Phys 325 Spring 2011 Math Practivce Problems

Phys 325 Spring 2011 Math Practivce Problems - Physics 325...

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Physics 325 Spring 2011 Math Review Practice 1. Consider the definite integrals 1 2 0 1 cos () a x I a dx x and 2 0 sin a x I a dx x a) Calculate the three lowest non-zero terms in the Taylor expansion of 1 Ia and 2 at 0. x b) Using the Taylor expansion of part (a), estimate the value of 1 (1) I and 2 I . c) What is that maximum error introduced by neglecting higher order terms (beyond the first three) in 1 I and 2 I ? 2. The height of a hill in meters is given by 22 2 3 4 18 28 12 z xy x y x y , where x is the distance east and y is the distance north of the origin. a) Where is the top of the hill and how high is it? b) How steep is the hill at 1 xy  ? That is, what is the angle between a vector perpendicular to the hill and the z -axis? c) In which compass direction is the slope at 1 steepest? 3. Consider a coordinate system that is rotated counter-clockwise by an angle of 30 degrees around the z -axis to create a new coordinate system. Furthermore, consider the following two
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This note was uploaded on 10/06/2011 for the course PHYS 325 taught by Professor Staff during the Spring '08 term at University of Illinois, Urbana Champaign.

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Phys 325 Spring 2011 Math Practivce Problems - Physics 325...

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