PMAT 41763: Complex Analysis

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Course Code    : PMAT 41763

Title                   : Complex Analysis

Pre-requisites   : PMAT 22583

 

Learning Outcomes:

At the end of this course, the student should be able to

  • demonstrate knowledge of the role of complex numbers in Mathematics and similarities and the differences of the results in both real and complex number systems.
  • use complex numbers, complex functions and advanced theoretical aspects involving complex functions.

 Course Contents:

Complex Numbers, Complex Valued Functions, Limits, Continuity, Differentiability, Cauchy-Riemann Equations, Elementary Functions, Line Integrals, Cauchy’s Integral Theorem, Taylor and Laurent Series, Singularities, Residue Theorem, Analytic functions, Maximum modulus theorem, Conformal mappings, Schwarz Christoeffel Transformation, Rouche's theorem.

 Method of Teaching and Learning: A combination of lectures, tutorial discussions and presentations.

 Assessment: Based on tutorials, tests, presentations and end of course examination.

 Recommended Reading:

  1. Brown, J.W., Churchill, R.V., (9th edition, 2014) Complex variables and applications, McGraw-Hill
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