BS-112 APPLIED Mathematics-II (credit: 3)

Examine the function f(x,y) = x^3 + y^2 - 12x - 3y + 20 for extremum.

State the convolution theorem and using it find the inverse Laplace transform of 1 / (s(s+1)).

Find the bilinear transformation which maps the points z = 1, -i, -1 into the points w = i, 0, -i.

Using half range sine series, expand the function f(x) = 1 for 0 < x < 1.

ntegrate the function f(z) = z along the curve C, where C is the square with vertices 0, 1, 1+i and i.