Syllabus
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Course Code: MMATH20- 102 Course Name: Complex Analysis |
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| MODULE NO / UNIT | COURSE SYLLABUS CONTENTS OF MODULE | NOTES |
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| 1 | Analytic functions; Harmonic functions; Reflection principle; Elementary functions: Exponential, Logarithmic, Trigonometric, Hyperbolic, Inverse trigonometric , Inverse hyperbolic, Complex exponents; Complex Integration: Definite integral; Contours; Branch cuts. (Relevant portions from the book recommended at Sr. No. 1) |
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| 2 | Cauchy-Goursat theorem; Simply/ multiply connected domains; Cauchy integral formula; Morera’s theorem; Liouville’s theorem; Fundamental theorem of algebra; Maximum modulus principle; Power series: Taylor series; Laurent series; Uniform/ absolute convergence. (Relevant portions from the book recommended at Sr. No. 1) |
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| 3 | Differentiation, integration, multiplication, division of power series; Singularities; Poles; Residues; Cauchy’s residue theorem; Zeros of an analytic function; Evaluation of improper integrals; Jordan’s lemma. (Relevant portions from the book recommended at Sr. No. 1) |
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| 4 | Indented paths; Integration along a branch cut; Definite integrals involving sines and cosines; Winding number of closed curve; Argument principle; Rouche’s theorem; Schwarz Lemma ; Transformations: linear, bilinear (Mobius), sine, z2 , z 1/2 ; Mapping: Isogonal; Conformal; Scale factors; Local inverses; harmonic conjugates. (Relevant portions from the book recommended at Sr. No. 1) |
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