math4250exam1

# math4250exam1 - Math 4250/6250 Exam #1 This take-home exam...

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Math 4250/6250 Exam #1 This take-home exam covers the material on curves (class notes #1 through #6 and DoCarmo Chapter #1). Please pick 4 of the following problems. If you are a graduate student, you must attempt the challenge problem. If you are an undergraduate, you can do the challenge problem as one of your four problems (and will get bonus credit if you get it right). You are permitted to use You are not permitted to use Maple (or Mathematica or MATLAB) The internet A calculator (or graphing calculator) DoCarmo Other books Your notes Other people’s notes Your brain Other people’s brains Class notes posted on the website 1. Find the curvature and torsion of the following curves (1) α ( t ) = ± t, 1+ t t , 1 - t 2 t ² , t > 0 . (2) β ( t ) = ( a (3 t - t 3 ) , 3 at 2 , a (3 t + t 3 )) . Please notice that neither curve is parametrized by arclength . Do you notice anything un- usual about either curve? (Look again after you do Problem 4.) 2. Suppose that α ( s ) : [0 , ` ] R 3 is a regular curve parametrized by arclength. The tangent indicatrix of α is the curve

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## This note was uploaded on 03/12/2012 for the course MATH 4250 taught by Professor Staff during the Spring '08 term at UGA.

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math4250exam1 - Math 4250/6250 Exam #1 This take-home exam...

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