Partial differential equations and mathematica:
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton [u.a.]
CRC Press
1997
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | 2. Aufl. u.d.T.: Kythe, Prem K.: Partial differential equations and boundary value problems with Mathematica |
| Physical Description: | XX, 378 S. graph. Darst. |
| ISBN: | 0849378532 |
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Record in the Search Index
| _version_ | 1804125955533307904 |
|---|---|
| adam_text | Contents
Preface, vii
Introduction to Mathematica, xiii
Chapter 1: Introduction, 1
1.1. Notation and Definitions, 1
1.2. Initial and Boundary Conditions, 3
1.3. Classification of Second Order Equations, 4
1.4. Some Known Equations, 7
1.5. Superposition Principle, 17
1.6. Exercises, 19
Chapter 2: Method of Characteristics, 22
First Order Equations, 22
2.1. Linear Equations with Constant Coefficients, 22
2.2. Linear Equations with Variable Coefficients, 28
2.3. First Order Quasi linear Equations, 33
2.4. First Order Nonlinear Equations, 38
2.5. Geometrical Considerations, 46
2.6. Some Theorem on Characteristics, 47
Second Order Equations, 49
2.7. Linear and Quasi linear Equations, 49
2.8. Exercises, 56
iii
iv CONTENTS
Chapter 3: Linear Equations with Constant Coefficients, 63
3.1. Inverse Operators, 63
3.2. Homogeneous Equations, 72
3.3. Nonhomogeneous Equations, 74
3.4. Exercises, 79
Chapter 4: Orthogonal Expansions, 82
4.1. Orthogonality, 82
4.2. Orthogonal Polynomials, 85
4.3. Series of Orthogonal Functions, 88
4.4. Trigonometric Fourier Series, 90
4.5. Eigenfunction Expansions, 103
4.6. Bessel Functions, 106
4.7. Exercises, 110
Chapter 5: Separation of Variables, 117
5.1. Introduction, 117
5.2. Hyperbolic Equation, 118
5.3. Parabolic Equation, 125
5.4. Elliptic Equation, 132
5.5. Cylindrical Coordinates, 142
5.6. Spherical Coordinates, 144
5.7. Nonhomogeneous Problems, 146
5.8. Exercises, 152
Chapter 6: Integral Transforms, 160
Laplace Transforms, 162
6.1. Notation, 162
6.2. Basic Laplace Transforms, 164
6.3. Inversion Theorem, 183
6.4. Exercises, 189
Fourier Transforms, 195
6.5. Fourier Integral Theorems, 195
6.6. Properties of Fourier Transforms, 196
6.7. Fourier Sine and Cosine Transforms, 204
6.8. Finite Fourier Transforms, 210
6.9. Exercises, 213
Chapter 7: Green s Functions, 217
7.1. Definitions, 217
7.2. Parabolic Equations, 231
7.3. Elliptic Equations, 238
7.4. Hyperbolic Equations, 244
CONTENTS v
7.5. Applications, 249
7.6. Exercises, 252
Chapter 8: Weighted Residual Methods, 266
8.1. Line Integrals, 267
8.2. Variational Notation, 270
8.3. Multiple Integrals, 273
8.4. Weak Variational Formulation, 274
8.5. Galerkin Method, 279
8.6. Rayleigh Ritz Method, 283
8.7. Choice of Test Functions, 287
8.8. Transient Problems, 292
8.9. Other Methods, 295
8.10. Exercises, 296
Chapter 9: Perturbation Methods, 305
9.1. Taylor Series Expansions, 306
9.2. Successive Approximations, 309
9.3. Boundary Perturbations, 311
9.4. Exercises, 314
Chapter 10: Finite Differences, 321
10.1. Finite Difference Schemes, 321
10.2. First Order Equations, 325
10.3. Second Order Equations, 328
10.4. Exercises, 343
Appendix A: Green s Identities, 350
A.I. Green s Identities, 350
A.2. Exercises, 352
Appendix B: Tables of Transform Pairs, 354
Appendix C: Glossary of Mathematica Functions, 361
Appendix D: Mathematica Packages and Notebooks, 368
Bibliography, 369
Index, 373
|
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| author | Kythe, Prem K. 1930- Puri, Pratap Schäferkotter, Michael R. |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| spelling | Kythe, Prem K. 1930- Verfasser (DE-588)12072362X aut Partial differential equations and mathematica Prem K. Kythe ; Pratap Puri ; Michael R. Schäferkotter Boca Raton [u.a.] CRC Press 1997 XX, 378 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier 2. Aufl. u.d.T.: Kythe, Prem K.: Partial differential equations and boundary value problems with Mathematica Mathematica (Computer file) Mathematica (logiciel) ram Équations aux dérivées partielles ram Differential equations, Partial Mathematica Programm (DE-588)4268208-3 gnd rswk-swf Randwertproblem (DE-588)4048395-2 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 s Mathematica Programm (DE-588)4268208-3 s DE-604 Randwertproblem (DE-588)4048395-2 s 1\p DE-604 Puri, Pratap Verfasser aut Schäferkotter, Michael R. Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007693231&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Kythe, Prem K. 1930- Puri, Pratap Schäferkotter, Michael R. Partial differential equations and mathematica Mathematica (Computer file) Mathematica (logiciel) ram Équations aux dérivées partielles ram Differential equations, Partial Mathematica Programm (DE-588)4268208-3 gnd Randwertproblem (DE-588)4048395-2 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd |
| subject_GND | (DE-588)4268208-3 (DE-588)4048395-2 (DE-588)4044779-0 |
| title | Partial differential equations and mathematica |
| title_auth | Partial differential equations and mathematica |
| title_exact_search | Partial differential equations and mathematica |
| title_full | Partial differential equations and mathematica Prem K. Kythe ; Pratap Puri ; Michael R. Schäferkotter |
| title_fullStr | Partial differential equations and mathematica Prem K. Kythe ; Pratap Puri ; Michael R. Schäferkotter |
| title_full_unstemmed | Partial differential equations and mathematica Prem K. Kythe ; Pratap Puri ; Michael R. Schäferkotter |
| title_short | Partial differential equations and mathematica |
| title_sort | partial differential equations and mathematica |
| topic | Mathematica (Computer file) Mathematica (logiciel) ram Équations aux dérivées partielles ram Differential equations, Partial Mathematica Programm (DE-588)4268208-3 gnd Randwertproblem (DE-588)4048395-2 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd |
| topic_facet | Mathematica (Computer file) Mathematica (logiciel) Équations aux dérivées partielles Differential equations, Partial Mathematica Programm Randwertproblem Partielle Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007693231&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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