Linear ordinary differential equations:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Philadelphia
SIAM
1997
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 341 S. graph. Darst. |
| ISBN: | 0898713889 |
Internformat
MARC
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| 100 | 1 | |a Coddington, Earl A. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Linear ordinary differential equations |c Earl A. Coddington ; Robert Carlson |
| 264 | 1 | |a Philadelphia |b SIAM |c 1997 | |
| 300 | |a XII, 341 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 0 | 7 | |a Lineare gewöhnliche Differentialgleichung |0 (DE-588)4353441-7 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Lineare gewöhnliche Differentialgleichung |0 (DE-588)4353441-7 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Carlson, Robert |e Verfasser |4 aut | |
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Datensatz im Suchindex
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|---|---|
| adam_text | Contents
Preface xi
1 Simple Applications 1
1.1 Introduction 1
1.2 Compartment systems 1
1.3 Springs and masses 5
1.4 Electric circuits 9
1.5 Notes 13
1.6 Exercises 13
2 Properties of Linear Systems 19
2.1 Introduction 19
2.2 Basic linear algebra 20
2.2.1 Vector spaces 20
2.2.2 Matrices 22
2.2.3 Vector spaces of functions 24
2.3 First order systems 25
2.3.1 Introduction 25
2.3.2 First order homogeneous systems 26
2.3.3 The Wronskian 30
2.3.4 First order nonhomogeneous systems 32
2.4 Higher order equations 34
2.4.1 Linear equations of order n 34
2.4.2 Nonhomogeneous linear equations of order n . . 37
2.5 Notes 40
2.6 Exercises 40
3 Constant Coefficients 49
3.1 Introduction 49
3.2 Properties of the exponential of a matrix 54
3.3 Nonhomogeneous systems 57
3.4 Structure of the solution space 57
3.4.1 A special case 57
3.4.2 The general case 61
vii
viii Contents
3.4.3 Some examples 65
3.4.4 Real solutions 68
3.5 The Jordan canonical form of a matrix 70
3.6 The behavior of solutions for large t 74
3.7 Higher order equations 76
3.8 Exercises 80
4 Periodic Coefficients 93
4.1 Introduction 93
4.2 Floquet s theorem 94
4.3 The logarithm of an invertible matrix 95
4.4 Multipliers 97
4.5 The behavior of solutions for large t 98
4.6 First order nonhomogeneous systems 100
4.7 Second order homogeneous equations 105
4.8 Second order nonhomogeneous equations 107
4.9 Notes 108
4.10 Exercises 109
5 Analytic Coefficients 119
5.1 Introduction 119
5.2 Convergence 120
5.2.1 Normed vector spaces 120
5.2.2 Normed vector spaces of functions 127
5.3 Analytic functions 130
5.4 First order linear analytic systems 136
5.5 Equations of order n 140
5.6 The Legendre equation and its solutions 142
5.6.1 The Legendre equation 142
5.6.2 The Legendre polynomials 145
5.6.3 Legendre functions of the second kind 147
5.7 Notes 150
5.8 Exercises 151
6 Singular Points 163
6.1 Introduction 163
6.2 Systems of equations with singular points 168
6.2.1 Singular points of the first kind: A special case . 168
6.2.2 Two results about matrices 174
6.2.3 The special case, continued 176
6.2.4 Singular points of the first kind: The general case 180
6.2.5 Singular points of the second kind 184
6.3 Single equations with singular points 185
6.3.1 Equations of order n 185
Contents ix
6.3.2 The Euler equation 189
6.3.3 The second order equation 190
6.3.4 The Bessel equation 195
6.3.5 The Bessel equation, continued 198
6.4 Infinity as a singular point 202
6.5 Notes 205
6.6 Exercises 205
7 Existence and Uniqueness 221
7.1 Introduction 221
7.2 Convergence of successive approximations 223
7.3 Continuity of solutions 231
7.4 More general linear equations 234
7.5 Estimates for second order equations 236
7.6 Notes 240
7.7 Exercises 240
8 Eigenvalue Problems 245
8.1 Introduction 245
8.2 Inner products 249
8.3 Boundary conditions and operators 251
8.4 Eigenvalues 255
8.4.1 Selfadjoint eigenvalue problems 255
8.4.2 Eigenvalue asymptotics 262
8.5 Nonhomogeneous boundary value problems 266
8.5.1 Nonhomogeneous problems 266
8.5.2 Green s functions 269
8.6 Notes 275
8.7 Exercises 275
9 Eigenfunction Expansions 281
9.1 Introduction 281
9.2 Selfadjoint integral operators 284
9.3 Eigenvalues for Green s operator 288
9.4 Convergence of eigenfunction expansions 291
9.5 Extensions of the expansion results 295
9.6 Notes 299
9.7 Exercises 300
10 Control of Linear Systems 305
10.1 Introduction 305
10.2 Convex sets 308
10.3 Control of general linear systems 312
10.4 Constant coefficient equations 319
10.5 Time optimal control 324
x Contents
10.6 Notes 329
10.7 Exercises 329
Bibliography 333
Index 335
|
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| id | DE-604.BV011530810 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:11:19Z |
| institution | BVB |
| isbn | 0898713889 |
| language | English |
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| physical | XII, 341 S. graph. Darst. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | SIAM |
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| spelling | Coddington, Earl A. Verfasser aut Linear ordinary differential equations Earl A. Coddington ; Robert Carlson Philadelphia SIAM 1997 XII, 341 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lineare gewöhnliche Differentialgleichung (DE-588)4353441-7 gnd rswk-swf Lineare gewöhnliche Differentialgleichung (DE-588)4353441-7 s DE-604 Carlson, Robert Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007760529&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Coddington, Earl A. Carlson, Robert Linear ordinary differential equations Lineare gewöhnliche Differentialgleichung (DE-588)4353441-7 gnd |
| subject_GND | (DE-588)4353441-7 |
| title | Linear ordinary differential equations |
| title_auth | Linear ordinary differential equations |
| title_exact_search | Linear ordinary differential equations |
| title_full | Linear ordinary differential equations Earl A. Coddington ; Robert Carlson |
| title_fullStr | Linear ordinary differential equations Earl A. Coddington ; Robert Carlson |
| title_full_unstemmed | Linear ordinary differential equations Earl A. Coddington ; Robert Carlson |
| title_short | Linear ordinary differential equations |
| title_sort | linear ordinary differential equations |
| topic | Lineare gewöhnliche Differentialgleichung (DE-588)4353441-7 gnd |
| topic_facet | Lineare gewöhnliche Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007760529&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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