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Course description:
M427K is a basic course in ordinary and partial differential equations, with Fourier sreies. Ir should be taken
before most other upper division, “applied” mathematics courses. The course meets three times a week for
lecture and twice more for problem sessions. Geared to the audience primarily consisting of engineering and
science students, the course aims to teach the basic techniques for solving differential equations which arise in
applications. The approach is problem-oriented and not particularly theoretical. Most of the time is devoted to
first and second order ordinary differential equations with an introduction to Fourier series and partial
differential equations at the end. Depending on the instructor, some time may be spent on applications, Laplace
transformations, or numerical methods. Five sessions a week for one semester.
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Required Topics
It will be impossible to cover everything here adequately. The core material which must be covered is selected
sections from Chapters 1, 2, 3, 5, 10. Chapter 7 is so important that it ought to be covered, but be aware that
most students have not already had matrix methods, and you will likely find yourself covering the 2 by 2 case.
You might then do stability, etc. Numerical methods are becoming increasingly important, and covering this
topic here is a good lead in to the department’s new computational science degree. Engineers like their
students to have seen some Laplace transforms. This will leave time for other topics, and you may choose to
emphasize some over others: stability, higher order equations, applications. Whichever approach you take, you
will have to carefully plan your sections and time to be spent on them.
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Resources
If you are new to this course, you might talk to the senior faculty who teach this course regularly: Beckner, de
la Llave, Dollard, Friedman, Gamba, Koch, Showalter, Uhlenbeck and others.
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