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Unit 10: Infinite Series

Infinite series is one of those topics that you can spend either an
entire course on, or a week. We'll take the later approach, and just
touch on the basic concepts. Infinite series are often useful when
playing with calculus and differential equations.

### Objectives

After completing this unit you should
- Be able to take the Taylor series of any function around a point
where it is infinitely differentiable.
- Be able to work with Taylor series in terms of differentiation,
integration, etc.

### Suggested Procedure

- In
*Simmons*, read chapter 13 and 14.1-14.7 casually and
concentrate on 14.8-14.12.
- Concentrate on problems involving finding and manipulating
Taylor series. Don't worry much about convergence problems and such.
(Do a few of those though; it's good for the soul.)
- Take a
**Practice
Test** (sorry, not currently available online, but the
**Sample Final Exam**, Xdvi or PDF, has some
series problems).
- Ask your instructor to give you a unit test

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watko@mit.edu
Last modified August 1, 1998