search for books and compare prices
Tables of Contents for Differential Equations
Chapter/Section Title
Page #
Page Count
1 FIRST-ORDER DIFFERENTIAL EQUATIONS
1
138
1.1 Modeling Via Differential Equations
2
17
1.2 Analytic Technique: Separation of Variables
19
16
1.3 Qualitative Technique: Slope Fields
35
17
1.4 Numerical Technique: Euler's Method
52
11
1.5 Existence and Uniqueness of Solutions
63
11
1.6 Equilibria and the Phase Line
74
19
1.7 Bifurcations
93
14
1.8 Linear Differential Equations
107
10
1.9 Changing Variables
117
15
Labs for Chapter 1
132
7
2 FIRST-ORDER SYSTEMS
139
72
2.1 Modeling Via Systems
140
16
2.2 The Geometry of Systems
156
17
2.3 Analytic Methods for Special Systems
173
11
2.4 Euler's Method for Systems
184
14
2.5 The Lorenz Equations
198
9
Labs for Chapter 2
207
4
3 LINEAR SYSTEMS
211
136
3.1 Properties of Linear Systems and the Linearity Principle
212
23
3.2 Straight-Line Solutions
235
15
3.3 Phase Planes for Linear Systems with Real Eigenvalues
250
14
3.4 Complex Eigenvalues
264
18
3.5 Special Cases: Repeated and Zero Eigenvalues
282
15
3.6 Second-Order Linear Equations
297
15
3.7 The Trace-Determinant Plane
312
13
3.8 Linear Systems in Three Dimensions
325
16
Labs for Chapter 3
341
6
4 FORCING AND RESONANCE
347
56
4.1 Forced Harmonic Oscillators
348
14
4.2 Sinusoidal Forcing
362
11
4.3 Undamped Forcing and Resonance
373
12
4.4 Amplitude and Phase of the Steady State
385
6
4.5 The Tacoma Narrows Bridge
391
10
Labs for Chapter 4
401
2
5 NONLINEAR SYSTEMS
403
94
5.1 Equilibrium Point Analysis
404
18
5.2 Qualitative Analysis
422
12
5.3 Hamiltonian Systems
434
19
5.4 Dissipative Systems
453
17
5.5 Nonlinear Systems in Three Dimensions
470
7
5.6 Periodic Forcing of Nonlinear Systems and Chaos
477
16
Labs for Chapter 5
493
4
6 LAPLACE TRANSFORMS
497
64
6.1 Laplace Transforms
498
12
6.2 Discontinuous Functions
510
9
6.3 Second-Order Equations
519
14
6.4 Delta Functions and Impulse Forcing
533
8
6.5 Convolutions
541
8
6.6 The Qualitative Theory of Laplace Transforms
549
9
Labs for Chapter 6
558
3
7 NUMERICAL METHODS
561
38
7.1 Numerical Error in Euler's Method
562
12
7.2 Improving Euler's Method
574
8
7.3 The Runge-Kutta Method
582
10
7.4 The Effects of Finite Arithmetic
592
4
Labs for Chapter 7
596
3
8 DISCRETE DYNAMICAL SYSTEMS
599
51
8.1 The Discrete Logistic Equation
600
12
8.2 Fixed Points and Periodic Points
612
9
8.3 Bifurcations
621
9
8.4 Chaos
630
8
8.5 Chaos in the Lorenz System
638
6
Labs for Chapter 8
644
6
Appendix A First-Order Linear Equations Revisited
650
11
Appendix B Complex Numbers and Euler's Formula
661
4
Hints and Answers
665
60
Index
725