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Unit I
Complex Analysis – I : Complex Numbers and Their Geometric Representation, Polar Form of Complex Numbers. Powers and Roots, Derivative. Analytic Function, Cauchy–Riemann Equations.
Laplace’s Equation, Exponential Function, Trigonometric and Hyperbolic Functions. Euler’s Formula, de’Moivre’s theorem (without proof), Logarithm. General Power. Principal Value. Singularities and Zeros. Infinity, Line Integral in the Complex Plane, Cauchy’s Integral Theorem, Cauchy’s Integral Formula, Derivatives of Analytic Functions, Taylor and Maclaurin Series.
[10Hrs]
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