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Complex functions

  •  Analytic functions, Introduction to Complex numbers, Properties of Complex numbers, Some elementary functions, Basic properties of Analytic functions
  •  Cantour  Integrals, Cauchy's Theorem, Cauchy's Integral Formula,  Maximum Modules Theorem  and Harmonic Functions.
  •  Series representation of Analytic Functions
  • Convergent Series of Analytic  Functions, Poer Series and Taylor Functions, Laurent Series and Classification of Singularities.
  • Calculus of Residues, Residue Theorem, Evaluation of Definite Integrals, Evaluations of Infinite Series
  • MappingElementary mapping, Basic Theory of Conformal mapping,  Mobius Transformation.

Text book:

1. W. Brown, R.V. Churchil,  Complex Variables and Applications, Sixth edition, Mc Graw-Hill, 1996

2. J. Marsden, M. J. Hoffman, Basic Complex Analysis, Third edition,, 1999

Prerequisites: 

 1. Foundation of Mathematical Analysis

Grading Policy: 

 

1. Quiz 1, 5%,  1395/7/6

 2. Quiz 2, 5%, 1395/7/ 27

3. Midterm, 30%, 1395/8/11

4. Quiz 3, 5%, 1395/8/25

5. Quiz 4, 5%, 1395/9/23

6. Final, 50%

 

Time: 

 Time and Place: Sunday-Tuesday, 10:00-12:00 A.M., Class 2

Office hours: Sunday-Tuesday, 9:00-10:00 A.M.

Term: 
Fall,2016
Grade: 
Undergraduate