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# Test1prep - complex exponential I’m quite fond of having...

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Preparing for the In-Class Part of the First Exam The test covers everything we ve covered up through the material on the convergence of Fourier series in chapter 13. Reviewing the homework given up through Wednesday, Sept. 21 may be a good idea. Know the basic terminology and notation. In particular be able to recognize when a function is or is not any of the following: bounded, continuous, piecewise continuous, smooth, piecewise smooth, even, odd, and/or periodic Questions on these would probably involve pictures — identifying whether a function is bounded/continuous/ from a sketch of its graph, and/or having you sketch an â appropriate graph illustrating what a bounded/continuous/ function can or cannot look â like. Know the material we covered on complex variables, especially the material on the
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Unformatted text preview: complex exponential. I’m quite fond of having you compute tricky trig. integrals or proving/deriving trig. identities using the complex exponential. ♦ Know the stuff we developed in class on inner products, orthogonality, and orthogonal function expansions. Remember, the quasi-theorem on orthogonal expansions (page 135) can be viewed as the most general way to develop “Fourier series”. ♦ Be able to compute any of the Fourier series we’ve developed, especially the complex exponential Fourier series. ♦ Know the basic convergence results discussed in class on Monday (9/19) and Wednesday (9/21) well enough to answer questions similar to the homework I gave you on those days. ♦ Relax. Get a good night’s sleep the night before, and don’t cram at the last minute....
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