Real Analysis Answers

prove (A-B) Union B = A iff B contained in A

Find residues of f(z)=1/(z^4+1)

Find zeros of f(z)=1-exp(z) and define their order.

Find integral: int(dz/z) on curve C={z=x+iy| abs(z)=1, y>=0}

Find Laplace transform F(p) for function (show all work):
f(t)=tsin(at)

Find Laplace transform F(p) for function (show all work):
f(t)=Si(t) - integral sin using integration therem.

Find Laplace transform X(p) for function (show all work) in differential equation:
x''''(t)-5x'''(t)-4x''(t)+2x'(t)-x(t)+8=0
x(0)=5
x'(0)-0
x''(0)=-1
x'''(0)=2

Find Laplace transform F(p) for function (show all work)
f(t)=exp(-at)sh(wt)