Differential equations:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Wiley
1984
|
| Edition: | 3. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VII, 807 S. graph. Darst. |
| ISBN: | 0471032948 0471814504 |
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Record in the Search Index
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|---|---|
| adam_text | DIFFERENTIAL
EQUATIONS
Third Edition
Shepley L Ross
University of j ew Hampshire
John Wiley amp; Sons
New York • Chichester • Brisbane • Toronto • Singapore
CONTENTS
PART ONE FUNDAMENTAL METHODS AND APPLICATIONS
One Differential Equations and Their Solutions 3
1 1 Classification of Differential Equations; Their Origin and Application 3
1 2 Solutions 7
1 3— Initial-Value Problems, Boundary-Value Problems, and Existence of Solutions 15
Two First-Order Equations for Which Exact Solutions Are Obtainable 25
2 1 Exact Differential Equations and Integrating Factors 25
2 2 Separable Equations and Equations Reducible to This Form 39
2 3 Linear Equations and Bernoulli Equations 49
2 4 Special Integrating Factors and Transformations 61
Three Applications of First-Order Equations 70
3 1 Orthogonal and Oblique Trajectories 70
3 2 Problems in Mechanics 77
3 3 Rate Problems 89
Four Explicit Methods of Solving Higher-Order Linear
Differential Equations 102
4 1 Basic Theory of Linear Differential Equations 102
4 2 The Homogeneous Linear Equation with Constant Coefficients 125
V
VI CONTENTS
4 3 The Method of Undetermined Coefficients 137
4 4 Variation of Parameters 155
4 5 The Cauchy-Euler Equation 164
4 6 Statements and Proofs of Theorems on the Second-Order Homogeneous Linear
Equation 170
Five 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 206
5 6 Electric Circuit Problems 211
Six Series Solutions of Linear Differential Equations 221
6 1 Power Series Solutions About an Ordinary Point 221
6 2 Solutions About Singular Points; The Method of Frobenius 233
6 3 Bessel s Equation and Bessel Functions 252
Seven Systems of Linear Differential Equations 264
7 1 Differential Operators and an Operator Method 264
7 2 Applications 278
7 3 Basic Theory of Linear Systems in Normal Form: Two Equations in Two Unknown
Functions 290
7 4 Homogeneous Linear Systems with Constant Coefficients: Two Equations in Two
Unknown-FunctiQns 301
7 5 Matrices and Vectors — 312
7 6 The Matrix Method for Homogeneous Linear Systems with Constant Coefficients:
Two Equations in Two Unknown Functions 346
7 7 The Matrix Method for Homogeneous Linear Systems with Constant Coefficients:
n Equations in n Unknown Functions 355
Eight Approximate Methods of Solving First-Order Equations 377
8 1 Graphical Methods 377
8 2 Power Series Methods 384
8 3 The Method of Successive Approximations 390
8 4 Numerical Methods 394
Nine The Laplace Transform 411
9 1 Definition, Existence, and Basic Properties of the Laplace Transform 411
9 2 The Inverse Transform and the Convolution 431
9 3 Laplace Transform Solution of Linear Differential Equations with Constant
Coefficients 441
9 4 Laplace Transform Solution of Linear Systems 453
• •
CONTENTS VII
PART TWO FUNDAMENTAL THEORY AND FURTHER METHODS
Ten Existence and Uniqueness Theory 461
10 1 Some Concepts from Real Function Theory 461
10 2 The Fundamental Existence and Uniqueness Theorem 473
10 3 Dependence of Solutions on Initial Conditions and on the Function f 488
10 4 Existence and Uniqueness Theorems for Systems and Higher-Order Equations 495
Eleven The Theory of Linear Differential Equations 505
11 1 Introduction 505
11 2 Basic Theory of the Homogeneous Linear System 510
11 3 Further Theory of the Homogeneous Linear System 522
11 4 The Nonhomogeneous Linear System 533
11 5 Basic Theory of the nth-Order Homogeneous Linear Differential Equation 543
11 6 Further Properties of the nth-Order Homogeneous Linear Differential Equation 558
11 7 The nth-Order Nonhomogeneous Linear Equation 569
11 8 Sturm Theory 573
Twelve Sturm-Liouville Boundary-Value Problems and Fourier Series 588
12 1 Sturm-Liouville Problems 588
12 2 Orthogonality of Characteristic Functions 597
12 3 The Expansion of a Function in a Series of Orthonormal Functions 601
12 4 Trigonometric Fourier Series 608
Thirteen Nonlinear Differential Equations 632
13 1 Phase Plane, Paths, and Critical Points 632
13 2 Critical Points and Paths of Linear Systems 644
13 3 Critical Points and Paths of Nonlinear Systems 658
13 4 Limit Cycles and Periodic Solutions 692
13 5 The Method of Kryloff and Bogoliuboff 707
Fourteen Partial Differential Equations 715
14 1 Some Basic Concepts and Examples 715
14 2 The Method of Separation of Variables 722
14 3 Canonical Forms of Second-Order Linear Equations with Constant Coefficients 743
14 4 An Initial-Value Problem; Characteristics 757
Appendices 771
Answers 777
Suggested Reading 801
Index 803
|
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| illustrated | Illustrated |
| indexdate | 2024-07-09T15:40:28Z |
| institution | BVB |
| isbn | 0471032948 0471814504 |
| language | English |
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| physical | VII, 807 S. graph. Darst. |
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| spelling | Ross, Shepley L. Verfasser aut Differential equations Shepley L. Ross 3. ed. New York [u.a.] Wiley 1984 VII, 807 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Differential equations 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 HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001382083&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ross, Shepley L. Differential equations 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 | Differential equations |
| title_auth | Differential equations |
| title_exact_search | Differential equations |
| title_full | Differential equations Shepley L. Ross |
| title_fullStr | Differential equations Shepley L. Ross |
| title_full_unstemmed | Differential equations Shepley L. Ross |
| title_short | Differential equations |
| title_sort | differential equations |
| topic | Differential equations Differentialgleichung (DE-588)4012249-9 gnd Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd |
| topic_facet | Differential equations Differentialgleichung Gewöhnliche Differentialgleichung |
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