Ordinary differential equations: a first course
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Menlo Park, Calif. u.a.
Benjamin
1973
|
| Edition: | 2. ed. |
| Series: | University mathematics series
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IX, 470 S. graph. Darst. |
| ISBN: | 0805312080 |
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MARC
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| 245 | 1 | 0 | |a Ordinary differential equations |b a first course |c Fred Brauer ; John A. Nohel |
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Record in the Search Index
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| adam_text | Contents
Chapter 1 Introduction to First Order Differential Equations
1.1 Some population and closely related growth problems 1
1.2 First order equations 5
1.3 Equations with variables separable 9
1.4 Linear equations of the first order 20
1.5 Direction fields 28
1.6 Existence and uniqueness for first order equations 30
Chapter 2 Introduction to Second Order Differential Equations
2.1 The mass spring system 38
2.2 The pendulum problem 43
2.3 Further examples of motion problems 48
2.4 Second order equations solvable by first order methods 49
2.5 The existence and uniqueness theorems for second and higher order equa¬
tions 60
Chapter 3 Linear Differential Equations
3.1 Introduction 65
3.2 Linearity 68
3.3 Linear homogeneous equations 70
3.4 Solution of linear homogeneous differential equations of second order with
constant coefficients 83
3.5 Linear homogeneous equations of arbitrary order with constant co¬
efficients 93
3.6 Reduction of order 95
3.7 Linear nonhomogeneous equations 99
3.8 Resonance 111
Chapter 4 Linear System of Differential Equations
4.1 Introduction 114
vii
viii Contents
4.2 The existence and uniqueness theorem 130
4.3 Linear homogeneous systems 134
4.4 Linear nonhomogeneous systems 147
4.5 Nonlinear system of first order equations 156
Chapter 5 Eigenvalues, Eigenvectors, and Linear Systems with Constant Coefficients
5.1 The exponential of a matrix 165
5.2 Eigenvalues and eigenvectors of matrices 169
5.3 Calculation of a fundamental matrix 174
5.4 Two dimensional linear systems 180
5.5 Some population problems 192
5.6 The general case 197
5.7 Solution of Example 9, Section 4.2: An electric circuit 206
Chapter 6 Series Solutions of Linear Differential Equations
6.1 Introduction 212
6.2 Review of properties of power series 214
6.3 Second order linear equations with analytic coefficients 217
6.4 Proof of theorem on solutions in power series 223
6.5 Singular points of linear differential equations 228
6.6 Solutions about a regular singular point: Examples 232
6.7 Solutions about a regular singular point: Theorem 239
6.8 Solutions about regular singular point: Exceptional cases 244
6.9 The Bessel equation and some properties of Bessel functions 253
6.10 Singularities at infinity 263
6.11 Irregular singular points, with an introduction to
asymptotic expansions 266
Chapter 7 Boundary Value Problems
7.1 Introduction 278
7.2 Examples of homogeneous boundary value problems 281
7.3 Examples of nonhomogeneous boundary value problems The Green s
function 288
7.4 Self adjoint boundary value problems for the operator L(y)= —y 293
7.5 Sturm Liouville problems 298
7.6 Remarks on a singular boundary value problem 303
7.7 Nonhomogeneous boundary value problems and Green s function 306
Chapter 8 Existence Theory
8.1 Existence of solutions 314
8.2 Uniqueness of solutions 329
8.3 Continuation of solutions 333
8.4 The nonlinear simple pendulum 340
8.5 Existence theory for systems of first order equations and higher order
equations 346
8.6 Linear systems 349
8.7 Dependence on initial conditions 353
Contents ix
Chapter 9 Numerical Methods of Solution
9.1 The Euler method 357
9.2 The modified Euler method 368
9.3 The Milne method 372
9.4 Stability, consistency, and convergence 381
9.5 Runge kutta methods 385
9.6 Numerical methods for systems and equations of higher order 389
Chapter 10 The Laplace Transform
10.1 Introduction 392
10.2 Basic properties of the Laplace transform 393
10.3 The inverse transform 401
10.4 Applications to linear equations with constant coefficients 406
10.5 Applications to linear systems 415
10.6 A table of Laplace transforms 422
Appendix 1 Determinants and Linear Systems 424
Appendix 2 Polynomial Equations 427
Appendix 3 Complex Numbers and Complex Valued Functions 429
Appendix 4 The Exponential Matrix 433
Appendix 5 Generalized Eigenvectors, Invariant Subspaces, and
Canonical Forms of Matrices 436
Bibliography 449
Answers to Selected Exercises 450
Index 465
|
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| discipline | Mathematik |
| edition | 2. ed. |
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| indexdate | 2024-07-09T17:20:07Z |
| institution | BVB |
| isbn | 0805312080 |
| language | English |
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| owner | DE-29T DE-706 |
| owner_facet | DE-29T DE-706 |
| physical | IX, 470 S. graph. Darst. |
| publishDate | 1973 |
| publishDateSearch | 1973 |
| publishDateSort | 1973 |
| publisher | Benjamin |
| record_format | marc |
| series2 | University mathematics series |
| spelling | Brauer, Fred 1932- Verfasser (DE-588)12370085X aut Ordinary differential equations a first course Fred Brauer ; John A. Nohel 2. ed. Menlo Park, Calif. u.a. Benjamin 1973 IX, 470 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier University mathematics series 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 1\p DE-604 Nohel, John A. 1924- Verfasser (DE-588)118120921 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005578171&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 |
| spellingShingle | Brauer, Fred 1932- Nohel, John A. 1924- Ordinary differential equations a first course 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 | Ordinary differential equations a first course |
| title_auth | Ordinary differential equations a first course |
| title_exact_search | Ordinary differential equations a first course |
| title_full | Ordinary differential equations a first course Fred Brauer ; John A. Nohel |
| title_fullStr | Ordinary differential equations a first course Fred Brauer ; John A. Nohel |
| title_full_unstemmed | Ordinary differential equations a first course Fred Brauer ; John A. Nohel |
| title_short | Ordinary differential equations |
| title_sort | ordinary differential equations a first course |
| title_sub | a first course |
| 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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