Handbook of Differential Equations
Description
Table of Contents
Preface
Introduction
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 Inverse Problems
14 Limit Cycles
15 Natural Boundary Conditions for a PDE
16 Normal Forms: Near-Identity Transformations
17 Self-Adjoint Eigenfunction Problems
18 Stability Theorems
19 Sturm-Liouville Theory
20 Variational Equations
21 Well-Posedness of Differential Equations
22 Wronskians and Fundamental Solutions
I.B Transformations
23 Canonical Forms
24 Canonical Transformations
25 Darboux Transformation
26 An Involutory Transformation
27 Liouville Transformation - 1
28 Liouville Transformation - 2
29 Reduction of Linear ODEs to a First Order System
30 Prüfer Transformation
31 Modified Prüfer Transformation
32 Transformations of Second Order Linear ODEs - 1
33 Transformations of Second Order Linear ODEs - 2
34 Transformation of an ODE to an Integral Equation
35 Miscellaneous ODE Transformations
36 Reduction of PDEs to a First Order System
37 Transforming Partial Differential Equations
38 Transformations of Partial Differential Equations
II Exact Analytical Methods
39 Introduction to Exact Analytical Methods
40 Look Up Technique
41 Look Up ODE Forms
II.A Exact Methods for ODEs
42 An N-th Order Equation
43 Use of the Adjoint Equation
44 Autonomous Equations
45 Bernoulli Equation
46 Clairaut's Equation
47 Computer-Aided Solution
48 Constant Coefficient Linear Equations
49 Contact Transformation
50 Delay Equations
51 Dependent Variable Missing
52 Differentiation Method
53 Differential Equations with Discontinuities*
54 Eigenfunction Expansions*
55 Equidimensional-in-x Equations
56 Equidimensional-in-y Equations
57 Euler Equations
58 Exact First Order Equations
59 Exact Second Order Equations
60 Exact N-th Order Equations
61 Factoring Equations*
62 Factoring Operators*
63 Factorization Method
64 Fokker-Planck Equation
65 Fractional Differential Equations*
66 Free Boundary Problems*
67 Generating Functions*
68 Green's Functions*
69 Homogeneous Equations
70 Method of Images*
71 Integrable Combinations
72 Integral Representations: Laplace's Method*
73 Integral Transforms: Finite Intervals*
74 Integral Transforms: Infinite Intervals*
75 Integrating Factors*
76 Interchanging Dependent and Independent Variables
77 Lagrange's Equation
78 Lie Groups: ODEs
79 Operational Calculus*
80 Pfaffian Differential Equations
81 Reduction of Order
82 Riccati Equation
83 Matrix Riccati Equations
84 Scale Invariant Equations
85 Separable Equations
86 Series Solution*
87 Equations Solvable for x
88 Equations Solvable for y
89 Superposition*
90 Method of Undetermined Coefficients*
91 Variation of Parameters
92 Vector Ordinary Differential Equations
II.B Exact Methods for PDEs
93 Bäcklund Transformations
94 Method of Characteristics
95 Characteristic Strip Equations
96 Conformai Mappings
97 Method of Descent
98 Diagonalization of a Linear System of PDEs
99 Duhamel's Principle
100 Exact Equations
101 Hodograph Transformation
102 Inverse Scattering
103 Jacobi's Method
104 Legendre Transformation
105 Lie Groups: PDEs
106 Poisson Formula
107 Riemann's Method
108 Separation of Variables
109 Similarity Methods
110 Exact Solutions to the Wave Equation
111 Wiener-Hopf Technique
III Approximate Analytical Methods
112 Introduction to Approximate Analysis
113 Chaplygin's Method
114 Collocation
115 Dominant Balance
116 Equation Splitting
117 Floquet Theory
118 Graphical Analysis: The Phase Plane
119 Graphical Analysis: The Tangent Field
120 Harmonic Balance
121 Homogenization
122 Integral Methods
123 Interval Analysis
124 Least Squares Method
125 Lyapunov Functions
126 Equivalent Linearization and Nonlinearization
127 Maximum Principles
128 McGarvey Iteration Technique
129 Moment Equations: Closure
130 Moment Equations: Itô Calculus
131 Monge's Method
132 Newton's Method
133 Padé Approximants
134 Perturbation Method: Method of Averaging
135 Perturbation Method: Boundary Layer Method
136 Perturbation Method: Functional Iteration
137 Perturbation Method: Multiple Scales
138 Perturbation Method: Regular Perturbation
139 Perturbation Method: Strained Coordinates
140 Picard Iteration
141 Reversion Method
142 Singular Solutions
143 Soliton Type Solutions
144 Stochastic Limit Theorems
145 Taylor Series Solutions
146 Variational Method: Eigenvalue Approximation
147 Variational Method: Rayleigh-Ritz
148 WKB Method
IV.A Numerical Methods: Concepts
149 Introduction to Numerical Methods
150 Definition of Terms for Numerical Methods
151 Available Software
152 Finite Difference Methodology
153 Finite Difference Formulas
154 Excerpts from GAMS
155 Grid Generation
156 Richardson Extrapolation
157 Stability: ODE Approximations
158 Stability: Courant Criterion
159 Stability: Von Neumann Test
IV.B Numerical Methods for ODEs
160 Analytic Continuation*
161 Boundary Value Problems: Box Method
162 Boundary Value Problems: Shooting Method*
163 Continuation Method*
164 Continued Fractions
165 Cosine Method*
166 Differential Algebraic Equations
167 Eigenvalue/Eigenfunction Problems
168 Euler's Forward Method
169 Finite Element Method*
170 Hybrid Computer Methods*
171 Invariant Imbedding*
172 Multigrid Methods*
173 Parallel Computer Methods
174 Predictor-Corrector Methods
175 Runge-Kutta Methods
176 Stiff Equations*
177 Integrating Stochastic Equations
178 Weighted Residual Methods*
IV.C Numerical Methods for PDEs
179 Boundary Element Method
180 Differential Quadrature
181 Domain Decomposition
182 Elliptic Equations: Finite Differences
183 Elliptic Equations: Monte Carlo Method
184 Elliptic Equations: Relaxation
185 Hyperbolic Equations: Method of Characteristics
186 Hyperbolic Equations: Finite Differences
187 Lattice Gas Dynamics
188 Method of Lines
189 Parabolic Equations: Explicit Method
190 Parabolic Equations: Implicit Method
191 Parabolic Equations: Monte Carlo Method
192 Pseudo-Spectral Method
Mathematical Nomenclature
Differential Equation Index
Index
Product details
- No. of pages: 808
- Language: English
- Copyright: © Academic Press 1992
- Published: January 28, 1992
- Imprint: Academic Press
- eBook ISBN: 9781483263960
About the Author
Daniel Zwillinger
Dr. Daniel Zwillinger is a Senior Principal Systems Engineer for the Raytheon Company. He was a systems requirements “book boss” for the Cobra Judy Replacement (CJR) ship and was a requirements and test lead for tracking on the Ungraded Early Warning Radars (UEWR). He has improved the Zumwalt destroyer’s software accreditation process and he was test lead on an Active Electronically Scanned Array (AESA) radar. Dan is a subject matter expert (SME) in Design for Six Sigma (DFSS) and is a DFSS SME in Test Optimization, Critical Chain Program Management, and Voice of the Customer. He is currently leading a project creating Trust in Autonomous Systems. At Raytheon, he twice won the President’s award for best Six Sigma project of the year: on converting planning packages to work packages for the Patriot missile, and for revising Raytheon’s timecard system. He has managed the Six Sigma white belt training program. Prior to Raytheon, Dan worked at Sandia Labs, JPL, Exxon, MITRE, IDA, BBN, and The Mathworks (where he developed an early version of their Statistics Toolbox).
For ten years, Zwillinger was owner and president of Aztec Corporation. As a small business, Aztec won several Small Business Innovation Research (SBIR) contracts. The company also created several software packages for publishing companies. Prior to Aztec, Zwillinger was a college professor at Rensselaer Polytechnic Institute in the department of mathematics.
Dan has written several books on mathematics on the topics of differential equations, integration, statistics, and general mathematics. He is editor-in-chief of the Chemical Rubber Company’s (CRC’s) “Standard Mathematical Tables and Formulae”, and is on the editorial board for CRC’s “Handbook of Chemistry and Physics”. Zwillinger holds a bachelor's degree in mathematics from the Massachusetts Institute of Technology (MIT). He earned his doctorate in applied mathematics from the California Institute of Technology (Caltech). Zwillinger is a certified Raytheon Six Sigma Expert and an ASQ certified Six Sigma Black Belt. He also holds a pilot’s license.
Affiliations and Expertise
Ratings and Reviews
There are currently no reviews for "Handbook of Differential Equations"