An introduction to the theory of ordinary differential equations:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Belmont, Calif.
Wadsworth
1976
|
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 249 S. |
| ISBN: | 0534004326 |
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MARC
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| 100 | 1 | |a Leighton, Walter |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a An introduction to the theory of ordinary differential equations |c Walter Leighton |
| 264 | 1 | |a Belmont, Calif. |b Wadsworth |c 1976 | |
| 300 | |a XII, 249 S. | ||
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Record in the Search Index
| _version_ | 1804116486572212224 |
|---|---|
| adam_text | Contents
Preface XI
1. Review of Elementary Methods 1
1 Introduction 1
2 Linear differential equations of first order 3
3 Exact differential equations of first order 8
4 Variables separable 15
5 Homogeneous differential equations of first order 17
6 Equations reducible to differential equations of first order 21
2. Linear Differential Equations with
Constant Coefficients 25
1 Some generalities 25
2 Real roots 28
3 Imaginary roots 30
4 The nonhomogeneous case 33
5 Euler type equations 39
3. The Fundamental Existence Theorem 44
1 Introduction 44
2 The fundamental existence theorem 47
3 Existence of an integrating factor 57
4. Linear Differential Equations:
Elementary Theory 61
1 Definitions; the fundamental existence theorem 61
2 Linear dependence and linear independence 63
vii
viii Contents
3 Variation of parameters 69
4 The adjoint equation 74
5 The Riccati equation 82
6 Green s function 86
5. Oscillation Theory for Linear Differential
Equations of Second Order 91
1 Self adjoint linear differential equations of second order 91
2 Abel s formula 92
3 The number of zeros on a finite interval 92
4 The Sturm separation theorem 93
5 The Sturm comparison theorem 98
6 The Sturm Picone theorem 105
7 The Bocher Osgood theorem 106
8 A special pair of solutions 109
9 Oscillation on a half axis 110
10 Two transformations 114
11 More on oscillation 119
12 Liapunov s inequality 122
13 Gronwall s inequality 124
6. Characteristic Functions;
Orthogonal Polynomials 128
1 Introduction 128
2 Orthogonality 133
3 The expansion of a function in a series of orthogonal
functions 135
4 The Bessel equation 138
5 Orthogonal polynomials 144
7. Systems of Linear Differential Equations 149
1 The existence theorem 149
2 Fundamental systems of solutions 154
3 Linear systems with constant coefficients; matrix notation 156
8. Autonomous Systems in the Plane 175
1 The Poincare phase plane 175
2 More general systems 187
9. Stability; Liapunov Functions 189
1 Nonlinear differential systems 189
2 Stability and instability 192
3 Characteristic roots 195
4 Liapunov functions 196
5 Stability of linear systems with constant coefficients 207
6 The theorems of LaSalle and of Cetaev 216
10. Quadratic Functionals 230
1 The fundamental problem 230
2 The conjugate point 231
3 Some examples and applications 235
4 Focal points 238
Supplementary Reading 245
Index 247
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| building | Verbundindex |
| bvnumber | BV002036420 |
| classification_rvk | SK 520 |
| ctrlnum | (OCoLC)247415929 (DE-599)BVBBV002036420 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV002036420 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:39:17Z |
| institution | BVB |
| isbn | 0534004326 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001331461 |
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| physical | XII, 249 S. |
| publishDate | 1976 |
| publishDateSearch | 1976 |
| publishDateSort | 1976 |
| publisher | Wadsworth |
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| spelling | Leighton, Walter Verfasser aut An introduction to the theory of ordinary differential equations Walter Leighton Belmont, Calif. Wadsworth 1976 XII, 249 S. txt rdacontent n rdamedia nc rdacarrier HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001331461&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Leighton, Walter An introduction to the theory of ordinary differential equations |
| title | An introduction to the theory of ordinary differential equations |
| title_auth | An introduction to the theory of ordinary differential equations |
| title_exact_search | An introduction to the theory of ordinary differential equations |
| title_full | An introduction to the theory of ordinary differential equations Walter Leighton |
| title_fullStr | An introduction to the theory of ordinary differential equations Walter Leighton |
| title_full_unstemmed | An introduction to the theory of ordinary differential equations Walter Leighton |
| title_short | An introduction to the theory of ordinary differential equations |
| title_sort | an introduction to the theory of ordinary differential equations |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001331461&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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