• 1.1 Differential Equations and Mathematical Models
• 1.2 Integrals as General and Particular Solutions
• 1.3 Slope Fields and Solution Curves
• 1.4 Separable Equations and Applications
• 1.5 Linear First-Order Equations
• 1.6 Substitution Methods and Exact Equations
• 1.7 Population Models
• 1.8 Acceleration-Velocity Models

• 2.1 Introduction: Second-Order Linear Equations
• 2.2 General Solutions of Linear Equations
• 2.3 Homogeneous Equations with Constant Coefficients
• 2.4 Mechanical Vibrations
• 2.5 Nonhomogeneous Equations and Undetermined Coefficients
• 2.6 Forced Oscillations and Resonance
• 2.7 Electrical Circuits
• 2.8 Endpoint Problems and Eigenvalues

• 3.1 Introduction and Review of Power Series
• 3.2 Series Solutions Near Ordinary Points
• 3.3 Regular Singular Points
• 3.4 Method of Frobenius: The Exceptional Cases
• 3.5 Bessel's Equation
• 3.6 Applications of Bessel Functions

• 4.1 Laplace Transforms and Inverse Transforms
• 4.2 Transformation of Initial Value Problems
• 4.3 Translation and Partial Fractions
• 4.4 Derivatives, Integrals, and Products of Transforms
• 4.5 Periodic and Piecewise Continuous Input Functions
• 4.6 Impulses and Delta Functions

• 5.1 First-Order Systems and Applications
• 5.2 The Method of Elimination
• 5.3 Matrices and Linear Systems
• 5.4 The Eigenvalue Method for Homogeneous Systems
• 5.5 Second-Order Systems and Mechanical Applications
• 5.6 Multiple Eigenvalue Solutions
• 5.7 Matrix Exponentials and Linear Systems
• 5.8 Nonhomogeneous Linear Systems

• 6.1 Numerical Approximation: Euler's Method
• 6.2 A Closer Look at the Euler Method
• 6.3 The Runge-Kutta Method
• 6.4 Numerical Methods for Systems

• 7.1 Equilibrium Solutions and Stability
• 7.2 Stability and the Phase Plane
• 7.3 Linear and Almost Linear Systems
• 7.4 Ecological Models: Predators and Competitors
• 7.5 Nonlinear Mechanical Systems
• 7.6 Chaos in Dynamical Systems

• 8.1 Periodic Functions and Trigonometric Series
• 8.2 General Fourier Series and Convergence
• 8.3 Fourier Sine and Cosine Series
• 8.4 Applications of Fourier Series
• 8.5 Heat Conduction and Separation of Variables
• 8.6 Vibrating Strings and the One-Dimensional Wave Equation
• 8.7 Steady-State Temperature and Laplace's Equation

• 9.1 Sturm-Liouville Problems and Eigenfunction Expansions
• 9.2 Applications of Eigenfunction Series
• 9.3 Steady Periodic Solutions and Natural Frequencies
• 9.4 Cylindrical Coordinate Problems
• 9.5 Higher-Dimensional Phenomena

References for Further Study

Appendix: Existence and Uniqueness of Solutions

Answers to Selected Problems

Index