# Test2_prep - formula ♦ Expect to prove/derive one of the...

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Preparing for the Second Exam The test covers everything we’ve done concerning the Fourier transforms, up through the material on Gaussian functions in §23.1. For details on what we covered over that period, look at the assigned homework from Friday 9/23 to Friday 10/21. There will be two slightly different tests: One for the 460 students, and one for the 561 students. Each will be accompanied by a copy of the Short Tables for the Fourier Transform (same as at the web site). In particular: Know the basic notation and terminology. 561ers, at least, should expect at least one problem specifically relating to whether certain functions are or are not absolutely integrable/in /classically transformable. Everyone should be aware of the importance g that functions satisfy appropriate conditions before applying identities with those functions (e.g.: The requirement that be continuous when applying the differential 0 identity for computing ). Y Ò0 Ó w Be able to compute a Fourier transform (or inverse transform) using the integral
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Unformatted text preview: formula. ♦ Expect to prove/derive one of the identities (I ll probably give you one of the near-’ equivalence or translation or scaling or differentiation identities). 460ers will be able to assume the function being transformed is in . 561ers won t be so lucky. T ’ ♦ Much of the test will concern computing transforms and inverse transforms using the tables given. Expect pages and pages of these sorts of computations. Your work will have to be based on those tables. For example, the modulation identities are not on the tables, so know other ways for computing the transforms for which you may normally use the modulation identies. And don t expect much credit for just writing down the ’ answer without giving any indication of how you got it! Question: Which identities from the table are you most likely to use? Answer: All of them. You may even have one transform to compute requiring the use of more than one identity (as in problem 21.13)....
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