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• Week1: Introduction to Complex Numbers, Basic Algebraic Properties
• Week 2: Geometric representation of complex numbers, Modulus and Complex Conjugates, Exponential Form of Complex Number
• Week 3: Arguments of Products and Quotients, Powers and roots of Complex Numbers, Regions in Complex Plane
• Week 4: Introduction to Functions of Complex Variables: Definition, limit and continuity
• Week 5: Derivatives of a Complex valued Function, Rules for Differentiation, Cauchy Riemann Equations in Rectangular Coordinates
• Week 6: Cauchy Riemann Equations in Polar Coordinates, Analytic Function, Harmonic Function
• Week 7: Introduction to Elementary functions: The Exponential and the Logarithmic Function, Branches of Logarithmic function
• Week 8: Introduction to Trigonometric, Hyperbolic and Inverse Trigonometric and Hyperbolic functions
• Week 9: Mid Term
• Week 10: Introduction to Complex Integrals: Contours and Contour Integrals, Upper Bounds for the Moduli of Contour Integrals
• Week 11: Introduction to Cauchy - Goursat theorem, Simply Connected Domains, Multiply Connected Domains
• Week 12: Cauchy Integral Formula, Morera's Theorem, Liouville’s Theorem, . Maximum Modulus Theorem.
• Week 13: Convergence of Sequence and Series, Introduction to Taylor and Maclaurin Series
• Week 14: Laurent Series
• Week 15: Integration and Differentiation of Power Series, Multiplication and division of power series
• Week 16: Isolated Singular Point, Introduction to Residues, Introduction to Cauchy’s residue theorem with applications, Residue at Infinity
• Week 17: The Three Types of Isolated Singular Points, Residue at Poles, Zero of Analytic Function,
• Week 18: Final Term