Systems of ordinary differential equations: an introduction
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York, NY u.a.
Harper & Row
1972
|
| Series: | Harper's series in modern mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 315 S. |
| ISBN: | 0060423846 |
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MARC
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| 100 | 1 | |a Goldberg, Jack L. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Systems of ordinary differential equations |b an introduction |c Jack L. Goldberg ; Arthur J. Schwartz |
| 264 | 1 | |a New York, NY u.a. |b Harper & Row |c 1972 | |
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Record in the Search Index
| _version_ | 1804117094665551872 |
|---|---|
| adam_text | CONTENTS
Preface xi
CHAPTER 1 VECTORS AND MATRICES
1.1. The Solution of Simultaneous Equations 1
1.2. The Arithmetic of Matrices 4
1.3. Matrix Multiplication 8
1.4. The Inverse of a Matrix 13
1.5. Determinants of n X n Matrices 19
1.6. Vector Spaces of « Tuples 26
1.7. Linear Independence 30
1.8. Bases and Dimension 34
1.9.* Vector Norms 40
1.10.* Matrix and Vector Calculus 45
CHAPTER 2 LINEAR HOMOGENEOUS SYSTEMS AND EIGENVECTORS
2.1. The First Order Equation in One Dimension 50
2.2. The Origin of Linear Systems of Linear Differential
Equations 52
2.3. Eigenvalues, Eigenvectors, and Systems of Equations 56
2.4. Initial Value Problems 62
2.5. Symmetric Matrices 71
2.6. Dilute Solutions: A Symmetric Example 73
2.7. Complex Eigenvalues and Eigenvectors 76
2.8. A Summary 79
vii
viii Contents
CHAPTER 3 LINEAR SYSTEMS AND ROOT VECTORS
3.1. New Solutions of x = Ax 82
3.2. Root Vectors 87
3.3. The Root Vector and Solutions of x = Ax 94
3.4. A Recapitulation 102
3.5. Another View of the Initial Value Problem 104
3.6.* The General Theory 110
3.7. Electrical Networks 117
CHAPTER 4 APPLICATIONS OF THE THEORY OF THE HOMOGENEOUS
EQUATION
4.1. Fundamental Matrices 123
4.2. The Uniqueness Theorem 130
4.3. Some Consequences of the Uniqueness Theorem 135
4.4. The Inhomogeneous Problem: Variation of
Parameters 140
4.5. The Inhomogeneous Problem: Some Special Methods 145
4.6.* Gronwall s Inequality 150
4.7.* The Growth of Solutions 153
CHAPTER 5 HIGHER ORDER EQUATIONS
5.1. The nth Order Linear Equation in One Variable 156
5.2. The Companion System 157
5.3. The Auxiliary Equation: Distinct Roots 164
5.4. The Auxiliary Equation: Repeated Roots 170
5.5.* The General Theory of the rcth Order Linear Equation with
Constant Coefficients 173
5.6.* An Example from Mechanics 180
5.7.* The General System of Second Order Equations 181
5.8.* An Important Special Case 187
CHAPTER 6 AN INTRODUCTION TO THE THEORY OF ANALYTIC
DIFFERENTIAL SYSTEMS
6.1. Introduction 192
6.2. Power Series Expansions of Analytic Functions 194
6.3. Series Solutions of x = A (t) x 201
6.4. The Legendre Equation: An Example of the Ordinary Point
for One Dimensional Equations 209
6.5. The Exponential of a Matrix 211
6.6.* The Regular Singular Point 215
6.7.* The Bessel Equation 223
Contents ix
CHAPTER 7 AN INTRODUCTION TO NONLINEAR EQUATIONS
7.1. What is a Nonlinear Equation? 227
7.2. Some Predators and Their Prey 229
7.3. Nonlinear Equations in One Dimension 231
7.4. The Euler Method in One Dimension: An Example 234
7.5. The Euler Method 236
7.6.* Existence and Uniqueness 240
7.7.* The Accuracy of the Euler Method 244
CHAPTER 8 TWO DIMENSIONAL AUTONOMOUS SYSTEMS:
AN INTRODUCTION TO THE QUALITATIVE THEORY OF
DIFFERENTIAL EQUATIONS
8.1. Introduction: The Phase Plane 249
8.2. Orbits and Their Properties: I 252
8.3. Orbits and Their Properties: II 256
8.4. The Geometry of Critical Points of x = Ax 261
8.5. Stability of Critical Points 270
8.6. Perturbations of Linear Systems 274
8.7.* The Equation of First Variation 284
8.8.* Stability of Periodic Orbits 289
Answers to Odd Numbered Problems 292
Index 313
|
| any_adam_object | 1 |
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| id | DE-604.BV002741759 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:48:56Z |
| institution | BVB |
| isbn | 0060423846 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001753012 |
| oclc_num | 375531 |
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| physical | XIII, 315 S. |
| publishDate | 1972 |
| publishDateSearch | 1972 |
| publishDateSort | 1972 |
| publisher | Harper & Row |
| record_format | marc |
| series2 | Harper's series in modern mathematics |
| spelling | Goldberg, Jack L. Verfasser aut Systems of ordinary differential equations an introduction Jack L. Goldberg ; Arthur J. Schwartz New York, NY u.a. Harper & Row 1972 XIII, 315 S. txt rdacontent n rdamedia nc rdacarrier Harper's series in modern mathematics Équations différentielles Differential equations Schwartz, Arthur J. Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001753012&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Goldberg, Jack L. Schwartz, Arthur J. Systems of ordinary differential equations an introduction Équations différentielles Differential equations |
| title | Systems of ordinary differential equations an introduction |
| title_auth | Systems of ordinary differential equations an introduction |
| title_exact_search | Systems of ordinary differential equations an introduction |
| title_full | Systems of ordinary differential equations an introduction Jack L. Goldberg ; Arthur J. Schwartz |
| title_fullStr | Systems of ordinary differential equations an introduction Jack L. Goldberg ; Arthur J. Schwartz |
| title_full_unstemmed | Systems of ordinary differential equations an introduction Jack L. Goldberg ; Arthur J. Schwartz |
| title_short | Systems of ordinary differential equations |
| title_sort | systems of ordinary differential equations an introduction |
| title_sub | an introduction |
| topic | Équations différentielles Differential equations |
| topic_facet | Équations différentielles Differential equations |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001753012&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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