Stark

Using the convolution theorem find the inverse Laplace transform of Answer:-

Find the Laplace transform of the square–wave function of period a given byf(t)= 1, 0<t<a/2-1, a/2<t<2 Answer:-

Find the Laplace transform ofi) e-3t sin5t cos3tii) Answer:-

Obtain half-range sine series for𝑓(𝑥) = x, Answer:-

Find half-range Fourier cosine series for the function f(x)= (x-1)2 , in 0<x<1, and hence show that Answer:-

Solve by using Laplace transform techniques 𝑦′′ − 3 𝑦′ + 2𝑦 = 𝑒3𝑡 ,𝑦(0) = 1, 𝑦′(0) = −1 Answer:-

Express the following function in terms of unit step function and hence find its Laplace transform f(t)= 1, 0<t<1 2t, 1<t<2 3t, 2<t<3 Answer:-

Find the Fourier transform off(x)= 1-x2, 0, |x|>1Hence evaluate Answer:-