PMAT 41343: Complex Analysis

Course Code    : PMAT 41343

Title                   : Complex Analysis

Pre-requisites   : PMAT 22293

Learning Outcomes:

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

• identify regions in the complex plane

• explain the concepts of analytic functions and harmonic functions and then the important of Cauchy-Riemann equations

• explain the convergence power series and develop analytical capabilities in Taylor or Laurent series in a given domain

• describe the basic properties of singularities and zeros of analytic functions and calculate residues and use these to evaluate real integrals

• describe conformal mappings between various plane regions

 Course Contents:

• Complex Numbers, Complex Valued Functions, Limits, Continuity, Differentiability, Analytic functions, Cauchy Riemann Equations, Elementar, Functions, Line Integrals, Cauchy-Goursat Theorem, Morera’s Theorem, Cauchy’s Integral Formula, Cauchy’s Inequality, Lioville’s Theorem, Fundamental Theorem of Algebra, Maximum Modulus Principle, Minimum modulus Principle, Taylor and Laurent Series, Singularities, Argument Principle, Rouche's theorem, Residue Theorem, Maximum modulus theorem, Conformal mappings, Schwarz Christoffel Transformation.

 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 Ed., 2014). Complex variables and applications, McGraw-Hill.

2. Spiegel, M., Lipschutz, S. & Schiller, J. (2nd Ed., 2009). Schaum’s Outline of Complex Variables, McGraw Hill.

3. Hann, L. & Epstein, B. (1st Ed., 1996). Classical Complex Analysis, Jones and Bartlett Publishers.

4. Ponnusamy, S. (2nd Ed., 2005). Foundation of Complex Analysis, Alpha Science.