Chapter 1

First-Order Differential Equations

1-1	Differential Equations and Mathematical Models	Problems	p.8
1-2	Integrals as General and Particular Solutions	Problems	p.15
1-3	Slope Fields and Solutions Curves	Problems	p.25
1-4	Separable equations and Applications	Problems	p.41
1-5	Linear First-Order Equations	Problems	p.53
1-6	Substitution Methods and Exact Equations	Problems	p.70
		Review Problems	p.74

Chapter 2

Mathematical Models And Numerical Methods

2-1	Population Models	Problems	p.82
2-2	Equilibrium Solutions and Stability	Problems	p.92
2-3	Acceleration-Velocity Models	Problems	p.101
2-4	Numerical Approximation: Euler's Method	Problems	p.114
2-5	A Closer Look at the Euler Method	Problems	p.124
2-6	The Runge-Kutta Method	Problems	p.133

Chapter 3

Linear Systems And Matrices

3-1	Introduction to Linear Systems	Problems	p.145
3-2	Matrices and Gaussian Elimination	Problems	p.154
3-3	Reduced Row-Echelon Matrices	Problems	p.162
3-4	Matrix Operations	Problems	p.173
3-5	Inverses of Matrices	Problems	p.185
3-6	Determinants	Problems	p.201
3-7	Linear Equations and Curve Fitting	Problems	p.209

Chapter 4

Vector Spaces

4-1	The Vector Space R3	Problems	p.220
4-2	The Vector Space Rn and Subspaces	Problems	p.227
4-3	Linear Combinations and Independence of Vectors	Problems	p.234
4-4	Bases and Dimension for Vector Spaces	Problems	p.241
4-5	Row and Column Spaces	Problems	p.249
4-6	Orthogonal Vectors in Rn	Problems	p.256
4-7	General Vector Spaces	Problems	p.263

Chapter 5

Higher-Order Linear Differential Equations

5-1	Introduction: Second-Order Linear Equations	Problems	p.276
5-2	General Solutions of Linear Equations	Problems	p.288
5-3	Homogeneous Equations with Constant Coefficients	Problems	p.300
5-4	Mechanical Vibrations	Problems	p.311
5-5	Nonhomogeneous Equations and Undetermined Coefficients	Problems	p.325
5-6	Forced Oscillations and Resonance	Problems	p.335

Chapter 6

Eigenvalues And Eigenvectors

6-1	Introduction to Eigenvalues	Problems	p.346
6-2	Diagonalization of Matrices	Problems	p.353
6-3	Applications Involving Powers of Matrices	Problems	p.363

Chapter 7

Linear Systems Of Differential Equations

7-1	First-Order Systems and Applications	Problems	p.371
7-2	Matrices and Linear Systems	Problems	p.384
7-3	The Eigenvalue Method for Linear Systems	Problems	p.395
7-4	A Gallery of Solution Curves of Linear Systems	Problems	p.419
7-5	Second-Order Systems and Mechanical Applications*	Problems	p.433
7-6	Multiple Eigenvalue Solutions	Problems	p.451
7-7	Numerical Methods for Systems	Problems	p.463

Chapter 8

Matrix Exponential Methods

8-1	matrix Exponentials and Linear Systems	Problems	p.479
8-2	Nonhomogeneous Linear Systems	Problems	p.489
8-3	Spectral Decomposition Methods	Problems	p.502

Chapter 9

Nonlinear Systems And Phenomena

9-1	Stability and the Phase Plane	Problems	p.511
9-2	Linear and Almost Linear Systems	Problems	p.522
9-3	Ecological Models: Predators and Competitors	Problems	p.535
9-4	Nonlinear Mechanical Systems	Problems	p.549

Chapter 10

Laplace Transform Methods

10-1	Laplace Transforms and Inverse Transforms	Problems	p.565
10-2	Transformation of Initial Value Problem	Problems	p.576
10-3	Translation and Partial Fractions	Problems	p.584
10-4	Derivatives, Integrals, and Products of Transforms	Problems	p.593
10-5	Periodic and Piecewise Continuous Input Functions	Problems	p.601

Chapter 11

Power Series Methods

11-1	Introduction and Review of Power Series	Problems	p.615
11-2	Power Series Solutions	Problems	p.624
11-3	Frobenius Series Solutions	Problems	p.638
11-4	Bessel Functions	Problems	p.650

Chapter Appendix A

Existence And Uniqueness Of Solutions

Problems

p.666