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# hw09 - MTH 201 Problem Set#9 Due Thursday June 10 5:00pm 1...

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MTH 201 Problem Set #9 Due: Thursday, June 10, 5:00pm 1. Solve the following diffusion equation. 2 2 (0, ) 0, ( , ) 0 1 if 0 / 2 ( , 0) 0 if / 2 u x u t u L t x L u u t x L x L 2. Solve the following Laplace equation. 2 2 2 2 0 0 0, 0 ( , 0) , ( , ) 0 x x a u u x y u u x x u x x u x b 3. Solve the following wave equation. 2 2 2 2 0 2 (0, ) 0, ( , ) 0 1 ( , 0) ( ), 0 4 t u x u t u L t u u x x L x t u c t 4. Find the steady-state temperature distribution ( , ) u r in a semicircular plate of radius a by solving the following Laplace equation in the polar coordinate system. 2 2 2 2 2 0 1 1 0, 0 , 0 ( , ) ( , 0) 0, ( , ) 0 u u u r a r r r r u a u u r u r 5. Find the temperature distribution ( , ) u r t in a circular plate of radius a by solving the following heat equation in the cylindrical coordinate system. 2 2 1 ( , ) 0 ( , 0) ( ) u u r r r u a t u r f r u t 6. Find the steady-state temperature distribution

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• Spring '10
• LimMiKyoung
• Coordinate system, Spherical coordinate system, Polar coordinate system, Coordinate systems, Cylindrical coordinate system, following Laplace equation

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hw09 - MTH 201 Problem Set#9 Due Thursday June 10 5:00pm 1...

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