Daniel Zwillinger
Handbook of Differential Equations
Daniel Zwillinger
Handbook of Differential Equations
- Gebundenes Buch
- Merkliste
- Auf die Merkliste
- Bewerten Bewerten
- Teilen
- Produkt teilen
- Produkterinnerung
- Produkterinnerung
Handbook of Differential Equations, Third Edition compiles the most widely applicable methods for solving and approximating differential equations, also providing numerous examples that show methods being used. Topics include ordinary differential equations, symplectic integration of differential equations, and the use of wavelets when numerically solving differential equations.
Andere Kunden interessierten sich auch für
- Alfredo BellenNumerical Methods for Delay Differential Equations94,99 €
- Antonio Bove / Ferruccio Colombini / Daniele Del Santo (eds.)Phase Space Analysis of Partial Differential Equations113,50 €
- Imre CsiszárStochastic Differential and Difference Equations37,99 €
- Helge HoldenStochastic Partial Differential Equations116,99 €
- Ravi P AgarwalAn Introduction to Ordinary Differential Equations93,99 €
- Maria ColomboFlows of Non-Smooth Vector Fields and Degenerate Elliptic Equations23,99 €
- V. LakshmikanthamGeneralized Quasilinearization for Nonlinear Problems184,99 €
-
-
-
Handbook of Differential Equations, Third Edition compiles the most widely applicable methods for solving and approximating differential equations, also providing numerous examples that show methods being used. Topics include ordinary differential equations, symplectic integration of differential equations, and the use of wavelets when numerically solving differential equations.
Produktdetails
- Produktdetails
- Verlag: Academic Press / Elsevier Science & Technology
- Artikelnr. des Verlages: C2009-0-20860-9
- 3. Aufl.
- Englisch
- Abmessung: 43mm x 152mm x 232mm
- Gewicht: 1240g
- ISBN-13: 9780127843964
- ISBN-10: 0127843965
- Artikelnr.: 22154501
- Verlag: Academic Press / Elsevier Science & Technology
- Artikelnr. des Verlages: C2009-0-20860-9
- 3. Aufl.
- Englisch
- Abmessung: 43mm x 152mm x 232mm
- Gewicht: 1240g
- ISBN-13: 9780127843964
- ISBN-10: 0127843965
- Artikelnr.: 22154501
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.
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.
1. Definitions and Concepts
2. Transformations
3. Exact Analytical Methods
4. Exact Methods for ODEs
5. Exact Methods for PDEs
6. Approximate Analytical Methods
7. Numerical Methods: Concepts
8. Numerical Methods for ODEs
9. Numerical Methods for PDEs
2. Transformations
3. Exact Analytical Methods
4. Exact Methods for ODEs
5. Exact Methods for PDEs
6. Approximate Analytical Methods
7. Numerical Methods: Concepts
8. Numerical Methods for ODEs
9. Numerical Methods for PDEs
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. 47. Introduction to Exact Analytical Methods. 48. Look-Up
Technique. 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 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.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.
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. 47. Introduction to Exact Analytical Methods. 48. Look-Up
Technique. 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 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.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.
1. Definitions and Concepts
2. Transformations
3. Exact Analytical Methods
4. Exact Methods for ODEs
5. Exact Methods for PDEs
6. Approximate Analytical Methods
7. Numerical Methods: Concepts
8. Numerical Methods for ODEs
9. Numerical Methods for PDEs
2. Transformations
3. Exact Analytical Methods
4. Exact Methods for ODEs
5. Exact Methods for PDEs
6. Approximate Analytical Methods
7. Numerical Methods: Concepts
8. Numerical Methods for ODEs
9. Numerical Methods for PDEs
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. 47. Introduction to Exact Analytical Methods. 48. Look-Up
Technique. 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 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.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.
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. 47. Introduction to Exact Analytical Methods. 48. Look-Up
Technique. 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 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.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.