Math background answers for Physics 316, Modern Physics I (HoFstaetter/Hinderer/Thibault) Date: Wednesday, 01/28/04 0) Have you taken the prerequisite math courses? These are: coregistration in at least MATH 294 (linear algebra) or equivalent. MATH 294 has the prerequisit MATH 192, covering polar coordinates, in±nite series, and power series, vectors and calculus of functions of several variables, double and triple integrals. Result: 85% yes, 12% don’t know, 3% no. 1) Use complex numbers to derive the following equation: sin(2 α ) = 2 sin( α ) cos( α ). Solution: sin(2 α ) = e i 2 α-e i 2 α 2 i = ( e iα-e iα )( e iα + e iα ) 2 i = 2 e i 2 α-e i 2 α 2 i e i 2 α + e i 2 α 2 = 2 sin( α ) cos( α ). Result: 42% correct, 58% wrong. 2) What is the general solution of the following ODE: x 00 = kx for k < 0 and for k > 0? Solution: ²or k < 0 it is
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