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