640:252 Elementary Differential Equations
Class
meets: (fill-in-time), SEC-217
(change as needed)
Text:
Blanchard, Devaney, and Hall,
Differential Equations, Brookes/Cole, 1998
Instructor:
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Information and Resources
reading and homework assignments
additional course notes
projects
applet for direction fields
(use it!)
additional links (please follow for much relevant material!)
maple help:
- 1-dim direction fields
- 2-dim phase planes, and also how to plot solutions
- info sheet used in math 244
- list of tutorial sites
Your grade will be determined as follows:
- 40% two midterm exams (20% each)
- 20% projects and quizzes
- 40% final exam
Important Note
Of course, numerical methods are not perfect for a complete understanding of the behavior of a system. This may be due to many reasons, among then: the possibility of round-off errors, an unsuitable method being used, or the wrong choice of a "window". In addition, computers only help in analyzing individual trajectories, as opposed to giving a "wholistic" picture. Therefore, numerical techniques must be supplemented, indeed must be based upon, a fundamental understanding of the meaning of differential equations. Because of this, the course will also emphasize geometric aspects and qualitative behavior, in the style of modern dynamical systems theory.
Last, but definitely not least, there is no reason to study differential equations unless you know how to apply them in practice. Thus, we will also talk a lot about modeling using ODEs.