Introduction to ordinary differential equations:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Wiley
1989
|
| Edition: | 4. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 609 S. graph. Darst. |
| ISBN: | 0471098817 |
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MARC
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| 245 | 1 | 0 | |a Introduction to ordinary differential equations |c Shepley L. Ross |
| 250 | |a 4. ed. | ||
| 264 | 1 | |a New York [u.a.] |b Wiley |c 1989 | |
| 300 | |a XI, 609 S. |b graph. Darst. | ||
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Record in the Search Index
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| adam_text | Contents
1 Differential Equations and Their Solutions 1
1.1 Classification of Differential Equations; Their Origin and
Application 1
1.2 Solutions 6
1.3 Initial Value Problems, Boundary Value Problems, and
Existence of Solutions 14
2 First Order Equations for Which Exact Solutions
Are Obtainable 24
2.1 Exact Differential Equations and Integrating Factors 24
2.2 Separable Equations and Equations Reducible to This Form 38
2.3 Linear Equations and Bernoulli Equations 48
2.4 Special Integrating Factors and Transformations 60
3 Applications of First Order Equations 71
3.1 Orthogonal and Oblique Trajectories 71
3.2 Problems in Mechanics 78
3.3 Rate Problems 91
4 Explicit Methods of Solving Higher Order Linear
Differential Equations 110
4.1 Basic Theory of Linear Differential Equations 110
4.2 The Homogeneous Linear Equation with Constant Coefficients 134
4.3 The Method of Undetermined Coefficients 145
4.4 Variation of Parameters 162
4.5 The Cauchy Euler Equation 171
ix
X CONTENTS
4.6 Statements and Proofs of Theorems on the Second Order
Homogeneous Linear Equation 177
5 Applications of Second Order Linear Differential Equations
with Constant Coefficients 189
5.1 The Differential Equation of the Vibrations of a Mass on a
Spring 189
5.2 Free, Undamped Motion 192
5.3 Free, Damped Motion 200
5.4 Forced Motion 212
5.5 Resonance Phenomena 219
5.6 Electric Circuit Problems 224
6 Series Solutions of Linear Differential Equations 237
6.1 Power Series Solutions About an Ordinary Point 237
6.2 Solutions About Singular Points; The Method of Frobenius 250
6.3 Bessel s Equation and Bessel Functions 270
7 Systems of Linear Differential Equations 283
7.1 Differential Operators and an Operator Method 283
7.2 Applications 297
7.3 Basic Theory of Linear Systems in Normal Form: Two
Equations in Two Unknown Functions 308
7.4 Homogeneous Linear Systems with Constant Coefficients: Two
Equations in Two Unknown Functions 319
7.5 Matrices and Vectors 331
7.6 The Matrix Method for Homogeneous Linear Systems with
Constant Coefficients: Two Equations in Two Unknown
Functions 368
7.7 The Matrix Method for Homogeneous Linear Systems with
Constant Coefficients: n Equations in n Unknown Functions 378
7.8 Statements and Proofs of Basic Theorems on Homogeneous
Linear Systems 402
8 Approximate Methods of Solving First Order Equations 417
8.1 Graphical Methods 417
8.2 Power Series Methods 428
8.3 The Method of Successive Approximations 434
8.4 Numerical Methods I: The Euler Method 438
8.5 Numerical Methods II: The Improved Euler Method 449
8.6 Numerical Methods III: The Runge Kutta Method 455
8.7 Numerical Method* IV: The Adams Bashforth/Adams
Moulton (ABAM) Method 463
8.8 Numerical Methods V: Higher Order Equations; Systems 469
CONTENTS Xi
9 The Laplace Transform 480
9.1 Definition, Existence, and Basic Properties of the Laplace
Transform 480
9.2 The Inverse Transform and the Convolution 497
9.3 Laplace Transform Solution of Linear Differential Equations
with Constant Coefficients 510
9.4 Laplace Transform Solution of Linear Differential Equations
With Discontinuous Nonhomogeneous Terms 520
9.5 Laplace Transform Solution of Linear Systems 539
Appendix 1 547
Appendix 2 551
Appendix 3 556
Suggested Reading 558
Answers to Odd Numbered Exercises 559
Index 605
|
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| indexdate | 2024-07-09T17:12:16Z |
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| isbn | 0471098817 |
| language | English |
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| physical | XI, 609 S. graph. Darst. |
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| spelling | Ross, Shepley L. Verfasser aut Introduction to ordinary differential equations Shepley L. Ross 4. ed. New York [u.a.] Wiley 1989 XI, 609 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Equations différentielles ram Differential equations Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 gnd rswk-swf 1\p (DE-588)4151278-9 Einführung gnd-content Gewöhnliche Differentialgleichung (DE-588)4020929-5 s DE-604 Differentialgleichung (DE-588)4012249-9 s 2\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005240669&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 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Ross, Shepley L. Introduction to ordinary differential equations Equations différentielles ram Differential equations Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd Differentialgleichung (DE-588)4012249-9 gnd |
| subject_GND | (DE-588)4020929-5 (DE-588)4012249-9 (DE-588)4151278-9 |
| title | Introduction to ordinary differential equations |
| title_auth | Introduction to ordinary differential equations |
| title_exact_search | Introduction to ordinary differential equations |
| title_full | Introduction to ordinary differential equations Shepley L. Ross |
| title_fullStr | Introduction to ordinary differential equations Shepley L. Ross |
| title_full_unstemmed | Introduction to ordinary differential equations Shepley L. Ross |
| title_short | Introduction to ordinary differential equations |
| title_sort | introduction to ordinary differential equations |
| topic | Equations différentielles ram Differential equations Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd Differentialgleichung (DE-588)4012249-9 gnd |
| topic_facet | Equations différentielles Differential equations Gewöhnliche Differentialgleichung Differentialgleichung Einführung |
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