Book/CD-ROM package that provides a traditional treatment of elementary ordinary differential equations while introducing computer-assisted methods available with Mathematica. Classical solution methods are presented in parallel with those in Mathematica. Models are developed from classical physics, population biology, electrical circuits, and elementary mechanics. Requires knowledge of calculus of one variable. Knowledge of multi-variable calculus and linear algebra is recommended.
Basic Concepts | Using Mathematica to Study Differential Equations | First Order Differential Equations | The Package ODE.m | Existence and Uniqueness of Solutions of First Order Differential Equations | Applications of First Order Equations I | Applications of First Order Equations II | Second Order Linear Differential Equations | Second Order Linear Differential Equations with Constant Coefficients | Using ODE.m to Solve Second Order Linear Differential Equations | Applications of Linear Second Order Equations | Higher Order Linear Differential Equations | Numerical Solutions of Differential Equations | The Laplace Transform | Systems of Linear Differential Equations | Linear Systems II | Stability of Nonlinear Systems | Applications of Systems | Power Series Solutions of Second Order Equations | Frobenius Solutions of Second Order Equations | Appendices: Review of Linear Algebra and Matrix Theory; Systems of Units