MTH305 : Complex Analysis II (2017)

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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