2. (a) U is a function of x and t for 0...

 

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2. (a) U is a function of x and t for 0<x<L, t> 0. OU OU Calculate F Ox 2 = 2 Fe Ox F S o²U 2 əx (b) Use finite Fourier transforms to solve OU 0²U dt Ox Give a physical interpretation of the solution. and F C o²U 2 dx 0<x<4, t>0, U(0,t) = 0, U(4,t) = 0 U(x,0) = 3 sin лx - 2sin 5лx. 3 (a) A circular plate of unit radius, whose faces are insulated, has half of its boundary kept at constant temperature u₁ and the other half at constant temperature u₂. Find the steady state temperature of the plate. (b) Solve the partial differential equation px + qy = pq using Charpit's method. 2. (a) U is a function of x and t for 0<x<L, t> 0. OU OU Calculate F Ox 2 = 2 Fe Ox F S o²U 2 əx (b) Use finite Fourier transforms to solve OU 0²U dt Ox Give a physical interpretation of the solution. and F C o²U 2 dx 0<x<4, t>0, U(0,t) = 0, U(4,t) = 0 U(x,0) = 3 sin лx - 2sin 5лx. 3 (a) A circular plate of unit radius, whose faces are insulated, has half of its boundary kept at constant temperature u₁ and the other half at constant temperature u₂. Find the steady state temperature of the plate. (b) Solve the partial differential equation px + qy = pq using Charpit's method.

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2a To calculate the Fourier sine and cosine transforms of the given functions well start with the general definitions of these transforms Fourier Sine Transform Fs Fsfx 2L 0 to L fx sinnxL dx Fourier ... View the full answer