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Unformatted text preview: y (0) = 1 using the method of Laplace transforms. 4 M427K Exam 3 May 4, 2006 Question 4 [10 Points] Solve the twopoint boundary value problem y 00 + λy = 0 , y (0) = y ( L ) = 0 by ﬁnding the eigenvalues and eigenfunctions. You may assume that there are no negative eignevalues. 5 M427K Exam 3 May 4, 2006 Question 5 [10 Points] Compute the Fourier cosine series for the function f : [0 , 1] → R given by f ( x ) = 1x 2 . 6 M427K Exam 3 May 4, 2006 Question 6 [10 Points] Solve the homogeneous heat conduction equation for a bar of length 1 100 u xx = u t , < x < 1 , t > subject to the homogeneous boundary values u (0 , t ) = 0 , u (1 , t ) = 0 and the initial condition u ( x, 0) = sin(3 πx )sin(7 πx ) . You do not need to ﬁnd the basic solutions, you may use the solutions found in class. Hint: No Fourier series is required. 7...
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This note was uploaded on 04/30/2009 for the course M 58055 taught by Professor Windsor during the Spring '07 term at University of Texas at Austin.
 Spring '07
 Windsor
 Math, Calculus

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