1. INTRODUCTION TO DIFFERENTIAL EQUATIONS.

Definitions and Terminology. Initial-Value Problems. Differential Equations as Mathematical Models. Chapter 1 in Review. Project 1: Diving Deception Pass.

2. FIRST-ORDER DIFFERENTIAL EQUATIONS.

Solution Curves Without a Solution. Separable Variables. Linear Equations. Exact Equations. Solutions by Substitutions. A Numerical Method. Chapter 2 in Review. Project 2: Harvesting Natural Resources.

3. MODELING WITH FIRST-ORDER DIFFERENTIAL EQUATIONS.

Linear Models. Nonlinear Models. Modeling with Systems of Differential Equations. Chapter 3 in Review. Project 3: Swimming the Salmon River.

4. HIGHER-ORDER DIFFERENTIAL EQUATIONS.

Linear Differential Equations: Basic Theory. Reduction of Order. Homogeneous Linear Equations with Constant Coefficients. Undetermined Coefficients- Superposition Approach. Undetermined Coefficients- Annihilator Approach. Variation of Parameters. Cauchy-Euler Equation. Solving Systems of Linear Equations by Elimination. Nonlinear Differential Equations. Chapter 4 in Review. Project 4: Bungee Jumping.

5. MODELING WITH HIGHER-ORDER DIFFERENTIAL EQUATIONS.

Linear Models: Initial-Value Problems. Linear Models: Boundary-Value Problems. Nonlinear Models. Chapter 5 in Review. Project 5: The Collapse of Galloping Gertie.

6: SERIES SOLUTIONS OF LINEAR EQUATIONS.

Solutions About Ordinary Points. Solutions About Singular Points. Special Functions. Chapter 6 in Review. Project 6: Defeating Tamarisk.

7. LAPLACE TRANSFORM.

Definition of the Laplace Transform. Inverse Transform and Transforms of Derivatives. Operational Properties I. Operational Properties II. Dirac Delta Function. Systems of Linear Differential Equations. Chapter 7 in Review. Project 7: Murder at the Mayfair.

8. SYSTEMS OF LINEAR FIRST-ORDER DIFFERENTIAL EQUATIONS.

Preliminary Theory. Homogeneous Linear Systems. Nonhomogeneous Linear Systems. Matrix Exponential. Chapter 8 in Review. Project 8: Designing for Earthquakes.

9. NUMERICAL SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS.

Euler Methods and Error Analysis. Runge-Kutta Methods. Multistep Methods. Higher-Order Equations and Systems. Second-Order Boundary-Value Problems. Chapter 9 in Review. Project 9: The Hammer.
Appendix I: Gamma Function.
Appendix II: Introduction to Matrices.
Appendix III: Laplace Transforms.
Selected Answers for Odd-Numbered Problems.