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midterm f02

# midterm f02 - Do question one and then as many other...

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Physics 498/MMA Handout MT Oct 28th 2002 Mathematical Methods in Physics I m-stone5 Prof. M. Stone 305 Loomis Laboratory University of Illinois Do question one, and then as many other questions as you can. Try to answer entire ques- tions. Little, if any, credit will be given for fragmentary answers. 1) Green Function : Consider the boundary value problem - y 00 = f ( x ) , y 0 (0) = y (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) Evaluate the x derivative of your solution, y ( x ), and confirm that y obeys both bound- ary conditions. (5 points) d) Take one further derivative of your y ( x ) and confirm that it does indeed solve the original problem. (5 points) 2) Bead and string : A bead of mass M is free to slide up and down the y axis.

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• Fall '07
• Stone
• Derivative, Boundary value problem, Lagrangian mechanics

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