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
  1. Be able to take the Taylor series of any function around a point where it is infinitely differentiable.
  2. Be able to work with Taylor series in terms of differentiation, integration, etc.

Suggested Procedure

  1. In Simmons, read chapter 13 and 14.1-14.7 casually and concentrate on 14.8-14.12.
  2. 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.)
  3. Take a Practice Test (sorry, not currently available online, but the Sample Final Exam, Xdvi or PDF, has some series problems).
  4. Ask your instructor to give you a unit test
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Last modified August 1, 1998