English | 2021 | ASIN: B092TCZX71 | 162 pages | PDF | 2.50 MB

SYLLABUS- B.Sc. OBJ. COMPLEX ANALYSIS,
Unit 1
Functions of a complex variable, Concepts of limit, continuity and differentiability of complex functions, Analytic
functions, Cauchy-Riemann equations (Cartesian and polar form), Harmonic functions, Orthogonal system,
Power series as an analytic function.
Unit 2
Elementary functions, Mapping by elementary functions, Linear and bilinear transformations, Fixed points, Cross
ratio, Inverse points and critical points, Conformal transformations.
Unit 3
Complex Integration, Line integral, Cauchy's fundamental theorem, Cauchy's integral formula, Morera's theorem,
Liouville theorem, Maximum Modulus theorem, Taylor and Laurent series.
Unit 4
Singularities and zeros of an analytic function, Rouche's theorem, Fundamental theorem of algebra, Analytic
continuation.
Unit 5
Residue theorem and its applications to the evaluation of definite integrals, Argument principle.
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