Handbook of Differential Equations 4th Edition by Daniel Zwillinger, Vladimir Dobrushkin ISBN 0367252570 9780367252571

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Product details:

ISBN 10: 0367252570 

ISBN 13: 9780367252571

Author: Daniel Zwillinger, Vladimir Dobrushkin 

Through the previous three editions, Handbook of Differential Equations has proven an invaluable reference for anyone working within the field of mathematics, including academics, students, scientists, and professional engineers.

The book is a compilation of methods for solving and approximating differential equations. These include the most widely applicable methods for solving and approximating differential equations,　as well as　numerous methods. Topics include methods for ordinary differential equations, partial differential equations, stochastic differential equations, and systems of such equations.

Included for nearly every method are:

• The types of equations to which the method is applicable
• The idea behind the method
• The procedure for carrying out the method
• At least one simple example of the method
• Any cautions that should be exercised
• Notes for more advanced users

The fourth edition includes corrections, many supplied by readers, as well as many new methods and techniques. These new and corrected entries make necessary improvements in this edition.

Table of contents:

I. Definitions, Concepts, and Transformations

I.A Definitions and Concepts

1. Definition of Terms
2. Alternative Theorems
3. Bifurcation Theory
4. Chaos in Dynamical Systems
5. Classification of Partial Differential Equations
6. Compatible Systems
7. Conservation Laws
8. Differential Equations – Diagrams
9. Differential Equations – Symbols
10. Differential Resultants
11. Existence and Uniqueness Theorems
12. Fixed Point Existence Theorems
13. Hamilton–Jacobi Theory
14. Infinite Order Differential Equations
15. Integrability of Systems
16. Inverse Problems
17. Limit Cycles
18. PDEs & Natural Boundary Conditions
19. Normal Forms: Near-Identity Transformations
20. q-Differential Equations
21. Quaternionic Differential Equations
22. Self-Adjoint Eigenfunction Problems
23. Stability Theorems
24. Stochastic Differential Equations
25. Sturm–Liouville Theory
26. Variational Equations
27. Web Resources
28. Well-Posed Differential Equations
29. Wronskians & Fundamental Solutions
30. Zeros of Solutions

I.B Transformations
31. Canonical Forms
32. Canonical Transformations
33. Darboux Transformation
34. An Involutory Transformation
35. Liouville Transformation – 1
36. Liouville Transformation – 2
37. Changing Linear ODEs to a First Order System
38. Transformations of Second Order Linear ODEs – 1
39. Transformations of Second Order Linear ODEs – 2
40. Transforming an ODE to an Integral Equation
41. Miscellaneous ODE Transformations
42. Transforming PDEs Generically
43. Transformations of PDEs
44. Transforming a PDE to a First Order System
45. Prüfer Transformation
46. Modified Prüfer Transformation

II. Exact Analytical Methods

II.A Exact Methods for ODEs
47. Introduction to Exact Analytical Methods
48. Look-Up Technique
49. Look-Up ODE Forms
50. Use of the Adjoint Equation
51. An Nth Order Equation
52. Autonomous Equations – Independent Variable Missing
53. Bernoulli Equation
54. Clairaut’s Equation
55. Constant Coefficient Linear ODEs
56. Contact Transformation
57. Delay Equations
58. Dependent Variable Missing
59. Differentiation Method
60. Differential Equations with Discontinuities
61. Eigenfunction Expansions
62. Equidimensional-in-x Equations
63. Equidimensional-in-y Equations
64. Euler Equations
65. Exact First Order Equations
66. Exact Second Order Equations
67. Exact Nth Order Equations
68. Factoring Equations
69. Factoring/Composing Operators
70. Factorization Method
71. Fokker–Planck Equation
72. Fractional Differential Equations
73. Free Boundary Problems
74. Generating Functions
75. Green’s Functions
76. ODEs with Homogeneous Functions
77. Hypergeometric Equation
78. Method of Images
79. Integrable Combinations
80. Integrating Factors
81. Interchanging Dependent and Independent Variables
82. Integral Representation: Laplace’s Method
83. Integral Transforms: Finite Intervals
84. Integral Transforms: Infinite Intervals
85. Lagrange’s Equation
86. Lie Algebra Technique
87. Lie Groups: ODEs
88. Non-normal Operators
89. Operational Calculus
90. Pfaffian Differential Equations
91. Quasilinear Second Order ODEs
92. Quasipolynomial ODEs
93. Reduction of Order
94. Resolvent Method for Matrix ODEs
95. Riccati Equation – Matrices
96. Riccati Equation – Scalars
97. Scale Invariant Equations
98. Separable Equations
99. Series Solution
100. Equations Solvable for x
101. Equations Solvable for y
102. Superposition
103. Undetermined Coefficients
104. Variation of Parameters
105. Vector ODEs

II.B Exact Methods for PDEs
106. Bäcklund Transformations
107. Cagniard–de Hoop Method
108. Method of Characteristics
109. Characteristic Strip Equations
110. Conformal Mappings
111. Method of Descent
112. Diagonalizable Linear Systems of PDEs
113. Duhamel’s Principle
114. Exact Partial Differential Equations
115. Fokas Method / Unified Transform
116. Hodograph Transformation
117. Inverse Scattering
118. Jacobi’s Method
119. Legendre Transformation
120. Lie Groups: PDEs
121. Many Consistent PDEs
122. Poisson Formula
123. Resolvent Method for PDEs
124. Riemann’s Method
125. Separation of Variables
126. Separable Equations: Stäckel Matrix
127. Similarity Methods
128. Exact Solutions to the Wave Equation
129. Wiener–Hopf Technique

III. Approximate Analytical Methods
130. Introduction to Approximate Analysis
131. Adomian Decomposition Method
132. Chaplygin’s Method
133. Collocation
134. Constrained Functions
135. Differential Constraints
136. Dominant Balance
137. Equation Splitting
138. Floquet Theory
139. Graphical Analysis: The Phase Plane
140. Graphical Analysis: Poincaré Map
141. Graphical Analysis: Tangent Field
142. Harmonic Balance
143. Homogenization
144. Integral Methods
145. Interval Analysis
146. Least Squares Method
147. Equivalent Linearization and Nonlinearization
148. Lyapunov Functional
149. Maximum Principles
150. McGarvey Iteration Technique
151. Moment Equations: Closure
152. Moment Equations: Itô Calculus
153. Monge’s Method
154. Newton’s Method
155. Padé Approximants
156. Parametrix Method
157. Perturbation Method: Averaging
158. Perturbation Method: Boundary Layers
159. Perturbation Method: Functional Iteration
160. Perturbation Method: Multiple Scales
161. Perturbation Method: Regular Perturbation
162. Perturbation Method: Renormalization Group
163. Perturbation Method: Strained Coordinates
164. Picard Iteration
165. Reversion Method
166. Singular Solutions
167. Soliton-Type Solutions
168. Stochastic Limit Theorems
169. Structured Guessing
170. Taylor Series Solutions
171. Variational Method: Eigenvalue Approximation
172. Variational Method: Rayleigh–Ritz
173. WKB Method

IV. Numerical Methods

IV.A Numerical Methods: Concepts
174. Introduction to Numerical Methods
175. Terms for Numerical Methods
176. Finite Difference Formulas
177. Finite Difference Methodology
178. Grid Generation
179. Richardson Extrapolation
180. Stability: ODE Approximations
181. Stability: Courant Criterion
182. Stability: Von Neumann Test
183. Testing Differential Equation Routines

IV.B Numerical Methods for ODEs
184. Analytic Continuation
185. Boundary Value Problems: Box Method
186. Boundary Value Problems: Shooting Method
187. Continuation Method
188. Continued Fractions
189. Cosine Method
190. Differential Algebraic Equations
191. Eigenvalue/Eigenfunction Problems
192. Euler’s Forward Method
193. Finite Element Method
194. Hybrid Computer Methods
195. Invariant Imbedding
196. Multigrid Methods
197. Neural Networks & Optimization
198. Nonstandard Finite Difference Schemes
199. ODEs with Highly Oscillatory Terms
200. Parallel Computer Methods
201. Predictor–Corrector Methods
202. Probabilistic Methods
203. Quantum Computing
204. Runge–Kutta Methods
205. Stiff Equations
206. Integrating Stochastic Equations
207. Symplectic Integration
208. System Linearization via Koopman
209. Using Wavelets
210. Weighted Residual Methods

IV.C Numerical Methods for PDEs
211. Boundary Element Method
212. Differential Quadrature
213. Domain Decomposition
214. Elliptic Equations: Finite Differences
215. Elliptic Equations: Monte–Carlo Method
216. Elliptic Equations: Relaxation
217. Hyperbolic Equations: Method of Characteristics
218. Hyperbolic Equations: Finite Differences
219. Lattice Gas Dynamics
220. Method of Lines
221. Parabolic Equations: Explicit Method
222. Parabolic Equations: Implicit Method
223. Parabolic Equations: Monte–Carlo Method
224. Pseudospectral Method

V. Computer Languages and Systems
225. Computer Languages and Packages
226. Julia Programming Language
227. Maple Computer Algebra System
228. Mathematica Computer Algebra System
229. MATLAB Programming Language
230. Octave Programming Language
231. Python Programming Language
232. R Programming Language
233. Sage Computer Algebra System

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Tags: Daniel Zwillinger, Vladimir Dobrushkin, Handbook, Differential Equations