Find the residue of f ( z) = zcosz/(z – π)³at z = π.

Using Rodrigue’s formula, obtain the expression for P₃ ( x) .

Using the method of Laplace transform, solve the following initial value problem:

y′′ − 2 y′ + y = e^t ; y(0) = −2, y′(0) = −3

A metal plate covering the first quadrant of the xy plane has its edge along the yaxis
kept at T = 0, and the edge along the x-axis is kept at an initial-temperature:

Obtain the steady state temperature distribution as a function of x and y.

Using the method of residues, show that 

What are symmetric and antisymmetric tensors? Show that the dot product of two
3-D vectors is a scalar.

Evaluate the integral  where C is the circle IzI = 2.

_C∫e^z(z²+1)/ (z- 1)² dz