Handbook of Differential Equations, 4th Edition
- Length: 736 pages
- Edition: 4
- Language: English
- Publisher: Chapman and Hall/CRC
- Publication Date: 2021-11-22
- ISBN-10: 0367252570
- ISBN-13: 9780367252571
- Sales Rank: #0 (See Top 100 Books)
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.
Cover Half Title Series Page Title Page Copyright Page Contents Preface Introduction How to Use This Book I.A. Definitions and Concepts 1. Definition of Terms 2. Alternative Theorems 3. Bifurcation Theory 4. Chaos in Dynamical Systems 5. Classi cation 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 47. Introduction to Exact Analytical Methods 48. Look-Up Technique* 48.1. Ordinary Differential Equations 48.2. Partial Differential Equations 48.3. Systems of Differential Equations 48.4. Hamiltonians Representing Differential Equations 48.5. The Laplacian in Different Coordinate Systems 48.6. Parametrized Differential Equations at Specific Values 49. Look-Up ODE Forms II.A. Exact Methods for ODEs 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 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. Backlund 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: StŁackel 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: Poincare 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: Ito Calculus 153. Monge's Method 154. Newton's Method 155. Pade 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.A. Numerical Methods: Concepts 174. Introduction to Numerical Methods* 175. Terms for Numerical Methods 176. Finite Difference Formulas 176.1. One Dimension: Rectilinear Grid 176.2. Two Dimensions: Rectilinear Grid 176.3. Two Dimensions: Irregular Grid 176.4. Two Dimensions: Triangular Grid 176.5. Numerical Schemes for the ODE: y' = f(x, y) 176.6. Explicit Numerical Schemes for the PDE: aux + ut = 0 176.7. Implicit Numerical Schemes for the PDE: aux + ut = S(x, t) 176.8. Numerical Schemes for the PDE: F(u)x + ut = 0 176.9. Numerical Schemes for the PDE: ux = utt 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 Mathematical Nomenclature Named Differential Equations Index
Donate to keep this site alive
1. Disable the AdBlock plugin. Otherwise, you may not get any links.
2. Solve the CAPTCHA.
3. Click download link.
4. Lead to download server to download.