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FromRobin Gottlieb
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Subject[Mathematics 1b] upcoming exam
DateAPR 08, 2005 07:46:06 A.M.

 

Dear Folks:

Here are a few notes about your upcoming exam:

1. There is a review Friday, April 8 12-2 in SC D. It will be taped.

2. There will be a CA coursewide review on Monday. Look for the place and time on the mainpage of the course website.

3. The exam is 7-9 in SC C on Wed. April 13th.

Here is a basic list of topics:

What does it mean for a series to converge? You must be able to distinguish between the terms of the series and the partial sums of the series.

Power Series: radius and intervals of convergence,

Getting new series from old series by substit, integration, differentiation . . . (this means you must be able to produce, off the top of your head, series for cos x , sin x, e^x and 1/(1-x) and know their intervals of convergence.)

Taylor series: getting them from scratch, getting new from old, understanding the graphical implications (as we did at the beginning of this unit) Be able to use Taylor series to do integrals and to use the AST error estimate (when appropriate) to analyze error.

Error: you need only know about the error estimate that goes along with the alternating series test - the Taylor remainder will not be tested.

Geometric series: be able to set one up in context and be able to compute partial sums. Know when a geometric series will converge and what it converges to.

Convergence tests: know the tests and be able to apply them. Know about p-series. Be able to write a clear, complete argument about whether a series converges or diverges by invoking the appropriate convergence/divergence tests. (Know that the AST is a test for convergence only; the nth term test is a test for divergence only, that comparison and integral tests can only be used for series with positive terms. . . . when the tests are conclusive and when they're inconclusive.

Know the monotonic bounded sequence theorem.

Best wishes,
Robin