Introduction to ordinary differential equations:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York u.a.
Wiley
1980
|
| Edition: | 3. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 503 S. graph. Darst. |
| ISBN: | 0471032956 |
Staff View
MARC
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| 100 | 1 | |a Ross, Shepley L. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Introduction to ordinary differential equations |
| 250 | |a 3. ed. | ||
| 264 | 1 | |a New York u.a. |b Wiley |c 1980 | |
| 300 | |a 503 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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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 5
1.3 Initial Value Problems, Boundary Value Problems, and Existence of
Solutions 13
2 FIRST ORDER EQUATIONS FOR WHICH EXACT SOLUTIONS ARE OBTAINABLE 23
2.1 Exact Differential Equations and Integrating Factors 23
2.2 Separable Equations and Equations Reducible to This Form 37
2.3 Linear Equations and Bernoulli Equations 47
2.4 Special Integrating Factors and Transformations 60
3 APPLICATIONS OF FIRST ORDER EQUATIONS 69
3.1 Orthogonal and Oblique Trajectories 69
3.2 Problems in Mechanics 76
3.3 Rate Problems 88
4 EXPLICIT METHODS OF SOLVING HIGHER ORDER LINEAR DIFFERENTIAL
EQUATIONS 101
4.1 Basic Theory of Linear Differential Equations 101
4.2 The Homogeneous Linear Equation with Constant Coefficients 124
4.3 The Method of Undetermined Coefficients 136
4.4 Variation of Parameters 154
4.5 The Cauchy— Euler Equation 164
4.6 Statements and Proofs of Theorems on the Second Order Homogeneous
Linear Equation 170
5 APPLICATIONS OF SECOND ORDER LINEAR DIFFERENTIAL EQUATIONS WITH
CONSTANT COEFFICIENTS 179
5.1 The Differential Equation of the Vibrations of a Mass on a Spring 179
5.2 Free, Undamped Motion 182
5.3 Free, Damped Motion 189
5.4 Forced Motion 199
5.5 Resonance Phenomena 207
5.6 Electric Circuit Problems 212
6 SERIES SOLUTIONS OF LINEAR DIFFERENTIAL EQUATIONS 222
6.1 Power Series Solutions About an Ordinary Point 222
6.2 Solutions About Singular Points; the Method of Frobenius 234
6.3 Bessel s Equation and Bessel Functions 254
7 SYSTEMS OF LINEAR DIFFERENTIAL EQUATIONS 265
7.1 Differential Operators and an Operator Method 265
7.2 Applications 280
7.3 Basic Theory of Linear Systems in Normal Form: Two Equations in Two
Unknown Functions 291
7.4 Homogeneous Linear Systems with Constant Coefficients: Two Equations
in Two Unknown Functions 302
7.5 Matrices and Vectors 313
7.6 Basic Theory of Linear Systems in Normal Form: n Equations in
n Unknown Functions 344
7.7 Homogeneous Linear Systems with Constant Coefficients: n Equations in
n Unknown Functions 379
8 APPROXIMATE METHODS OF SOLVING FIRST ORDER EQUATIONS 392
8.1 Graphical Methods 392
8.2 Power Series Methods 399
8.3 The Method of Successive Approximations 406
8.4 Numerical Methods 409
9 THE LAPLACE TRANSFORM 427
9.1 Definition, Existence, and Basic Properties of the Laplace Transform 427
9.2 The Inverse Transform and the Convolution 448
9.3 Laplace Transform Solution of Linear Differential Equations with
Constant Coefficients 457
9.4 Laplace Transform Solution of Linear Systems 470
Appendices 475
Suggested Reading 481
Answers 482
Index 501
|
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| indexdate | 2024-07-09T15:38:38Z |
| institution | BVB |
| isbn | 0471032956 |
| language | English |
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| physical | 503 S. graph. Darst. |
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| spelling | Ross, Shepley L. Verfasser aut Introduction to ordinary differential equations 3. ed. New York u.a. Wiley 1980 503 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Équations différentielles Differential equations Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Gewöhnliche Differentialgleichung (DE-588)4020929-5 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=001303643&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 Équations différentielles 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 (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 |
| title_fullStr | Introduction to ordinary differential equations |
| title_full_unstemmed | Introduction to ordinary differential equations |
| title_short | Introduction to ordinary differential equations |
| title_sort | introduction to ordinary differential equations |
| topic | Équations différentielles Differential equations Differentialgleichung (DE-588)4012249-9 gnd Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd |
| topic_facet | Équations différentielles Differential equations Differentialgleichung Gewöhnliche Differentialgleichung Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001303643&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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