Complex
numbers and functions: Complex number—addition, multiplication, subtraction,
division, complex plane, polar form of complex numbers, power and roots:
Complex function-limits, derivatives; Cauchy-Riemann equations; Laplace’s
equation; Harmonic functions and conjugate harmonic function; Exponential
functions, Trigonometric functions, hyperbolic functions, logarithm and general
power; Complex integration: Line integral in the complex plane, bounded for
absolute value on integral, Cauchy integral theorem, Cauchy Integral formula:
Derivatives of analytic functions; Power series: Sequences, series, tests for
convergence and divergence of series; Convergence behavior of power series,
radius of convergence of a power series, Taylor series and McLaurin series;
Laurent series and residue integration; singularities and zeros, residue
integration