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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