Differential Equations with Matlab, 2nd Edition
January 2005, ©2005
2 Getting Started with MATLAB
3 Doing Mathematics with MATLAB
4 Using M-files and M-books
5 Solutions of Differential Equations
6 A Qualitative Approach to Differential Equations
7 Numerical Methods
8 Features of MATLAB
9 Using Simulink
10 Solving and Analyzing Second Order Linear Equations
11 Series Solutions
12 Laplace Transforms
13 Higher Order Equations and Systems of First Order Equations
14 Qualitative Theory for Systems of Differential Equations
- Symbolic Computation
Students use “dsolve” to find exact symbolic solutions to a wide variety of differential equations. These solutions are often in terms of elementary functions, but sometimes they involve special functions.
- Geometric/Qualitative Analysis
Discusses direction fields, solution curves, stability, and the qualitative analysis of differential equations (especially autonomous equations). Students become proficient in using MATLAB to draw direction fields, to understand the implications of the direction field for the solutions, and to plot solution curves and phase portraits.
- Numerical Computation
Students become proficient in using MATLAB’s ode45, a state-of-the-art numerical solver, and they develop a general understanding of numerical methods based on practical experience. This skill and understanding is developed in close connection with the usual elementary numerical methods (Euler, Improved Euler, and Runge-Kutta).
- Use of Simulink
Simulink is a software package that enables one to model, simulate, and analyze systems whose outputs change over time. It is a convenient way to study the behavior of important dynamic systems: systems involving electric circuits, mechanical systems, etc. We present a concise, but accessible, introductory treatment.