Syllabus of Complex Analysis
Complex numbers and elementary properties.
Limits, continuity and differentiation.
Cauchy-Riemann equations. Analytic functions, Harmonic
functions. Elementary Analytic functions.
Contour integrals, Anti-derivatives and path
independent of contour integrals.
Cauchy-Goursat Theorem. Cauchy’s integral formula, Morera’s
Theorem. Liouville’s Theorem, Fundamental Theorem of Algebra,
Maximum Modulus Principle and its consequences.
Taylor series, Laurent series.
Zeros and Singularities:
Zeros of Analytic Functions, Singularities,
Argument Principle, Rouche’s Theorem.
Residues and Applications:
Cauchy’s Residue Theorem and
Conformal Mappings, Mobius
MGPP, DCD, AC, ST
Topic 01 Complex Numbers and its Algebra, Topology of Sets
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