The theory of differential equations : classical and qualitative

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Title:

Personal Author:

Kelley, Walter G.

Publication Information:

Upper Saddle River, NJ : Pearson Education, 2004

ISBN:

9780131020269

Subject Term:

Differential equations

Added Author:

Peterson, Allan C.

Available:*

Library	Item Barcode	Call Number	Material Type	Item Category 1	Status
Searching... PSZ JB	30000010124576	QA431 K44 2004	Open Access Book	Book	Searching... Unknown

Designed for second or a first honours course in differential equations, this book introduces many of the important topics associated with modern and classical approaches to ordinary differential equations.

Preface	p. ix
Chapter 1 First-Order Differential Equations	p. 1
1.1 Basic Results	p. 1
1.2 First-Order Linear Equations	p. 4
1.3 Phase Line Diagrams	p. 6
1.4 Bifurcation	p. 11
1.5 Exercises	p. 15
Chapter 2 Linear Systems	p. 20
2.1 Introduction	p. 20
2.2 The Vector Equation x' = A(t)x	p. 24
2.3 The Matrix Exponential Function	p. 40
2.4 Induced Matrix Norm	p. 54
2.5 Floquet Theory	p. 60
2.6 Exercises	p. 72
Chapter 3 Autonomous Systems	p. 81
3.1 Introduction	p. 81
3.2 Phase Plane Diagrams	p. 84
3.3 Phase Plane Diagrams for Linear Systems	p. 90
3.4 Stability of Nonlinear Systems	p. 101
3.5 Linearization of Nonlinear Systems	p. 107
3.6 Existence and Nonexistence of Periodic Solutions	p. 114
3.7 Three-Dimensional Systems	p. 127
3.8 Differential Equations and Mathematica	p. 138
3.9 Exercises	p. 142
Chapter 4 Perturbation Methods	p. 153
4.1 Introduction	p. 153
4.2 Periodic Solutions	p. 164
4.3 Singular Perturbations	p. 170
4.4 Exercises	p. 179
Chapter 5 The Self-Adjoint Second-Order Differential Equation	p. 185
5.1 Basic Definitions	p. 185
5.2 An Interesting Example	p. 190
5.3 Cauchy Function and Variation of Constants Formula	p. 192
5.4 Sturm-Liouville Problems	p. 197
5.5 Zeros of Solutions and Disconjugacy	p. 205
5.6 Factorizations and Recessive and Dominant Solutions	p. 213
5.7 The Riccati Equation	p. 222
5.8 Calculus of Variations	p. 234
5.9 Green's Functions	p. 244
5.10 Exercises	p. 264
Chapter 6 Linear Differential Equations of Order n	p. 272
6.1 Basic Results	p. 272
6.2 Variation of Constants Formula	p. 274
6.3 Green's Functions	p. 278
6.4 Factorizations and Principal Solutions	p. 288
6.5 Adjoint Equation	p. 294
6.6 Exercises	p. 298
Chapter 7 BVPs for Nonlinear Second-Order DEs	p. 300
7.1 Contraction Mapping Theorem (CMT)	p. 300
7.2 Application of the CMT to a Forced Equation	p. 302
7.3 Applications of the CMT to BVPs	p. 304
7.4 Lower and Upper Solutions	p. 316
7.5 Nagumo Condition	p. 325
7.6 Exercises	p. 331
Chapter 8 Existence and Uniqueness Theorems	p. 335
8.1 Basic Results	p. 335
8.2 Lipschitz Condition and Picard-Lindelof Theorem	p. 338
8.3 Equicontinuity and the Ascoli-Arzela Theorem	p. 346
8.4 Cauchy-Peano Theorem	p. 348
8.5 Extendability of Solutions	p. 353
8.6 Basic Convergence Theorem	p. 359
8.7 Continuity of Solutions with Respect to ICs	p. 362
8.8 Kneser's Theorem	p. 366
8.9 Differentiating Solutions with Respect to ICs	p. 369
8.10 Maximum and Minimum Solutions	p. 377
8.11 Exercises	p. 386
Solutions to Selected Problems	p. 393
Bibliography	p. 405
Index	p. 409

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