MATHEMATICS-III sem 3rd

Uttarakhand tech. university

b tech

sub:- mathamatics iii

utu previous year question papers

time : 3hr]

Total marks :100

SECTION A

Q1:- Attempt any two of the following :

1. (i) Show that function u = x³ – 3xy² is harmonic and find the corresponding analytic function.
   (ii) If   w = f (z) = u + iv and u - v =  e^x (cosy – siny), find w in terms of z.
2. Evaluate 
                    where C is the circle
   (i) |z| = 2 ,  
3. Apply  calculus of residues to evaluate