NATIONAL OPEN UNIVERSITY OF NIGERIA
14/16 AHMADU BELLO WAY, VICTORIA ISLAND, LAGOS
SCHOOL OF SCIENCE AND TECHNOLOGY
MARCH/APRIL 2014 EXAMINATION
COURSE CODE: MTH305
COURSE TITLE: COMPLEX ANALYSIS II
TIME ALLOWED: 3 HOURS
INSTRUCTION: ANSWER ANY 4 QUESTIONS
1. (a) Evaluate each of the following using theorems on limits
5 marks
(ii) 5 marks
(b) Prove the 7 ½ marks
2. (a) Prove that the function U = 2x(1- y) is harmonic 7 ½ marks
(b) Find a function V such that f (z) = u + i v and express f (z) in terms of z 8 marks
3. (a) Prove that is uniformly continous in the region 7 ½ marks
(b) Using the definition,find the derivative of at the point where
(i) (ii) 10 marks
4. (a) Expand is a Laurent series valid for (i) (ii) 7 ½ marks
(b) Find the value of the integral ,where is the line segment from z = 0 to z = 2+i 10 marks
5. (a) Expand f (z) = Cos z in Taylor series about and determine its region of convergence 7 ½ marks
(b) Find the value of the integral ,where is the line segment from z = 0 to z = 2+i 10 marks
6.(a) Expand f (z) = Cos z in Taylor series about and determine its region of convergence 7 ½ marks
(b) For each of the following functions,determine the poles and residuces at the poles
(i) (ii) 10 marks
- You can get the soft copy for this course (2014 – to date) or the exam summary answers for any course from 08039407882
- You can as well solve your course past questions for us and get paid. CONTACT TO KNOW HOW
Exam summary sample below
