Syllabus
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Course Code: ST-303 & ST-304 Course Name: (vii) Real and Complex Analysis |
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| MODULE NO / UNIT | COURSE SYLLABUS CONTENTS OF MODULE | NOTES |
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| 1 | Topology of Real Numbers: Open Set, Closed Set, Limit Point of a Set, Bounds of a Set. Convergence and Divergence of Sequences.Cauchy’s Theorem on Limits, Sequence and Series of Functions and Their Convergence Properties. | |
| 2 | Functions of a Complex Variable and Their Analytic Properties.Cauchy’s Riemann equations.Power Series and its Radius of Convergence.Elementary idea of Mobius Transformation, Cross Ratio, Invariant Point and Criticalpoint. | |
| 3 | Regular and Rectifiable Arcs. Contour. Domains: Connected, Simply Connected and Multiply Connected. Complex Line integrals.Cauchy’s Theorem, Cauchy’s Integral Formulae and Inequality.Morera’s Theorem.Liouvelle’s Theorem. Taylor and Laurent Series | |
| 4 | Singularities and Their Classification.Poles and Zeros of a Meromorphic Function, Argument Principle.Rouches Theorem. Fundamental Theorem of Algebra.Residues. Cauchy’s Residue Theorem. Application of Cauchy’s Residue Theorem for Evaluation of Integrals of Real Valued Functions. | |
