MTH324: Complex Analysis (Fall 2025)

At the end of this course the students will be able to understand the basic properties of functions of a complex variable with the theory of analytic functions and its applications.

Functions of a Complex Variable, Limits, Continuity and Derivatives, Differentiation Formulas. Cauchy-Riemann (C-R) Equations. Analytic Functions, Harmonic Functions, Elementary Functions, Exponential, Trigonometric, Hyperbolic, Logarithmic and Inverse Trigonometric Functions. Contour Integral, simple closed Contours, simply and multiply connected Domains, Cauchy Integral Formula, Cauchy Integral Theorem, Derivatives of Analytic Functions, Morera's Theorem, Liouville's Theorem, Power series (Definition and properties), Uniform Convergence. Taylor's and Laurent's series, Integration and Differentiation of Power series. Zeros and Poles, Residues, Residue theorem, Evaluation of Integrals.

1. Assignment 1
   1. Download PDF
   2. View Online
2. Sample Quiz (will be uploaded here).

Please click on View Online to see inside the PDF.

1. Zill, D. G., & Shanahan, P. D. (2003). A first course in complex analysis with applications (2nd ed.). Jones & Bartlett Publishers.
2. Brown, J. W., & Churchill, R. V. (2009). Complex variables and applications (8th ed.). McGraw-Hill.