f_spring09 - Final Exam Math 2930 Spring 2009 show work, 14...

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Unformatted text preview: Final Exam Math 2930 Spring 2009 show work, 14 problems, no calculators 1) (4 points) Write your name and section number at the top of this page. 2) (16 points) Let f ( t ) = sin ( t 2 ) when | t | < , and f has period 2 . Sketch the graph of f on the interval [- , 4 ] and work out the Fourier series of f . [Do simplify any trig functions of multiples of .] 1 3) (10 points) A population p ( t ) [hundred crocodiles] is modeled by the equation dp dt = 1- p 2 9 . Sketch a slope field (including negative values of p ), and decide from your sketch which of the two equilibrium solutions is stable. 4) (10 points) Here y ( x, t ) is a sum of traveling waves, y ( x, t ) = f ( x + ct ) + g ( x- ct ). a) To achieve the boundary condition y (6 , t ) = 0 for all t , show that the functions f and g must be related by g ( s ) =- f (12- s ) for every number s . b) Give an example of an even function f of period 12. Using your f and the result of part a), show that you automatically get the initial condition y ( x, 0) = 0....
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f_spring09 - Final Exam Math 2930 Spring 2009 show work, 14...

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