Elementary differential equations and boundary value problems:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Wiley
1977
|
| Ausgabe: | 3. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Getr. Zählung graph. Darst. |
| ISBN: | 0471093343 |
Internformat
MARC
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| 100 | 1 | |a Boyce, William E. |d 1930- |e Verfasser |0 (DE-588)11468409X |4 aut | |
| 245 | 1 | 0 | |a Elementary differential equations and boundary value problems |c William E. Boyce and Richard C. DiPrima |
| 250 | |a 3. ed. | ||
| 264 | 1 | |a New York [u.a.] |b Wiley |c 1977 | |
| 300 | |a Getr. Zählung |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Boundary value problems | |
| 650 | 4 | |a Differential equations | |
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| 650 | 0 | 7 | |a Gewöhnliche Differentialgleichung |0 (DE-588)4020929-5 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1804119872501710848 |
|---|---|
| adam_text | Contents
1. INTRODUCTION 1
1.1 Ordinary Differential Equations 2
1.2 Historical Remarks 5
2. FIRST ORDER DIFFERENTIAL EQUATIONS 11
2.1 Linear Equations 11
2.2 Further Discussion of Linear Equations 19
2.3 Nonlinear Equations 24
2.4 Separable Equations 31
2.5 Exact Equations 36
2.6 Integrating Factors 42
2.7 Homogeneous Equations 45
2.8 Miscellaneous Problems 49
2.9 Applications of First Order Equations 51
2.10 Elementary Mechanics 62
*2.11 The Existence and Uniqueness Theorem 70
Appendix. Derivation of Equation of Motion of a Body with
Variable Mass 80
3. SECOND ORDER LINEAR EQUATIONS 82
3.1 Introduction 82
3.2 Fundamental Solutions of the Homogeneous Equation 87
3.3 Linear Independence 96
3.4 Reduction of Order 99
3.5 Homogeneous Equations with Constant Coefficients 103
xi
xii Contents
3.5.1 Complex Roots 107
3.6 The Nonhomogeneous Problem 112
3.6.1 The Method of Undetermined Coefficients 115
3.6.2 The Method of Variation of Parameters 121
3.7 Mechanical Vibrations 127
3.7.1 Free Vibrations 130
3.7.2 Forced Vibrations 135
3.8 Electrical Networks 139
4. SERIES SOLUTIONS OF SECOND ORDER LINEAR
EQUATIONS 145
4.1 Introduction. Review of Power Series 145
4.2 Series Solutions Near an Ordinary Point, Part I 152
4.2.1 Series Solutions Near an Ordinary Point, Part II 161
4.3 Regular Singular Points 169
4.4 Euler Equations 174
4.5 Series Solutions Near a Regular Singular Point, Part I 179
4.5.1 Series Solutions Near a Regular Singular Point, Part II 186
*4.6 Series Solutions Near a Regular Singular Point; rx = r2
and r1 ri=N 192
*4.7 Bessel s Equation 195
5. HIGHER ORDER LINEAR EQUATIONS 207
5.1 Introduction 207
5.2 General Theory of wth Order Linear Equations 208
5.3 Homogeneous Equations with Constant Coefficients 213
5.4 The Method of Undetermined Coefficients 219
5.5 The Method of Variation of Parameters 222
6. THE LAPLACE TRANSFORM 226
6.1 Introduction. Definition of the Laplace Transform 226
6.2 Solution of Initial Value Problems 233
6.3 Step Functions 242
Contents xiii
6.3.1 A Differential Equation with a Discontinuous Forcing Function 249
6.4 Impulse Functions 252
6.5 The Convolution Integral 257
6.6 General Discussion and Summary 263
7. SYSTEMS OF FIRST ORDER LINEAR EQUATIONS 265
7.1 Introduction 265
7.2 Solution of Linear Systems by Elimination 272
7.3 Review of Matrices 277
7.4 Systems of Linear Algebraic Equations; Linear Independence,
Eigenvalues, Eigenvectors 287
7.5 Basic Theory of Systems of First Order Linear Equations 299
7.6 Homogeneous Linear Systems with Constant Coefficients 304
7.7 Complex Eigenvalues 312
7.8 Repeated Eigenvalues 317
7.9 Fundamental Matrices 324
7.10 Nonhomogeneous Linear Systems 329
8. NUMERICAL METHODS 336
8.1 Introduction 336
8.2 The Euler or Tangent Line Method 338
8.3 The Error 344
8.4 An Improved Euler Method 351
8.5 The Three Term Taylor Series Method 356
8.6 The Runge Kutta Method 358
8.7 Some Difficulties with Numerical Methods 363
8.8 A Multistep Method 367
8.9 Systems of First Order Equations 374
9. NONLINEAR DIFFERENTIAL EQUATIONS AND
STABILITY 378
9.1 Introduction 378
9.2 Solutions of Autonomous Systems 386
xiv Contents
9.3 The Phase Plane; Linear Systems 397
9.4 Stability; Almost Linear Systems 409
9.5 Competing Species and Predator Prey Problems 421
9.6 Liapounov s Second Method 434
*9.7 Periodic Solutions and Limit Cycles 443
10. PARTIAL DIFFERENTIAL EQUATIONS
AND FOURIER SERIES 452
10.1 Introduction 452
10.2 Heat Conduction and Separation of Variables 453
10.3 Fourier Series 461
10.4 The Fourier Theorem 470
10.5 Even and Odd Functions 476
10.6 Solution of Other Heat Conduction Problems 483
10.7 The Wave Equation; Vibrations of an Elastic String 491
10.8 Laplace s Equation * 503
Appendix A. Derivation of the Heat Conduction Equation 511
Appendix B. Derivation of the Wave Equation 515
11. BOUNDARY VALUE PROBLEMS AND
STURM LIOUVILLE THEORY 519
11.1 Introduction 519
11.2 Linear Homogeneous Boundary Value Problems; Eigenvalues
and Eigenfunctions 523
11.3 Sturm Liouville Boundary Value Problems 531
11.4 Nonhomogeneous Boundary Value Problems 544
*11.5 Singular Sturm Liouville Problems 560
* 11.6 Further Remarks on the Method of Separation of Variables;
A Bessel Series Expansion 568
*11.7 Series of Orthogonal Functions; Mean Convergence 574
ANSWERS TO PROBLEMS A l
INDEX 1 1
|
| any_adam_object | 1 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 3. ed. |
| format | Book |
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| language | English |
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| spelling | Boyce, William E. 1930- Verfasser (DE-588)11468409X aut Elementary differential equations and boundary value problems William E. Boyce and Richard C. DiPrima 3. ed. New York [u.a.] Wiley 1977 Getr. Zählung graph. Darst. txt rdacontent n rdamedia nc rdacarrier Boundary value problems Differential equations Randwertproblem (DE-588)4048395-2 gnd rswk-swf Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Gewöhnliche Differentialgleichung (DE-588)4020929-5 s DE-604 Differentialgleichung (DE-588)4012249-9 s Randwertproblem (DE-588)4048395-2 s 1\p DE-604 DiPrima, Richard C. 1927-1984 Verfasser (DE-588)114684103 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003550108&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 | Boyce, William E. 1930- DiPrima, Richard C. 1927-1984 Elementary differential equations and boundary value problems Boundary value problems Differential equations Randwertproblem (DE-588)4048395-2 gnd Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd Differentialgleichung (DE-588)4012249-9 gnd |
| subject_GND | (DE-588)4048395-2 (DE-588)4020929-5 (DE-588)4012249-9 (DE-588)4123623-3 |
| title | Elementary differential equations and boundary value problems |
| title_auth | Elementary differential equations and boundary value problems |
| title_exact_search | Elementary differential equations and boundary value problems |
| title_full | Elementary differential equations and boundary value problems William E. Boyce and Richard C. DiPrima |
| title_fullStr | Elementary differential equations and boundary value problems William E. Boyce and Richard C. DiPrima |
| title_full_unstemmed | Elementary differential equations and boundary value problems William E. Boyce and Richard C. DiPrima |
| title_short | Elementary differential equations and boundary value problems |
| title_sort | elementary differential equations and boundary value problems |
| topic | Boundary value problems Differential equations Randwertproblem (DE-588)4048395-2 gnd Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd Differentialgleichung (DE-588)4012249-9 gnd |
| topic_facet | Boundary value problems Differential equations Randwertproblem Gewöhnliche Differentialgleichung Differentialgleichung Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003550108&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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