NATIONAL OPEN UNIVERSITY OF NIGERIA
Plot 91, Cadastral Zone, Nnamdi Azikwe Express Way, Jabi-Abuja
FACULTY OF SCIENCES
DEPARTMENT OF MATHEMATICS
July Examination 2017_1
Course Code: MTH305
Course Title: Complex Analysis II
Credit Unit: 3
Time Allowed: 3 Hours
Total: 70 Marks
Instruction: Answer Question one and Any other 4 Questions
1. Evaluate along :
(a) the parabola , ; (5 marks)
(b) straight lines from to and then from to (5 marks)
(c) a straight line from to (6 marks)
(b) Evaluate from to along the curve given by
(6 marks)
2. Verify Green’s theorem in the plane for where C is the closed curve of the region bounded by and (12 marks)
3. (a) Let for , evaluate (7 marks)
(b) Determine (5 marks)
4. Evaluate (a) (7 marks)
(b) where C is the circle . (5 marks)
5. (a) Expand in a Taylor series about (5 marks)
(b) Expand in a Taylor series about (7 marks)
6. Find Laurent series about the indicated singularity for the following functions
(a) (5 marks)
(b) . (7 marks)
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Exam summary sample below
