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Unformatted text preview: Physics 498/MMA Handout 0 Fall 2007 Mathematical Methods in Physics I http://w3.physics.uiuc.edu/ ∼ m-stone5 Prof. M. Stone 2117 ESB University of Illinois Revision and Warm-up 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
- Derivative, 2m, Prof. M. Stone, ESB University of Illinois, timedependent Schr¨dinger equation