2.7 Notes and references.- 3 The Cauchy Problem.- 3.1 The abstract Cauchy problem.- 3.2 Perturbations and composite systems.- 3.3 Boundary control systems.- 3.4 Exercises.- 3.5 Notes and references.- 4 Inputs and Outputs.- 4.1 Controllability and observability.- 4.2 Tests for approximate controllability and observability.- 4.3 Input-output maps.- 4.4 Exercises.- 4.5 Notes and references.- 5 Stability, Stabilizability, and Detectability.- 5.1 Exponential stability.- 5.2 Exponential stabilizability and detectability.- 5.3 Compensator design.- 5.4 Exercises.- 5.5 Notes and references.- 6 Linear Quadratic Optimal Control.- 6.1 The problem on a finite-time interval.- 6.2 The problem on the infinite-time interval.- 6.3 Exercises.- 6.4 Notes and references.- 7 Frequency-Domain Descriptions.- 7.1 The Callier-Desoer class of scalar transfer functions.- 7.2 The multivariable extension.- 7.3 State-space interpretations.- 7.4 Exercises.- 7.5 Notes and references.- 8 Hankel Operators and the Nehari Problem.- 8.1 Frequency-domain formulation.- 8.2 Hankel operators in the time domain.- 8.3The Nehari extension problem for state linear systems.- 8.4 Exercises.- 8.5 Notes and references.- 9 Robust Finite-Dimensional Controller Synthesis.- 9.1 Closed-loop stability and coprime factorizations.- 9.2 Robust stabilization of uncertain systems.- 9.3 Robust stabilization under additive uncertainty.- 9.4 Robust stabilization under normalized left-coprime-factor uncertainty.- 9.5 Robustness in the presence of small delays.- 9.6 Exercises.- 9.7 Notes and references.- A. Mathematical Background.- A.1 Complex analysis.- A.2 Normed linear spaces.- A.2.1 General theory.- A.2.2 Hilbert spaces.- A.3 Operators on normed linear spaces.- A.3.1 General theory.- A.3.2 Operators on Hilbert spaces.- A.4 Spectral theory.- A.4.1 General spectral theory.- A.4.2 Spectral theory for compact normal operators.- A.5 Integration and differentiation theory.- A.5.1 Integration theory.- A.5.2 Differentiation theory.- A.6 Frequency-domain spaces.- A.6.1 Laplace and Fourier transforms.- A.6.2 Frequency-domain spaces.- A.6.3 The Hardy spaces.- A.7 Algebraic concepts.- A.7.1 General definitions.- A.7.2 Coprime factorizations over principal ideal domains.- A.7.3 Coprime factorizations over commutative integral domains.- References.- Notation.
£68.88
Springer Mathematical Analysis
Book Synopsis1 Real Numbers.- 1.1 Sets, Relations, Functions.- 1.2 Numbers.- 1.3 Infinite Sets.- 1.4 Incommensurability.- 1.5 Ordered Fields.- 1.6 Functions on R.- 1.7 Intervals in R.- 1.8 Algebraic and Transcendental Numbers.- 1.9 Existence of R.- 1.10 Exercises.- 1.11 Notes.- 2 Sequences and Series.- 2.1 Sequences.- 2.2 Continued Fractions.- 2.3 Infinite Series.- 2.4 Rearrangements of Series.- 2.5 Unordered Series.- 2.6 Exercises.- 2.7 Notes.- 3 Continuous Functions on Intervals.- 3.1 Limits and Continuity.- 3.2 Two Fundamental Theorems.- 3.3 Uniform Continuity.- 3.4 Sequences of Functions.- 3.5 The Exponential function.- 3.6 Trigonometric Functions.- 3.7 Exercises.- 3.8 Notes.- 4 Differentiation.- 4.1 Derivatives.- 4.2 Derivatives of Some Elementary Functions.- 4.3 Convex Functions.- 4.4 The Differential Calculus.- 4.5 L'Hospital's Rule.- 4.6 Higher Order Derivatives.- 4.7 Analytic Functions.- 4.8 Exercises.- 4.9 Notes.- 5 The Riemann Integral.- 5.1 Riemann Sums.- 5.2 Existence Results.- 5.3 ProTrade ReviewThis is a very good textbook presenting a modern course in analysis both at the advanced undergraduate and at the beginning graduate level. It contains 14 chapters, a bibliography, and an index. At the end of each chapter interesting exercises and historical notes are enclosed.\par From the cover: ``The book begins with a brief discussion of sets and mappings, describes the real number field, and proceeds to a treatment of real-valued functions of a real variable. Separate chapters are devoted to the ideas of convergent sequences and series, continuous functions, differentiation, and the Riemann integral (of a real-valued function defined on a compact interval). The middle chapters cover general topology and a miscellany of applications: the Weierstrass and Stone-Weierstrass approximation theorems, the existence of geodesics in compact metric spaces, elements of Fourier analysis, and the Weyl equidistribution theorem. Next comes a discussion of differentiation of vector-valued functions of several real variables, followed by a brief treatment of measure and integration (in a general setting, but with emphasis on Lebesgue theory in Euclidean spaces). The final part of the book deals with manifolds, differential forms, and Stokes' theorem [in the spirit of M. Spivak's: ``Calculus on manifolds'' (1965; Zbl 141.05403)] which is applied to prove Brouwer's fixed point theorem and to derive the basic properties of harmonic functions, such as the Dirichlet principle''. ZENTRALBLATT MATH A. Browder Mathematical Analysis An Introduction "Everything needed is clearly defined and formulated, and there is a reasonable number of examples…. Anyone teaching a year course at this level to should seriously consider this carefully written book. In the reviewer's opinion, it would be a real pleasure to use this text with such a class."—MATHEMATICAL REVIEWSTable of Contents1 Real Functions 2 Sequences and Series 3 Continuous Functions on Intervals 4 Differentiation 5 The Riemann Integral 6 Topology 7 Function Spaces 8 Differentiable Maps 9 Measures 10 Integration 11 Manifolds 12 Multilinear Algebra 13 Differential Forms 14 Integration on Manifolds
£44.99
Springer The Fundamental Theorem of Algebra
a huge range and FREE tracked UK delivery on ALL orders.
£66.49
Springer Animating Calculus Mathematica Notebooks for the Laboratory TELOS The Electronic Library of Science
a huge range and FREE tracked UK delivery on ALL orders.
£68.40
Springer Topics in Complex Analysis
a huge range and FREE tracked UK delivery on ALL orders.
£49.49
Copernicus How Nature Works
Book Synopsis1 Complexity and Criticality.- 2 The Discovery of Self-Organized Criticality.- 3 The Sandpile Paradigm.- 4 Real Sandpiles and Landscape Formation.- 5 Earthquakes, Starquakes, and Solar Flares.- 6 The Game of Life: Complexity Is Criticality.- 7 Is Life a Self-Organized Critical Phenomenon?.- 8 Mass Extinctions and Punctuated Equilibria in a Simple Model of Evolution.- 9 Theory of the Punctuated Equilibrium Model.- 10 The Brain.- 11 On Economics and Traffic Jams.Table of Contents1 Complexity and Criticality.- 2 The Discovery of Self-Organized Criticality.- 3 The Sandpile Paradigm.- 4 Real Sandpiles and Landscape Formation.- 5 Earthquakes, Starquakes, and Solar Flares.- 6 The “Game of Life”: Complexity Is Criticality.- 7 Is Life a Self-Organized Critical Phenomenon?.- 8 Mass Extinctions and Punctuated Equilibria in a Simple Model of Evolution.- 9 Theory of the Punctuated Equilibrium Model.- 10 The Brain.- 11 On Economics and Traffic Jams.
£35.99
Springer InfiniteDimensional Dynamical Systems in Mechanics and Physics
a huge range and FREE tracked UK delivery on ALL orders.
£104.49
Springer Discovering Curves and Surfaces with Maple
a huge range and FREE tracked UK delivery on ALL orders.
£54.99
Springer The LebesgueStieltjes Integral
a huge range and FREE tracked UK delivery on ALL orders.
£54.99
Springer-Verlag New York Inc. Iteration of Rational Functions
Book Synopsis1 Examples.- 1.1. Introduction.- 1.2. Iteration of Möbius Transformations.- 1.3. Iteration of z ? z2.- 1.4. Tchebychev Polynomials.- 1.5. Iteration of z ? z2 ? 1.- 1.6. Iteration of z ? z2 + c.- 1.7. Iteration of z ? z + 1/z.- 1.8. Iteration of z ? 2z ? 1/z.- 1.9. Newton's Approximation.- 1.10. General Remarks.- 2 Rational Maps.- 2.1. The Extended Complex Plane.- 2.2. Rational Maps.- 2.3. The Lipschitz Condition.- 2.4. Conjugacy.- 2.5. Valency.- 2.6. Fixed Points.- 2.7. Critical Points.- 2.8. A Topology on the Rational Functions.- 3 The Fatou and Julia Sets.- 3.1. The Fatou and Julia Sets.- 3.2. Completely Invariant Sets.- 3.3. Normal Families and Equicontinuity.- Appendix I. The Hyperbolic Metric.- 4 Properties of the Julia Set.- 4.1. Exceptional Points.- 4.2. Properties of the Julia Set.- 4.3. Rational Maps with Empty Fatou Set.- Appendix II. Elliptic Functions.- 5 The Structure of the Fatou Set.- 5.1. The Topology of the Sphere.- 5.2. Completely Invariant Components of the Fatou SetTrade ReviewA.F. Beardon Iteration of Rational Functions Complex Analytic Dynamical Systems "This book makes available a comprehensive, detailed, and organized treatment of the foundations of the theory of iteration of rational functions of a complex variable. The material covered extends from the original memoirs of Fatou and Julia to the recent and important results and methods of Sullivan and Shishikura. Many of the details of the proofs have not occurred in print before."—ZENTRALBLATT MATHTable of Contents1 Examples.- 1.1. Introduction.- 1.2. Iteration of Möbius Transformations.- 1.3. Iteration of z ? z2.- 1.4. Tchebychev Polynomials.- 1.5. Iteration of z ? z2 ? 1.- 1.6. Iteration of z ? z2 + c.- 1.7. Iteration of z ? z + 1/z.- 1.8. Iteration of z ? 2z ? 1/z.- 1.9. Newton’s Approximation.- 1.10. General Remarks.- 2 Rational Maps.- 2.1. The Extended Complex Plane.- 2.2. Rational Maps.- 2.3. The Lipschitz Condition.- 2.4. Conjugacy.- 2.5. Valency.- 2.6. Fixed Points.- 2.7. Critical Points.- 2.8. A Topology on the Rational Functions.- 3 The Fatou and Julia Sets.- 3.1. The Fatou and Julia Sets.- 3.2. Completely Invariant Sets.- 3.3. Normal Families and Equicontinuity.- Appendix I. The Hyperbolic Metric.- 4 Properties of the Julia Set.- 4.1. Exceptional Points.- 4.2. Properties of the Julia Set.- 4.3. Rational Maps with Empty Fatou Set.- Appendix II. Elliptic Functions.- 5 The Structure of the Fatou Set.- 5.1. The Topology of the Sphere.- 5.2. Completely Invariant Components of the Fatou Set.- 5.3. The Euler Characteristic.- 5.4. The Riemann-Hurwitz Formula for Covering Maps.- 5.5. Maps Between Components of the Fatou Set.- 5.6. The Number of Components of the Fatou Set.- 5.7. Components of the Julia Set.- 6 Periodic Points.- 6.1. The Classification of Periodic Points.- 6.2. The Existence of Periodic Points.- 6.3. (Super) Attracting Cycles.- 6.4. Repelling Cycles.- 6.5. Rationally Indifferent Cycles.- 6.6. Irrationally Indifferent Cycles in F.- 6.7. Irrationally Indifferent Cycles in J.- 6.8. The Proof of the Existence of Periodic Points.- 6.9. The Julia Set and Periodic Points.- 6.10. Local Conjugacy.- Appendix III. Infinite Products.- Appendix IV. The Universal Covering Surface.- 7 Forward Invariant Components.- 7.1. The Five Possibilities.- 7.2. Limit Functions.- 7.3. Parabolic Domains.- 7.4. Siegel Discs and Herman Rings.- 7.5. Connectivity of Invariant Components.- 8 The No Wandering Domains Theorem.- 8.1. The No Wandering Domains Theorem.- 8.2. A Preliminary Result.- 8.3. Conformal Structures.- 8.4. Quasiconformal Conjugates of Rational Maps.- 8.5. Boundary Values of Conjugate Maps.- 8.6. The Proof of Theorem 8.1.2.- 9 Critical Points.- 9.1. Introductory Remarks.- 9.2. The Normality of Inverse Maps.- 9.3. Critical Points and Periodic Domains.- 9.4. Applications.- 9.5. The Fatou Set of a Polynomial.- 9.6. The Number of Non-Repelling Cycles.- 9.7. Expanding Maps.- 9.8. Julia Sets as Cantor Sets.- 9.9. Julia Sets as Jordan Curves.- 9.10. The Mandelbrot Set.- 10 Hausdorff Dimension.- 10.1. Hausdorff Dimension.- 10.2. Computing Dimensions.- 10.3. The Dimension of Julia Sets.- 11 Examples.- 11.1. Smooth Julia Sets.- 11.2. Dendrites.- 11.3. Components of F of Infinite Connectivity.- 11.4. F with Infinitely Connected and Simply Connected Components.- 11.5. J with Infinitely Many Non-Degenerate Components.- 11.6. F of Infinite Connectivity with Critical Points in J.- 11.7. A Finitely Connected Component of F.- 11.8. J Is a Cantor Set of Circles.- 11.9. The Function (z ? 2)2/z2.- References.- Index of Examples.
£64.99
Springer New York Harmonic Function Theory
Book SynopsisBasic Properties of Harmonic Functions.- Bounded Harmonic Functions.- Positive Harmonic Functions.- The Kelvin Transform.- Harmonic Polynomials.- Harmonic Hardy Spaces.- Harmonic Functions on Half-Spaces.- Harmonic Bergman Spaces.- The Decomposition Theorem.- Annular Regions.- The Dirichlet Problem and Boundary Behavior.Trade ReviewFrom the reviews of the second edition: "There are several major changes in this second edition … . Many exercises have been added and several photographs of mathematicians related to harmonic functions are included. The book is a nice introduction to the fundamental notions of potential theory." (European Mathematical Society Newsletter, June, 2002) "We warmly recommend this textbook to graduate students interested in Harmonic Function Theory and/or related areas. We are sure that the reader will be able to appreciate the lively and illuminating discussions in this book, and therefore, will certainly gain a better understanding of the subject." (Ferenc Móricz, Acta Scientiarum Mathematicarum, Vol. 67, 2001) "This is a new edition of a nice textbook … on harmonic functions in Euclidean spaces, suitable for a beginning graduate level course. … New exercises are added and numerous minor improvements throughout the text are made." (Alexander Yu. Rashkovsky, Zentralblatt MATH, Vol. 959, 2001)Table of Contents* Basic Properties of Harmonic Functions * Bounded Harmonic Functions * Positive Harmonic Functions * The Kelvin Transform * Harmonic Polynomials * Harmonic Hardy Spaces * Harmonic Functions on Half-Spaces * Harmonic Bergman Spaces * The Decomposition Theorem * Annular Regions * The Dirichlet Problem and Boundary Behavior * Volume, Surface Area, and Integration on Spheres * Harmonic Function Theory and Mathematica * References * Symbol Index * Index
£71.24
Springer Beginning Functional Analysis
a huge range and FREE tracked UK delivery on ALL orders.
£59.99
Springer Practical Analysis in One Variable
a huge range and FREE tracked UK delivery on ALL orders.
£64.99
Springer The Mathematics of Sonya Kovalevskaya
a huge range and FREE tracked UK delivery on ALL orders.
£85.49
Springer Papers on Fuchsian Functions
a huge range and FREE tracked UK delivery on ALL orders.
£123.49
Springer Nonlinear Functional Analysis and its Applications
a huge range and FREE tracked UK delivery on ALL orders.
£237.49
Springer Nonlinear Functional Analysis and Its Applications
a huge range and FREE tracked UK delivery on ALL orders.
£123.49
Springer New York Weakly Differentiable Functions
Book SynopsisThe term "weakly differentiable functions" in the title refers to those inte n grable functions defined on an open subset of R whose partial derivatives in the sense of distributions are either LP functions or (signed) measures with finite total variation.Table of Contents1 Preliminaries.- 1.1 Notation.- Inner product of vectors.- Support of a function.- Boundary of a set.- Distance from a point to a set.- Characteristic function of a set.- Multi-indices.- Partial derivative operators.- Function spaces—continuous, Hölder continuous, Hölder continuous derivatives.- 1.2 Measures on Rn.- Lebesgue measurable sets.- Lebesgue measurability of Borel sets.- Suslin sets.- 1.3 Covering Theorems.- Hausdorff maximal principle.- General covering theorem.- Vitali covering theorem.- Covering lemma, with n-balls whose radii vary in Lipschitzian way.- Besicovitch covering lemma.- Besicovitch differentiation theorem.- 1.4 Hausdorff Measure.- Equivalence of Hausdorff and Lebesgue measures.- Hausdorff dimension.- 1.5 Lp-Spaces.- Integration of a function via its distribution function.- Young’s inequality.- Hölder’s and Jensen’s inequality.- 1.6 Regularization.- Lp-spaces and regularization.- 1.7 Distributions.- Functions and measures, as distributions.- Positive distributions.- Distributions determined by their local behavior.- Convolution of distributions.- Differentiation of distributions.- 1.8 Lorentz Spaces.- Non-increasing rearrangement of a function.- Elementary properties of rearranged functions.- Lorentz spaces.- O’Neil’s inequality, for rearranged functions.- Equivalence of Lp-norm and (p, p)-norm.- Hardy’s inequality.- Inclusion relations of Lorentz spaces.- Exercises.- Historical Notes.- 2 Sobolev Spaces and Their Basic Properties.- 2.1 Weak Derivatives.- Sobolev spaces.- Absolute continuity on lines.- Lp-norm of difference quotients.- Truncation of Sobolev functions.- Composition of Sobolev functions.- 2.2 Change of Variables for Sobolev Functions.- Rademacher’s theorem.- Bi-Lipschitzian change of variables.- 2.3 Approximation of Sobolev Functions by Smooth Functions.- Partition of unity.- Smooth functions are dense in Wk,p.- 2.4 Sobolev Inequalities.- Sobolev’s inequality.- 2.5 The Rellich-Kondrachov Compactness Theorem.- Extension domains.- 2.6 Bessel Potentials and Capacity.- Riesz and Bessel kernels.- Bessel potentials.- Bessel capacity.- Basic properties of Bessel capacity.- Capacitability of Suslin sets.- Minimax theorem and alternate formulation of Bessel capacity.- Metric properties of Bessel capacity.- 2.7 The Best Constant in the Sobolev Inequality.- Co-area formula.- Sobolev’s inequality and isoperimetric inequality.- 2.8 Alternate Proofs of the Fundamental Inequalities.- Hardy-Littlewood-Wiener maximal theorem.- Sobolev’s inequality for Riesz potentials.- 2.9 Limiting Cases of the Sobolev Inequality.- The case kp=n by infinite series.- The best constant in the case kp = n.- An L?-bound in the limiting case.- 2.10 Lorentz Spaces, A Slight Improvement.- Young’s inequality in the context of Lorentz spaces.- Sobolev’s inequality in Lorentz spaces.- The limiting case.- Exercises.- Historical Notes.- 3 Pointwise Behavior of Sobolev Functions.- 3.1 Limits of Integral Averages of Sobolev Functions.- Limiting values of integral averages except for capacity null set.- 3.2 Densities of Measures.- 3.3 Lebesgue Points for Sobolev Functions.- Existence of Lebesgue points except for capacity null set.- Approximate continuity.- Fine continuity everywhere except for capacity null set.- 3.4 LP-Derivatives for Sobolev Functions.- Existence of Taylor expansions Lp.- 3.5 Properties of Lp-Derivatives.- The Spaces TktkTk,ptk,p.- The implication of a function being in Tk,pat all points of a closed set.- 3.6 An Lp-Version of the Whitney Extension Theorem.- Existence of a C? function comparable to the.- distance function to a closed set.- The Whitney extension theorem for functions in Tk,p and tk,p.- 3.7 An Observation on Differentiation.- 3.8 Rademacher’s Theorem in the Lp-Context.- A function in Tk,peverywhere implies it is in tk,palmost everywhere.- 3.9 The Implications of Pointwise Differentiability.- Comparison of Lp-derivatives and distributional derivatives.- If u ? tk,p(x)for everyxand if the.- LP-derivatives are in Lpthen u ? Wk,p.- 3.10 A Lusin-Type Approximation for Sobolev Functions.- Integral averages of Sobolev functions are uniformly close to their limits on the complement of sets of small capacity.- Existence of smooth functions that agree with Sobolev functions on the complement of sets of small capacity.- 3.11 The Main Approximation.- Existence of smooth functions that agree with Sobolev functions on the complement of sets of small capacity and are close in norm.- Exercises.- Historical Notes.- 4 Poincaré Inequalities—A Unified Approach.- 4.1 Inequalities in a General Setting.- An abstract version of the Poincaré inequality.- 4.2 Applications to Sobolev Spaces.- An interpolation inequality.- 4.3 The Dual of WM,p(?).- The representation of (W0M,p(?) )*.- 4.4 Some Measures in (W0M,p(?))*.- Poincaré inequalities derived from the abstract version by identifying Lebesgue and Hausdorff measure with elements in (WM,p(?))*.- The trace of Sobolev functions on the boundary of Lipschitz domains.- Poincaré inequalities involving the trace of a Sobolev function.- 4.5 Poincaré Inequalities.- Inequalities involving the capacity of the set on which a function vanishes.- 4.6 Another Version of Poincaré’s Inequality.- An inequality involving dependence on the set on which the function vanishes, not merely on its capacity.- 4.7 More Measures in (WM,p(?))*.- Sobolev’s inequality for Riesz potentials involving measures other than Lebesgue measure.- Characterization of measures in (WM,p(?))*.- 4.8 Other Inequalities Involving Measures in (WM,p)*.- Inequalities involving the restriction of Hausdorff measure to lower dimensional manifolds.- 4.9 The Case p= 1.- Inequalities involving the L1-norm of the gradient.- Exercises.- Historical Notes.- 5 Functions of Bounded Variation.- 5.1 Definitions.- Definition of BV functions.- The total variation measure ? Du?.- 5.2 Elementary Properties of BV Functions.- Lower semicontinuity of the total variation measure.- A condition ensuring continuity of the total variation measure.- 5.3 Regularization of BV Functions.- Regularization does not increase the BV norm.- Approximation of BV functions by smooth functions Compactness in L1of the unit ball in BV.- 5.4 Sets of Finite Perimeter.- Definition of sets of finite perimeter.- The perimeter of domains with smooth boundaries.- Isoperimetric and relative isoperimetric inequality for sets of finite perimeter.- 5.5 The Generalized Exterior Normal.- A preliminary version of the Gauss-Green theorem.- Density results at points of the reduced boundary.- 5.6 Tangential Properties of the Reduced Boundary and the Measure-Theoretic Normal.- Blow-up at a point of the reduced boundary.- The measure-theoretic normal.- The reduced boundary is contained in the measure-theoretic boundary.- A lower bound for the density of ?DXE?.- Hausdorff measure restricted to the reduced boundary is bounded above by ?DXE?.- 5.7 Rectifiability of the Reduced Boundary.- Countably (n — 1)-rectifiable sets.- Countable (n — 1)-rectifiability of the measure-theoretic boundary.- 5.8 The Gauss-Green Theorem.- The equivalence of the restriction of Hausdorff measure to the measure-theoretic boundary and ?DXE?.- The Gauss-Green theorem for sets of finite perimeter.- 5.9 Pointwise Behavior of BV Functions.- Upper and lower approximate limits.- The Boxing inequality.- The set of approximate jump discontinuities.- 5.10 The Trace of a BV Function.- The bounded extension of BV functions.- Trace of a BV function defined in terms of the upper and lower approximate limits of the extended function.- The integrability of the trace over the.- measure-theoretic boundary.- 5.11 Sobolev-Type Inequalities for BV Functions.- Inequalities involving elements in (BV(?))*.- 5.12 Inequalities Involving Capacity.- Characterization of measure in (BV(?))*.- Poincaré inequality for BV functions.- 5.13 Generalizations to the Case p> 1.- 5.14 Trace Defined in Terms of Integral Averages.- Exercises.- Historical Notes.- List of Symbols.
£71.24
Springer-Verlag New York Inc. Elementary Stability and Bifurcation Theory
Book SynopsisI Asymptotic Solutions of Evolution Problems.- II Bifurcation and Stability of Steady Solutions of Evolution Equations in One Dimension.- III Imperfection Theory and Isolated Solutions Which Perturb Bifurcation.- IV Stability of Steady Solutions of Evolution Equations in Two Dimensions and nDimensions.- V Bifurcation of Steady Solutions in Two Dimensions and the Stability of the Bifurcating Solutions.- VI Methods of Projection for General Problems of Bifurcation into Steady Solutions.- VII Bifurcation of Periodic Solutions from Steady Ones (Hopf Bifurcation) in Two Dimensions.- VIII Bifurcation of Periodic Solutions in the General Case.- IX Subharmonic Bifurcation of Forced T-Periodic Solutions.- X Bifurcation of Forced T-Periodic Solutions into Asymptotically Quasi-Periodic Solutions.- XI Secondary Subharmonic and Asymptotically Quasi-Periodic Bifurcation of Periodic Solutions (of Hopf's Type) in the Autonomous Case.- XII Stability and Bifurcation in Conservative Systems.Table of ContentsI Asymptotic Solutions of Evolution Problems.- I.1 One-Dimensional, Two-Dimensional n-Dimensional, and Infinite-Dimensional Interpretations of (I.1).- I.2 Forced Solutions; Steady Forcing and T-Periodic Forcing; Autonomous and Nonautonomous Problems.- I.3 Reduction to Local Form.- I.4 Asymptotic Solutions.- I.5 Asymptotic Solutions and Bifurcating Solutions.- I.6 Bifurcating Solutions and the Linear Theory of Stability.- I.7 Notation for the Functional Expansion of F(t µ,U).- Notes.- II Bifurcation and Stability of Steady Solutions of Evolution Equations in One Dimension.- II.1 The Implicit Function Theorem.- II.2 Classification of Points on Solution Curves.- 1I.3 The Characteristic Quadratic. Double Points, Cusp Points, and Conjugate Points.- II.4 Double-Point Bifurcation and the Implicit Function Theorem.- II.5 Cusp-Point Bifurcation.- II.6 Triple-Point Bifurcation.- II.7 Conditional Stability Theorem.- II.8 The Factorization Theorem in One Dimension.- II.9 Equivalence of Strict Loss of Stability and Double-Point Bifurcation.- II.10 Exchange of Stability at a Double Point.- II.1 1 Exchange of Stability at a Double Point for Problems Reduced to Local Form.- II.12 Exchange of Stability at a Cusp Point.- II.13 Exchange of Stability at a Triple Point.- II.14 Global Properties of Stability of Isolated Solutions.- III Imperfection Theory and Isolated Solutions Which Perturb Bifurcation.- III.1 The Structure of Problems Which Break Double-Point Bifurcation.- III.2 The Implicit Function Theorem and the Saddle Surface Breaking Bifurcation.- III.3 Examples of Isolated Solutions Which Break Bifurcation.- III.4 Iterative Procedures for Finding Solutions.- III.5 Stability of Solutions Which Break Bifurcation.- III.6 Isolas.- Exercise.- Notes.- IV Stability of Steady Solutions of Evolution Equations in Two Dimensions and nDimensions.- IV.1 Eigenvalues and Eigenvectors of an n x n Matrix.- IV.2 Algebraic and Geometric Multiplicity—The Riesz Index.- IV.3 The Adjoint Eigenvalue Problem.- IV.4 Eigenvalues and Eigenvectors of a 2 x 2 Matrix.- 4.1 Eigenvalues.- 4.2 Eigenvectors.- 4.3 Algebraically Simple Eigenvalues.- 4.4 Algebraically Double Eigenvalues.- 4.4.1 Riesz Index 1.- 4.4.2 Riesz Index 2.- IV.5 The Spectral Problem and Stability of the Solution u = 0 in ?n.- IV.6 Nodes, Saddles, and Foci.- IV.7 Criticality and Strict Loss of Stability.- Appendix IV.I Biorthogonality for Generalized Eigenvectors.- Appendix IV.2 Projections.- V Bifurcation of Steady Solutions in Two Dimensions and the Stability of the Bifurcating Solutions.- V.1 The Form of Steady Bifurcating Solutions and Their Stability.- V.2 Necessary Conditions for the Bifurcation of Steady Solutions.- V.3 Bifurcation at a Simple Eigenvalue.- V.4 Stability of the Steady Solution Bifurcating at a Simple Eigenvalue.- V.5 Bifurcation at a Double Eigenvalue of Index Two.- V.6 Stability of the Steady Solution Bifurcating at a Double Eigenvalue of Index Two.- V.7 Bifurcation and Stability of Steady Solutions in the Form (V.2) at a Double Eigenvalue of Index One (Semi-Simple).- V.8 Bifurcation and Stability of Steady Solutions (V.3) at a Semi-Simple Double Eigenvalue.- V.9 Examples of Stability Analysis at a Double Semi-Simple (Index-One) Eigenvalue.- V.10 Saddle-Node Bifurcation.- Appendix V.1 Implicit Function Theorem for a System of Two Equations in Two Unknown Functions of One Variable.- Exercises.- VI Methods of Projection for General Problems of Bifurcation into Steady Solutions.- VI.1 The Evolution Equation and the Spectral Problem.- VI.2 Construction of Steady Bifurcating Solutions as Power Series in the Amplitude.- VI.3 ?1 and ?1 in Projection.- VI.4 Stability of the Bifurcating Solution.- VI.5 The Extra Little Part for ?1 in Projection.- V1.6 Projections of Higher-Dimensional Problems.- VI.7 The Spectral Problem for the Stability of u = 0.- VI.8 The Spectral Problem and the Laplace Transform.- VI.9 Projections into ?1.- VI.10 The Method of Projection for Isolated Solutions Which Perturb Bifurcation at a Simple Eigenvalue (Imperfection Theory).- VI.1 1 The Method of Projection at a Double Eigenvalue of Index Two.- VI.12 The Method of Projection at a Double Semi-Simple Eigenvalue.- VI.13 Examples of the Method of Projection.- VI.14 Symmetry and Pitchfork Bifurcation.- VII Bifurcation of Periodic Solutions from Steady Ones (Hopf Bifurcation) in Two Dimensions.- VII.1 The Structure of the Two-Dimensional Problem Governing Hopf Bifurcation.- VII.2 Amplitude Equation for Hopf Bifurcation.- VII.3 Series Solution.- VII.4 Equations Governing the Taylor Coefficients.- VII.5 Solvability Conditions (the Fredholm Alternative).- VII.6 Floquet Theory.- 6.1 Floquet Theory in ?1.- 6.2 Floquet Theory in ?2 and ?n.- VII.7 Equations Governing the Stability of the Periodic Solutions.- VII.8 The Factorization Theorem.- VII.9 Interpretation of the Stability Result.- Example.- VIII Bifurcation of Periodic Solutions in the General Case.- VIII.1 Eigenprojections of the Spectral Problem.- VIII.2 Equations Governing the Projection and the Complementary Projection.- VIII.3 The Series Solution Using the Fredholm Alternative.- VIII.4 Stability of the Hopf Bifurcation in the General Case.- VIII.5 Systems with Rotational Symmetry.- Examples.- Notes.- IX Subharmonic Bifurcation of Forced T-Periodic Solutions.- Notation.- IX.1 Definition of the Problem of Subharmonic Bifurcation.- IX.2 Spectral Problems and the Eigenvalues ?( µ).- IX.3 Biorthogonality.- IX.4 Criticality.- IX.S The Fredholm Alternative for J( µ) —?( µ)and a Formula Expressing the Strict Crossing (IX.20).- IX.6 Spectral Assumptions.- IX.7 Rational and Irrational Points of the Frequency Ratio at Criticality.- IX.8 The Operator $$\mathbb{J}$$ and its Eigenvectors.- IX.9 The Adjoint Operator $${{\mathbb{J}}^{*}}$$ Biorthogonality, Strict Crossing, and the Fredholm Alternative for $$\mathbb{J}$$.- IX.10 The Amplitude ?and the Biorthogonal Decomposition of Bifurcating Subharmonic Solutions.- IX.11 The Equations Governing the Derivatives of Bifurcating Subharmonic Solutions with Respect to ?at ? =0.- IX.12 Bifurcation and Stability of T-Periodic and 2 T-Periodic Solutions.- IX.13 Bifurcation and Stability of n T-Periodic Solutions with n >2.- IX.14 Bifurcation and Stability of 3T-Periodic Solutions.- IX.15 Bifurcation of 4 T-Periodic Solutions.- IX.16 Stability of 4 T-Periodic Solutions.- IX.17 Nonexistence of Higher-Order Subharmonic Solutions and Weak Resonance.- IX.18 Summary of Results About Subharmonic Bifurcation.- IX.19 Imperfection Theory with a Periodic Imperfection.- Exercises.- IX.20 Saddle-Node Bifurcation of T-Periodic Solutions.- IX.21 General Remarks About Subharmonic Bifurcations.- X Bifurcation of Forced T-Periodic Solutions into Asymptotically Quasi-Periodic Solutions.- X.1 Decomposition of the Solution and Amplitude Equation.- Exercise.- X.2 Derivation of the Amplitude Equation.- X.3 The Normal Equations in Polar Coordinates.- X.4 The Torus and Trajectories on the Torus in the Irrational Case.- X.5 The Torus and Trajectories on the Torus When ?0T/2? Is a Rational Point of Higher Order (n?5).- X.6 The Form of the Torus in the Case n =5.- X.7 Trajectories on the Torus When n =5.- X.8 The Form of the Torus When n >5.- X.9 Trajectories on the Torus When n?5.- X.10 Asymptotically Quasi-Periodic Solutions.- X.11 Stability of the Bifurcated Torus.- X.12 Subharmonic Solutions on the Torus.- X.13 Stability of Subharmonic Solutions on the Torus.- X.14 Frequency Locking.- Appendix X.1 Direct Computation of Asymptotically Quasi-Periodic Solutions Which Bifurcate at Irrational Points Using the Method of Two Times, Power Series, and the Fredholm Alternative.- Appendix X.2 Direct Computation of Asymptotically Quasi-Periodic Solutions Which Bifurcate at Rational Points of Higher Order Using the Method of Two Times.- Exercise.- Notes.- XI Secondary Subharmonic and Asymptotically Quasi-Periodic Bifurcation of Periodic Solutions (of Hopf’s Type) in the Autonomous Case.- Notation.- XI.1 Spectral Problems.- XI.2 Criticality and Rational Points.- XI.3 Spectral Assumptions About J0.- XI.4 Spectral Assumptions About $$\mathbb{J}$$ in the Rational Case.- XI.5 Strict Loss of Stability at a Simple Eigenvalue of J0.- XI.6 Strict Loss of Stability at a Double Semi-Simple Eigenvalue of J0.- XI.7 Strict Loss of Stability at a Double Eigenvalue of Index Two.- XI.8 Formulation of the Problem of Subharmonic Bifurcation of Periodic Solutions of Autonomous Problems.- XI.9 The Amplitude of the Bifurcating Solution.- XI.10 Power-Series Solutions of the Bifurcation Problem.- XI.11 Subharmonic Bifurcation When n =2.- XI.12 Subharmonic Bifurcation When n >2.- XI.13 Subharmonic Bifurcation When n = 1in the Semi-Simple Case.- XI.14 “Subharmonic” Bifurcation When n =1 in the Case When Zero is an Index-Two Double Eigenvalue of Jo.- XI.15 Stability of Subharmonic Solutions.- XI.16 Summary of Results About Subharmonic Bifurcation in the Autonomous Case.- XI.17 Amplitude Equations.- XI.18 Amplitude Equations for the Cases n?3 or ?0/?0Irrational.- XI.19 Bifurcating Tori. Asymptotically Quasi-Periodic Solutions.- XI.20 Period Doubling n =2.- XI.21 Pitchfork Bifurcation of Periodic Orbits in the Presence of Symmetry n = 1.- Exercises.- XI.22 Rotationally Symmetric Problems.- Exercise.- XII Stability and Bifurcation in Conservative Systems.- XII.1 The Rolling Ball.- XII.2 Euler Buckling.- Exercises.- XII.3 Some Remarks About Spectral Problems for Conservative Systems.- XII.4 Stability and Bifurcation of Rigid Rotation of Two Immiscible Liquids.- Steady Rigid Rotation of Two Fluids.
£71.24
Springer Nonlinear Functional Analysis and its Applications
a huge range and FREE tracked UK delivery on ALL orders.
£208.99
Springer Theory of Complex Functions
a huge range and FREE tracked UK delivery on ALL orders.
£89.99
Springer Calculus Two
a huge range and FREE tracked UK delivery on ALL orders.
£66.49
Springer PAUL HALMOS Celebrating 50 Years of Mathematics
a huge range and FREE tracked UK delivery on ALL orders.
£85.49
Springer Complex Dynamics
a huge range and FREE tracked UK delivery on ALL orders.
£71.99
Springer Basic Multivariable Calculus
a huge range and FREE tracked UK delivery on ALL orders.
£54.99
Springer Real Analysis and Applications
a huge range and FREE tracked UK delivery on ALL orders.
£58.99
Springer Dynamics of Evolutionary Equations
a huge range and FREE tracked UK delivery on ALL orders.
£123.49
Springer Multivariable Calculus And Mathematica With Applications To Geometry And Physics
a huge range and FREE tracked UK delivery on ALL orders.
£37.99
Springer Calculus A Liberal Art
a huge range and FREE tracked UK delivery on ALL orders.
£54.99
Springer Fourier Analysis on Number Fields
a huge range and FREE tracked UK delivery on ALL orders.
£85.49
Springer An Introduction to Wavelets Through Linear Algebra
a huge range and FREE tracked UK delivery on ALL orders.
£53.99
Springer Symmetry and Integration Methods for Differential Equations
a huge range and FREE tracked UK delivery on ALL orders.
£151.99
Springer The Laplace Transform
a huge range and FREE tracked UK delivery on ALL orders.
£66.49
Springer New York Theory of Bergman Spaces
Book SynopsisFifteen years ago, most mathematicians who worked in the intersection of function theory and operator theory thought that progress on the Bergman spaces was unlikely, yet today the situation has completely changed.Trade Review“Each chapter ends with a section called Notes and another called Exercises and Further Results. … It would be quite suitable for graduate students in the field.” (Lou Zengjian, zbMATH 0955.32003, 2022)Table of Contents1 The Bergman Spaces.- 1.1 Bergman Spaces.- 1.2 Some Lp Estimates.- 1.3 The Bloch Space.- 1.4 Duality of Bergman Spaces.- 1.5 Notes.- 1.6 Exercises and Further Results.- 2 The Berezin Transform.- 2.1 Algebraic Properties.- 2.2 Harmonic Functions.- 2.3 Carleson-Type Measures.- 2.4 BMO in the Bergman Metric.- 2.5 A Lipschitz Estimate.- 2.6 Notes.- 2.7 Exercises and Further Results.- 3 Ap -Inner Functions.- 3.1 Ap? -Inner Functions.- 3.2 An Extremal Problem.- 3.3 The Biharmonic Green function.- 3.4 The Expansive Multiplier Property.- 3.5 Contractive Zero Divisors in Ap.- 3.6 An Inner-Outer Factorization Theorem for Ap.- 3.7 Approximation of Subinner Functions.- 3.8 Notes.- 3.9 Exercises and Further Results.- 4 Zero Sets.- 4.1 Some Consequences of Jensen’s Formula.- 4.2 Notions of Density.- 4.3 The Growth Spaces A-? and A-?.- 4.4 A-? Zero Sets, Necessary Conditions.- 4.5 A-? Zero Sets, a Sufficient Condition.- 4.6 Zero Sets for AP?.- 4.7 The Bergman-Nevanlinna Class.- 4.8 Notes.- 4.9 Exercises and Further Results.- 5 Interpolation and Sampling.- 5.1 Interpolation Sequences for AT-?.- 5.2 Sampling Sets for A-?.- 5.3 Interpolation and Sampling in Ap?.- 5.4 Hyperbolic Lattices.- 5.5 Notes.- 5.6 Exercises and Further Results.- 6 Invariant Subspaces.- 6.1 Invariant Subspaces of Higher Index.- 6.2 Inner Spaces in A2?.- 6.3 A Beurling-Type Theorem.- 6.4 Notes.- 6.5 Exercises and Further Results.- 7 Cyclicity.- 7.1 Cyclic Vectors as Outer functions.- 7.2 Cyclicity in Ap Versus in A-?.- 7.3 Premeasures for Functions in A-?.- 7.4 Cyclicity in A-?.- 7.5 Notes.- 7.6 Exercises and Further Results.- 8 Invertible Noncyclic Functions.- 8.1 An Estimate for Harmonic Functions.- 8.2 The Building Blocks.- 8.3 The Basic Iteration Scheme.- 8.4 The Mushroom Forest.- 8.5 Finishing the Construction.- 8.6 Two Applications.- 8.7 Notes.- 8.8 Exercises and Further Results.- 9 Logarithmically Subharmonic Weights.- 9.1 Reproducing Kernels.- 9.2 Green Functions with Smooth Weights.- 9.3 Green Functions with General Weights.- 9.4 An Application.- 9.5 Notes.- 9.6 Exercises and Further Results.- References.
£44.99
Springer Analysis and Simulation of Chaotic Systems
a huge range and FREE tracked UK delivery on ALL orders.
£44.99
Springer New York A Course in Robust Control Theory
Book SynopsisDuring the 90s robust control theory has seen major advances and achieved a new maturity, centered around the notion of convexity.Trade ReviewFrom the reviews"Because progress in LMI robust control theory has been explosive, only books published in the past 3 or 4 years can hope to adequatetely document the phenomenon. The textbook of Dullerud and Paganini rises admirably to the challenge, starting from the basics of linear algebra and system theory and leading the reader through the key 1990s breakthroughs in LMI robust control theory. To keep things simple, the authors relegate the issue of robustness against nonlinear uncertainties to the citations, focusing attention squarely on the linear case. (...)The book would make an excellent text for a two-semester or two-quarter course for first year graduate students beginning with no prior knowledge of state-space methods. Alternatively, for control students who already have a state-space background."IEEE Transactions on Automatics Control, Vol. 46, No. 9, September 2001Table of Contents0 Introduction.- 1 Preliminaries in Finite Dimensional Space.- 2 State Space System Theory.- 3 Linear Analysis.- 4 Model Realizations and Reduction.- 5 Stabilizing Controllers.- 6 H2 Optimal Control.- 7 H? Synthesis.- 8 Uncertain Systems.- 9 Feedback Control of Uncertain Systems.- 10 Further Topics: Analysis.- 11 Further Topics: Synthesis.- A Some Basic Measure Theory.- A.1 Sets of zero measure.- A.2 Terminology.- Notes and references.- B Proofs of Strict Separation.- Notes and references.- Notes and references.- Notation.- References.
£66.49
Elsevier Science Singularity and Dynamics on Discontinuous Vector Fields
£120.00
Cambridge University Press A Course of Modern Analysis
£84.81
Cambridge University Press A Radical Approach to Lebesgues Theory of Integration
a huge range and FREE tracked UK delivery on ALL orders.
£117.00
Springer Differential Geometry of Frame Bundles 47 Mathematics and Its Applications
a huge range and FREE tracked UK delivery on ALL orders.
£44.99
Springer Newtons Method and Dynamical Systems Spinoff Acta Applicandae Mathematical Vol 13 12
a huge range and FREE tracked UK delivery on ALL orders.
£123.49
Springer Discrete Groups in Space and Uniformization Problems 40 Mathematics and its Applications
a huge range and FREE tracked UK delivery on ALL orders.
£85.49
Springer Theory of Random Determinants 45 Mathematics and its Applications
a huge range and FREE tracked UK delivery on ALL orders.
£85.49
Springer Random Processes with Independent Increments 47 Mathematics and its Applications
a huge range and FREE tracked UK delivery on ALL orders.
£44.99
Springer Selected Papers of Antoni Zygmund Volume 3 41 Mathematics and its Applications
a huge range and FREE tracked UK delivery on ALL orders.
£44.99
Springer Applied and Industrial Mathematics Venice 1 1989 Conference Proceedings Mathematics and Its Applications
a huge range and FREE tracked UK delivery on ALL orders.
£44.99
