Assignment Task
Assignment #01
Q.1 State and Prove first Parseval’s Theorem of Fourier transform
Q.2 Use Laplace Transform to solve the given differential equation
y”+2y’+y=?(t-1) , y(0)=0 , y’0=0
Assignment #02
Q.1 Find the Complex Fourier Series of function f(x) on interval (-p, p). (5) Q.2 Define Legendre’s Differential Equations and converts it into Self Adjoint Form for n=1.
Q.3 Show that Eigen values of a Strum Liouville System are real.
Assignment #03
Q.1 Define orthogonal functions and find set of functions which are orthogonal for the following S-L problem.
d2ydx2+?y=0, y’0=0 , y’L=0Q.2 Find the extremal curve for functional
Iyx,zx=0?2(y’2+z’2+2yz)dx With y (0) =0=z (0) and y?2=1 ,z?2=-1 (7)
Assignment #04
Q.1 Expand f(x) in an appropriate Fourier cosine or sine series where
fx=sinx , -?<x<? (5)
Q.2Find approximate solution of problem for minimization of Functional Iy=01y’2-y2+2xydx , y (0) =0, y (1) =0
Compare it with exact solution.
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