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Handbook differential equations 3e by daniel zwillinger from www mathschoolinternational com

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  • Titlepage

  • Contents

  • Preface

  • Introduction

  • Introduction to the Electronic Version

  • How to Use This Book

  • I.A Definitions and Concepts

    • 1 Definition of Terms

    • 2 Alternative Theorems

    • 3 Bifurcation Theory

    • 4 A Caveat for Partial Differential Equations

    • 5 Chaos in Dynamical Systems

    • 6 Classification of Partial Differential Equations

    • 7 Compatible Systems

    • 8 Conservation Laws

    • 9 Differential Resultants

    • 10 Existence and Uniqueness Theorems

    • 11 Fixed Point Existence Theorems

    • 12 Hamilton-Jacobi Theory

    • 13 Integrability of Systems

    • 14 Internet Resources

    • 15 Inverse Problems

    • 16 Limit Cycles

    • 17 Natural Boundary Conditions for a PDE

    • 18 Normal Forms: Near-Identity Transformations

    • 19 Random Differential Equations

    • 20 Self-Adjoint Eigenfunction Problems

    • 21 Stability Theorems

    • 22 Sturm-Liouville Theory

    • 23 Variational Equations

    • 24 Well Posed Differential Equations

    • 25 Wronskians and Fundamental Solutions

    • 26 Zeros of Solutions

  • I.B Transformations

    • 27 Canonical Forms

    • 28 Canonical Transformations

    • 29 Darboux Transformation

    • 30 An Involutory Transformation

    • 31 Liouville Transformation - 1

    • 32 Liouville Transformation - 2

    • 33 Reduction of Linear ODEs to a First Order System

    • 34 Prufer Transformation

    • 35 Modified Prufer Transformation

    • 36 Transformations of Second Order Linear ODEs - 1

    • 37 Transformations of Second Order Linear ODEs - 2

    • 38 Transformation of an ODE to an Integral Equation

    • 39 Miscellaneous ODE Transformations

    • 40 Reduction of PDEs to a First Order System

    • 41 Transforming Partial Differential Equations

    • 42 Transformations of Partial Differential Equations

  • II Exact Analytical Methods

    • 43 Introduction to Exact Analytical Methods

    • 44 Look-Up Technique

    • 45 Look-Up ODE Forms

  • II.A Exact Methods for ODEs

    • 46 An Nth Order Equation

    • 47 Use of the Adjoint Equation

    • 48 Autonomous Equations - Independent Variable Missing

    • 49 Bernoulli Equation

    • 50 Clairaut's Equation

    • 51 Computer-Aided Solution

    • 52 Constant Coefficient Linear Equations

    • 53 Contact Transformation

    • 54 Delay Equations

    • 55 Dependent Variable Missing

    • 56 Differentiation Method

    • 57 Differential Equations with Discontinuities

    • 58 Eigenfunction Expansions

    • 59 Equidimensional-in-x Equations

    • 60 Equidimensional-in-y Equations

    • 61 Euler Equations

    • 62 Exact First Order Equations

    • 63 Exact Second Order Equations

    • 64 Exact Nth Order Equations

    • 65 Factoring Equations

    • 66 Factoring Operators

    • 67 Factorization Method

    • 68 Fokker-Planck Equation

    • 69 Fractional Differential Equations

    • 70 Free Boundary Problems

    • 71 Generating Functions

    • 72 Green's Functions

    • 73 Homogeneous Equations

    • 74 Method of Images

    • 75 Integrable Combinations

    • 76 Integral Representation: Laplace's Method

    • 77 Integral Transforms: Finite Intervals

    • 78 Integral Transforms: Infinite Intervals

    • 79 Integrating Factors

    • 80 Interchanging Dependent and Independent Variables

    • 81 Lagrange's Equation

    • 82 Lie Groups: ODEs

    • 83 Operational Calculus

    • 84 Pfaffian Differential Equations

    • 85 Reduction of Order

    • 86 Riccati Equations

    • 87 Matrix Riccati Equations

    • 88 Scale Invariant Equations

    • 89 Separable Equations

    • 90 Series Solution

    • 91 Equations Solvable for x

    • 92 Equations Solvable for y

    • 93 Superposition

    • 94 Method of Undetermined Coefficients

    • 95 Variation of Parameters

    • 96 Vector Ordinary Differential Equations

  • II.B Exact Methods for PDEs

    • 97 Backlund Transformations

    • 98 Method of Characteristics

    • 99 Characteristic Strip Equations

    • 100 Conformal Mappings

    • 101 Method of Descent

    • 102 Diagonalization of a Linear System of PDEs

    • 103 Duhamel's Principle

    • 104 Exact Equations

    • 105 Hodograph Transformation

    • 106 Inverse Scattering

    • 107 Jacobi's Method

    • 108 Legendre Transformation

    • 109 Lie Groups: PDEs

    • 110 Poisson Formula

    • 111 Riemann's Method

    • 112 Separation of Variables

    • 113 Separable Equations: Stackel Matrix

    • 114 Similarity Methods

    • 115 Exact Solutions to the Wave Equation

    • 116 Wiener-Hopf Technique

  • III Approximate Analytical Methods

    • 117 Introduction to Approximate Analysis

    • 118 Chaplygin's Method

    • 119 Collocation

    • 120 Dominant Balance

    • 121 Equation Splitting

    • 122 Floquet Theory

    • 123 Graphical Analysis: The Phase Plane

    • 124 Graphical Analysis: The Tangent Field

    • 125 Harmonic Balance

    • 126 Homogenization

    • 127 Integral Methods

    • 128 Interval Analysis

    • 129 Least Squares Method

    • 130 Lyapunov Functions

    • 131 Equivalent Linearization and Nonlinearization

    • 132 Maximum Principles

    • 133 McGarvey Iteration Technique

    • 134 Moment Equations: Closure

    • 135 Moment Equations: Ito Calculus

    • 136 Monge's Method

    • 137 Newton's Method

    • 138 Pade Approximants

    • 139 Perturbation Method: Method of Averaging

    • 140 Perturbation Method: Boundary Layer Method

    • 141 Perturbation Method: Functional Iteration

    • 142 Perturbation Method: Multiple Scales

    • 143 Perturbation Method: Regular Perturbation

    • 144 Perturbation Method: Strained Coordinates

    • 145 Picard Iteration

    • 146 Reversion Method

    • 147 Singular Solutions

    • 148 Soliton-Type Solutions

    • 149 Stochastic Limit Theorems

    • 150 Taylor Series Solutions

    • 151 Variational Method: Eigenvalue Approximation

    • 152 Variational Method: Rayleigh-Ritz

    • 153 WKB Method

  • IV.A Numerical Methods: Concepts

    • 154 Introduction to Numerical Methods

    • 155 Definition of Terms for Numerical Methods

    • 156 Available Software

    • 157 Finite Difference Formulas

    • 158 Finite Difference Methodology

    • 159 Grid Generation

    • 160 Richardson Extrapolation

    • 161 Stability: ODE Approximations

    • 162 Stability: Courant Criterion

    • 163 Stability: Von Neumann Test

    • 164 Testing Differential Equation Routines

  • IV.B Numerical Methods for ODEs

    • 165 Analytic Continuation

    • 166 Boundary Value Problems: Box Method

    • 167 Boundary Value Problems: Shooting Method

    • 168 Continuation Method

    • 169 Continued Fractions

    • 170 Cosine Method

    • 171 Differential Algebraic Equations

    • 172 Eigenvalue-Eigenfunction Problems

    • 173 Euler's Forward Method

    • 174 Finite Element Method

    • 175 Hybrid Computer Methods

    • 176 Invariant Imbedding

    • 177 Multigrid Methods

    • 178 Parallel Computer Methods

    • 179 Predictor-Corrector Methods

    • 180 Runge-Kutta Methods

    • 181 Stiff Equations

    • 182 Integrating Stochastic Equations

    • 183 Symplectic Integration

    • 184 Use of Wavelets

    • 185 Weighted Residual Methods

  • IV.C Numerical Methods for PDEs

    • 186 Boundary Element Method

    • 187 Differential Quadrature

    • 188 Domain Decomposition

    • 189 Elliptic Equations: Finite Differences

    • 190 Elliptic Equations: Monte-Carlo Method

    • 191 Elliptic Equations: Relaxation

    • 192 Hyperbolic Equations: Method of Characteristics

    • 193 Hyperbolic Equations: Finite Differences

    • 194 Lattice Gas Dynamics

    • 195 Method of Lines

    • 196 Parabolic Equations: Explicit Method

    • 197 Parabolic Equations: Implicit Method

    • 198 Parabolic Equations: Monte-Carlo Method

    • 199 Pseudospectral Method

  • Mathematical Nomenclature

  • Errata

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