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• Introduction: The algebra of complex numbers, Book
• Geometric representation of complex numbers
• Powers and roots of complex numbers
• Functions of Complex Variables, limit and continuity
• Differentiable functions and Cauchy-Riemann Equations
• Analytic functions, Entire functions, Harmonic functions
• Elementary functions: The exponential, Trigonometric functions, Hyperbolic
• Elementary functions: The exponential, Trigonometric functions, Hyperbolic, Logarithmic and Inverse elementary functions
• Mid Term Exam
• Open mapping theorem, Maximum modulus theorem
• Contours and contour integrals, Cauchy-Goursat theorem
• Cauchy integral formula, Lioville’s theorem, Morerea’s theorem
• Series: Power series, Radius of convergence and analyticity, Taylor’s series, Integration and differentiation of power series
• Laurent’s series and residues
• Poles and residues: Zero, singularities, Poles and Residues, Types of singular points, Calculus of residues
• Poles and residues: Zero, singularities, Poles and Residues, Types of singular points, Calculus of residues
• Contour integration, Cauchy’s residue theorem with applications, Mobius transforms, Conformal mappings
• Final Term Exams