Ordinary differential equations:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Wiley
1989
|
| Ausgabe: | 4. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XI, 339 S. |
| ISBN: | 0471860034 |
Internformat
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV008950818 | ||
| 003 | DE-604 | ||
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| 007 | t | ||
| 008 | 940206s1989 |||| 00||| eng d | ||
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| 100 | 1 | |a Birkhoff, Garrett |d 1911-1996 |e Verfasser |0 (DE-588)11882564X |4 aut | |
| 245 | 1 | 0 | |a Ordinary differential equations |c Garrett Birkhoff ; Gian-Carlo Rota |
| 250 | |a 4. ed. | ||
| 264 | 1 | |a New York [u.a.] |b Wiley |c 1989 | |
| 300 | |a XI, 339 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 0 | 7 | |a Differentialgleichung |0 (DE-588)4012249-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Gewöhnliche Differentialgleichung |0 (DE-588)4020929-5 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Gewöhnliche Differentialgleichung |0 (DE-588)4020929-5 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Differentialgleichung |0 (DE-588)4012249-9 |D s |
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| 700 | 1 | |a Rota, Gian-Carlo |d 1932-1999 |e Verfasser |0 (DE-588)119286416 |4 aut | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-005906331 | ||
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
Datensatz im Suchindex
| _version_ | 1804123284201013248 |
|---|---|
| adam_text | CONTENTS
1 FIRST ORDER OF DIFFERENTIAL EQUATIONS 1
1. Introduction 1
2. Fundamental Theorem of the Calculus 2
3. First order Linear Equations 7
4. Separable Equations 9
5. Quasilinear Equations; Implicit Solutions 11
6. Exact Differentials; Integrating Factors 15
7. Linear Fractional Equations 17
8. Graphical and Numerical Integration 20
9. The Initial Value Problem 24
*10. Uniqueness and Continuity 26
*11. A Comparison Theorem 29
*12. Regular and Normal Curve Families 31
2 SECOND ORDER LINEAR EQUATIONS 34
1. Bases of Solutions 34
2. Initial Value Problems 37
3. Qualitative Behavior, Stability 39
4. Uniqueness Theorem 40
5. The Wronskian 43
6. Separation and Comparison Theorems 47
7. The Phase Plane 49
8. Adjoint Operators; Lagrange Identity 54
9. Green s Functions 58
*10. Two endpoint Problems 63
*11. Green s Functions, II 65
3 LINEAR EQUATIONS WITH CONSTANT COEFFICIENTS 71
1. The Characteristic Polynomial 71
2. Complex Exponential Functions 72
3. The Operational Calculus 76
4. Solution Bases 78
5. Inhomogeneous Equations 83
vii
viii Contents
6. Stability 85
7. The Transfer Function 86
*8. The Nyquist Diagram 90
*9. The Green s Function 93
4 POWER SERIES SOLUTIONS 99
1. Introduction 99
2. Method of Undetermined Coefficients 101
3. More Examples 105
4. Three First order DEs 107
5. Analytic Functions 110
6. Method of Majorants 113
*7. Sine and Cosine Functions 116
*8. Bessel Functions 117
9. First order Nonlinear DEs 121
10. Radius of Convergence 124
*11. Method of Majorants, II 126
*12. Complex Solutions 128
5 PLANE AUTONOMOUS SYSTEMS 131
1. Autonomous Systems 131
2. Plane Autonomous Systems 134
3. The Phase Plane, II 136
4. Linear Autonomous Systems 141
5. Linear Equivalence 144
6. Equivalence Under Diffeomorphisms 151
7. Stability 153
8. Method of Liapunov 157
9. Undamped Nonlinear Oscillations 158
10. Soft and Hard Springs 159
11. Damped Nonlinear Oscillations 163
*12. Limit Cycles 164
6 EXISTENCE AND UNIQUENESS THEOREMS 170
1. Introduction 170
2. Lipschitz conditions 172
3. Well posed Problems 174
4. Continuity 177
*5. Normal Systems 180
6. Equivalent Integral Equation 183
7. Successive Approximation 185
8. Linear Systems 188
9. Local Existence Theorem 190
Contents ix
*10. The Peano Existence Theorem 191
*11. Analytic Equations 193
*12. Continuation of Solutions 197
*13. The Perturbation Equation 198
7 APPROXIMATE SOLUTIONS 204
1. Introduction 204
2. Error Bounds 205
*3. Deviation and Error 207
4. Mesh halving; Richardson Extrapolation 210
5. Midpoint Quadrature 212
6. Trapezoidal Quadrature 215
*7. Trapezoidal Integration 218
8. The Improved Euler Method 222
*9. The Modified Euler Method 224
*10. Cumulative Error Bound 226
8 EFFICIENT NUMERICAL INTEGRATION 230
1. Difference Operators 230
2. Polynomial Interpolation 232
*3. Interpolation Errors 235
4. Stability 237
*5. Numerical Differentiation; Roundoff 240
*6. Higher Order Quadrature 244
*7. Gaussian Quadrature 248
8. Fourth order Runge Kutta 250
*9. Milne s Method 256
*10. Multistep Methods 258
9 REGULAR SINGULAR POINTS 261
1. Introduction 261
*2. Movable Singular Points 263
3. First order Linear Equations 264
4. Continuation Principle; Circuit Matrix 268
5. Canonical Bases 270
6. Regular Singular Points 274
7. Bessel Equation 276
8. The Fundamental Theorem 281
*9. Alternative Proof of the Fundamental Theorem 285
*10. Hypergeometric Functions 287
*11. The Jacobi Polynomials 289
*12. Singular Points at Infinity 292
*13. Fuchsian Equations 294
x Contents
10 STURM LIOUVILLE SYSTEMS 300
1. Sturm Liouville Systems 300
2. Sturm Liouville Series 302
*3. Physical Interpretations 305
4. Singular Systems 308
5. Priifer Substitution 312
6. Sturm Comparison Theorem 313
7. Sturm Oscillation Theorem 314
8. The Sequence of Eigenfunctions 318
9. The Liouville Normal Form 320
10. Modified Priifer Substitution 323
*11. The Asymptotic Behavior of Bessel Functions 326
12. Distribution of Eigenvalues 328
13. Normalized Eigenfunctions 329
14. Inhomogeneous Equations 333
15. Green s Functions 334
*16. The Schroedinger Equation 336
*17. The Square well Potential 338
*18. Mixed Spectrum 339
11 EXPANSIONS IN EIGENFUNCTIONS 344
1. Fourier Series 344
2. Orthogonal Expansions 346
3. Mean square Approximation 347
4. Completeness 350
5. Orthogonal Polynomials 352
*6. Properties of Orthogonal Polynomials 354
*7. Chebyshev Polynomials 358
8. Euclidean Vector Spaces 360
9. Completeness of Eigenfunctions 363
*10. Hilbert Space 365
*11. Proof of Completeness 367
APPENDIX A: LINEAR SYSTEMS 371
1. Matrix Norm 371
2. Constant coefficient Systems 372
3. TheMatrizant 375
4. Floquet Theorem; Canonical Bases 377
APPENDIX B: BIFURCATION THEORY 380
1. What Is Bifurcation? 380
*2. Poincare Index Theorem 381
Contents xi
3. Hamiltonian Systems 383
4. Hamiltonian Bifurcations 386
5. Poincare Maps 387
6. Periodically Forced Systems 389
BIBLIOGRAPHY 392
INDEX 395
|
| any_adam_object | 1 |
| author | Birkhoff, Garrett 1911-1996 Rota, Gian-Carlo 1932-1999 |
| author_GND | (DE-588)11882564X (DE-588)119286416 |
| author_facet | Birkhoff, Garrett 1911-1996 Rota, Gian-Carlo 1932-1999 |
| author_role | aut aut |
| author_sort | Birkhoff, Garrett 1911-1996 |
| author_variant | g b gb g c r gcr |
| building | Verbundindex |
| bvnumber | BV008950818 |
| classification_rvk | SK 520 |
| ctrlnum | (OCoLC)632331196 (DE-599)BVBBV008950818 |
| discipline | Mathematik |
| edition | 4. ed. |
| format | Book |
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| id | DE-604.BV008950818 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:27:19Z |
| institution | BVB |
| isbn | 0471860034 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-005906331 |
| oclc_num | 632331196 |
| open_access_boolean | |
| owner | DE-29T DE-19 DE-BY-UBM DE-83 DE-188 |
| owner_facet | DE-29T DE-19 DE-BY-UBM DE-83 DE-188 |
| physical | XI, 339 S. |
| publishDate | 1989 |
| publishDateSearch | 1989 |
| publishDateSort | 1989 |
| publisher | Wiley |
| record_format | marc |
| spelling | Birkhoff, Garrett 1911-1996 Verfasser (DE-588)11882564X aut Ordinary differential equations Garrett Birkhoff ; Gian-Carlo Rota 4. ed. New York [u.a.] Wiley 1989 XI, 339 S. txt rdacontent n rdamedia nc rdacarrier Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd rswk-swf Gewöhnliche Differentialgleichung (DE-588)4020929-5 s DE-604 Differentialgleichung (DE-588)4012249-9 s 1\p DE-604 Rota, Gian-Carlo 1932-1999 Verfasser (DE-588)119286416 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005906331&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 | Birkhoff, Garrett 1911-1996 Rota, Gian-Carlo 1932-1999 Ordinary differential equations Differentialgleichung (DE-588)4012249-9 gnd Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd |
| subject_GND | (DE-588)4012249-9 (DE-588)4020929-5 |
| title | Ordinary differential equations |
| title_auth | Ordinary differential equations |
| title_exact_search | Ordinary differential equations |
| title_full | Ordinary differential equations Garrett Birkhoff ; Gian-Carlo Rota |
| title_fullStr | Ordinary differential equations Garrett Birkhoff ; Gian-Carlo Rota |
| title_full_unstemmed | Ordinary differential equations Garrett Birkhoff ; Gian-Carlo Rota |
| title_short | Ordinary differential equations |
| title_sort | ordinary differential equations |
| topic | Differentialgleichung (DE-588)4012249-9 gnd Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd |
| topic_facet | Differentialgleichung Gewöhnliche Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005906331&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT birkhoffgarrett ordinarydifferentialequations AT rotagiancarlo ordinarydifferentialequations |