# midterm f03 - Do question one and then any two of the other...

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Physics 498/MMA Handout MT Oct 29th 2003 Mathematical Methods in Physics I m-stone5 Prof. M. Stone 2117 ESB University of Illinois Do question one , and then any two of the other three questions. Try to answer entire questions. Little, if any, credit will be given for fragmentary answers. 1) Green Function : Consider the homogeneous boundary value problem - y 00 = f ( x ) , y (0) = y 0 (1) = 0 . a) Construct the explicit Green function appropriate to this problem. (5 points) b) Use your Green function to write down the solution of the boundary value problem as the sum of two explicit integrals over complementary components of the unit interval. (5 points) c) Confirm that your solution y ( x ) obeys both boundary conditions, and that it does indeed solve the original problem. (5 points) Now consider the inhomogeneous boundary value problem - y 00 = f ( x ) , y (0) = A, y 0 (1) = B. d) Use the method based Lagrange’s identity to obtain the solution to this boundary value problem. The points here are for exhibiting the method

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