PMAT 32043

>< Type/ Status : Elective
>< Title : Complex Variables
>< Pre-requisites : PMAT 12035
>< Objectives :
At the end of this course, the student will be familiar with a wide range of applications of complex numbers and functions.
>< Course Content :

Complex numbers, Triangle inequality, Curves and regions in the complex plane, Complex valued functions, Limits, Continuity Derivatives, Analytic functions, Cauchy Riemann equations, Rational functions, Exponential functions, Trigonometric and hyperbolic functions, Logarithm, General power, Line integral in the complex plane, Cauchy’s integral theorem, Cauchy’s integral formula, The derivatives of an analytic function, Taylor and Laurent series, Analyticity at infinity, Zeros and singularities, Residues, The Residue theorem, Evaluation of real integral.

>< Methodology : A combination of lectures and tutorial discussions
>< Scheme of Evaluation : Based on tutorials, tests and end of course examination
><Recommended Reading :
1. Murray, R.S. (1993). Complex Variables, McGraw-Hill, New York.
2. Churchill, R.V. (1960). Complex Variables and Applications, McGraw-Hill, New York.

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