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Unformatted text preview: Physics 498/MMA Handout 0 Fall 2007 Mathematical Methods in Physics I http://w3.physics.uiuc.edu/ ∼ mstone5 Prof. M. Stone 2117 ESB University of Illinois Revision and Warmup exercises These problems are designed to exercise your basic mathematical skills. They are not de signed to be easy! Each one has some twist that is designed to catch you out if you merely manipulate symbols without thinking. Differential Calculus : After taking a previous version of this course, a student claimed that the expression y ( x ) = sin ω ( x L ) ω sin ωL Z x f ( t ) sin ωt dt + sin ωx ω sin ωL Z L x f ( t ) sin ω ( t L ) dt is the solution to the problem: “Find y ( x ) obeying the differential equation d 2 y dx 2 + ω 2 y = f ( x ) on the interval [0 , L ] and satisfying the boundary conditions y (0) = 0 = y ( L ).” First examine her solution to see if it obeys the boundary conditions. Then, by differentiating her solution twice with respect to x and substituting the result into the differential equation, check to...
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 Fall '07
 Stone
 Derivative, 2m, Prof. M. Stone, ESB University of Illinois, timedependent Schr¨dinger equation

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