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Differential Equations (92.236)
Course Goals

There are a number of important goals for this course and many of these have already been mentioned in the section on Course Description and Requirements. However, since repetition is important to the learning process, we will repeat and expand upon some of these items here. In particular, when you have successfully completed this course you should be able to perform the following tasks:

Systematically analyze physical systems governed by one independent variable.
Develop mathematical models of common physical systems from basic principles (i.e. basic mass, energy, particle, and force balances, etc.)
Solve and interpret the ordinary differential equations that result from the modeling of physical systems:
- Identify an appropriate analytical solution technique and solve a variety of first order ODEs and linear constant coefficient ODEs for higher-order systems.
- Apply standard numerical solution techniques (in Matlab) to general initial value problems (IVPs).
- Use symbolic computational capability (in Matlab) to solve a variety of ODEs.
Implement computer programs (in Matlab) for evaluation, visualization, and analysis of a given system.

Overall, this course tries to develop a solid mathematical foundation in differential equations and to give the student practical skills for

modeling and analyzing physical systems,
solving ODEs both analytically and numerically, and
working with Matlab to help simulate, visualize, and understand the physical systems under study.

In addition, through a variety of class examples and student homework problems, a suite of useful tools for solving classical problems is developed. These tools and a traditional mathematical foundation in solving ODEs should give the student the necessary prerequisites for more advanced studies in his or her upper-level engineering science and engineering design courses.

Last updated by Prof. John R. White (January 2007)

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