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Tables of Contents for Differential Equations
Chapter/Section Title
Page #
Page Count
Computing Projects
v
Preface
vii
First-Order Differential Equations
1
74
Differential Equations and Mathematical Models
1
9
Integrals as General and Particular Solutions
10
8
Direction Fields and Solution Curves
18
12
Separable Equations and Applications
30
14
Linear First-Order Equations
44
14
Substitution Methods and Exact Equations
58
17
Mathematical Models and Numerical Methods
75
65
Population Models
75
13
Equilibrium Solutions and Stability
88
6
Acceleration-Velocity Models
94
11
Numerical Approximation: Euler's Method
105
11
A Closer Look at the Euler Method
116
12
The Runge-Kutta Method
128
12
Linear Equations of Higher Order
140
102
Introduction: Second-Order Linear Equations
140
14
General Solutions of Linear Equations
154
14
Homogeneous Equations with Constant Coefficients
168
12
Mechanical Vibrations
180
11
Nonhomogeneous Equations and the Method of Undetermined Coefficients
191
16
Forced Oscillations and Resonance
207
13
Electrical Circuits
220
8
Endpoint Problems and Eigenvalues
228
14
Introduction to Systems of Differential Equations
242
42
First-Order Systems and Applications
242
14
The Method of Elimination
256
11
Numerical Methods for Systems
267
17
Linear Systems of Differential Equations
284
91
Matrices and Linear Systems
284
20
The Eigenvalue Method for Homogeneous Systems
304
16
Second-Order Systems and Mechanical Applications
320
14
Multiple Eigenvalue Solutions
334
18
Matrix Exponentials and Linear Systems
352
14
Nonhomogeneous Linear Systems
366
9
Nonlinear Systems and Phenomena
375
70
Stability and the Phase Plane
375
13
Linear and Almost Linear Systems
388
15
Ecological Models: Predators and Competitors
403
13
Nonlinear Mechanical Systems
416
16
Chaos in Dynamical Systems
432
13
Laplace Transform Methods
445
67
Laplace Transforms and Inverse Transforms
445
12
Transformation of Initial Value Problems
457
12
Translation and Partial Fractions
469
10
Derivatives, Integrals, and Products of Transforms
479
9
Periodic and Piecewise Continuous Input Functions
488
13
Impulses and Delta Functions
501
11
References for Further Study
512
2
Appendix: Existence and Uniqueness of Solutions
514
16
Answers to Selected Problems
530
Index
1