# WS05 - sketch) for the following functions. Decide if the...

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APPM 4/5350 Worksheet Week 5 Figure 1: www.xkcd.com 1. Piecewise smoothness (a) Come up with an analogy (from a realm OUTSIDE of mathematics) for piece- wise smoothness. Put in haiku form if desired. BONUS! Come up with a more exciting (but nonetheless germane) name for piecewise smoothness. (b) Draw or write an equation for a function which is piecewise smooth. (c) Draw or write an equation for a function which is NOT piecewise smooth. 2. Qualitative Fourier Series Sketch the Fourier series of the following functions in the given domains; sketch the periodic extension for an additional period. Make sure you indicate the value of the function at any discontinuous locations. (a) f ( x ) = ± 0 x < 0 x x 0 - L/ 2 < x < L/ 2 (b) g ( x ) = x 3 - 1 < x < 1 3. Quantitative Fourier Series Find the Fourier sine series (and make a rough

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Unformatted text preview: sketch) for the following functions. Decide if the Fourier Series is continuous or not. (a) h ( x ) = x < x < L (b) k ( x ) = x, x < . 5 1-x, x ≥ . 5 < x < L Written by Anil Damle and Anna Lieb 1 revised September 2010 (c) You are a top-secret spy and have been captured by your nemesis. He is going to a villain conference and wants to appear smart, so he asks you to take the derivative of one of the two Fourier Series above. If the resultant series converges, he is happy and you are allowed to escape. If the resultant series diverges, he will feel foolish, and you will be thrown to the sharks. Which of the series do you pick? Written by Anil Damle and Anna Lieb 2 revised September 2010...
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## This note was uploaded on 10/24/2010 for the course APPM 4350 taught by Professor Ablowitz during the Fall '08 term at Colorado.

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WS05 - sketch) for the following functions. Decide if the...

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