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Tables of Contents for Elementary Differential Equations
Chapter/Section Title
Page #
Page Count
Preface
vii
 
First-Order Differential Equations
1
95
Differential Equations and Mathematical Models
1
9
Integrals as General and Particular Solutions
10
8
Slope Fields and Solution Curves
18
13
Separable Equations and Applications
31
14
Linear First-Order Equations
45
12
Substitution Methods and Exact Equations
57
14
Population Models
71
11
Acceleration-Velocity Models
82
14
Linear Equations of Higher Order
96
92
Introduction: Second-Order Linear Equations
96
13
General Solutions of Linear Equations
109
11
Homogeneous Equations with Constant Coefficients
120
11
Mechanical Vibrations
131
13
Nonhomogeneous Equations and Undetermined Coefficients
144
13
Forced Oscillations and Resonance
157
11
Electrical Circuits
168
8
Endpoint Problems and Eigenvalues
176
12
Power Series Methods
188
71
Introduction and Review of Power Series
188
13
Series Solutions Near Ordinary Points
201
11
Regular Singular Points
212
15
Method of Frobenius: The Exceptional Cases
227
14
Bessel's Equation
241
9
Applications of Bessel Functions
250
9
Laplace Transform Methods
259
58
Laplace Transforms and Inverse Transforms
259
10
Transformation of Initial Value Problems
269
11
Translation and Partial Fractions
280
7
Derivatives, Integrals, and Products of Transforms
287
8
Periodic and Piecewise Continuous Input Functions
295
11
Impulses and Delta Functions
306
11
Linear Systems of Differential Equations
317
103
First-Order Systems and Applications
317
12
The Method of Elimination
329
9
Matrices and Linear Systems
338
19
The Eigenvalue Method for Homogeneous Systems
357
15
Second-Order Systems and Mechanical Applications
372
11
Multiple Eigenvalue Solutions
383
16
Matrix Exponentials and Linear Systems
399
12
Nonhomogeneous Linear Systems
411
9
Numerical Methods
420
50
Numerical Approximation: Euler's Method
420
12
A Closer Look at the Euler Method
432
11
The Runge-Kutta Method
443
10
Numerical Methods for Systems
453
17
Nonlinear Systems and Phenomena
470
75
Equilibrium Solutions and Stability
470
8
Stability and the Phase Plane
478
12
Linear and Almost Linear Systems
490
13
Ecological Models: Predators and Competitors
503
13
Nonlinear Mechanical Systems
516
16
Chaos in Dynamical Systems
532
13
References for Further Study
545
4
Appendix: Existence and Uniqueness of Solutions
549
14
Answers to Selected Problems
563
 
Index
1