- Question One Section A 20 Marks Dz F Using The Method Of Separation Of Variables Solve 50 00 2 8 Where 8 0 6 1 (45.09 KiB) Viewed 14 times
Question One SECTION A (20 Marks) Dz (f) Using the method of separation of variables, solve 50 00 = 2 +8 where 8(,0) = 6e-¹ (a) Classify using value of the discriminant (b) Evaluate (c) Show that Beta integral is a symmetric function. (d) State Fourier integral theorem and write its significant. (e) Find VA and Curl(AB) if A=zy and B-2i+2y-ayak Question Two Given (h) Use appropriate integral function(s) to evaluate ملون +*8104 (1) Find the Fourier sine and cosine transform of f(x)= e. -{1- وتی (2 Marks) (g) Find the directional derivative of the function -+2ry² + y² of (1,2-1) in the direction of vector A = i-8k (2 Marks) f(x) = SECTION B (40 Marks) √ze Vidz find the following: (a) Fourier sine integral of the function f(x). (b) Fourier cosine integral of the function f(x). 2 1- for 0<x<2 for z > 2 برتر <-0. (2 Marks) (2 Marks) (3 Marks) (2 Marks) (3 Marks) (2 Marks) (2 Marks) (5 Marks) (5 Marks) Question Three Given the one-dimensional heat equation and c= 7, determine the solution U(x, t) subject to the boundary condition (0,t) = U(2 t) = 0 for t> 0 and the condition U(,0)= (16-2r)5r for 0 < x < 2 (10 Marks)