Syllabus
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Course Code: B-MAT 602 Course Name: Complex Analysis |
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| MODULE NO / UNIT | COURSE SYLLABUS CONTENTS OF MODULE | NOTES |
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| 1 | Complex numbers and their representation, algebra of complex numbers; Complex plane, Open
set, Domain and region in complex plane; Stereographic projection and Riemann sphere. De Moivre’s Theorem and its Applications. Expansion of trigonometrical functions. Direct circular and hyperbolic functions and their properties, Logarithm of a complex quantity, Summation of Trigonometric series |
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| 2 | Complex functions and their limits including limit at infinity; Continuity and differentiability of a complex valued function. Analytic functions; CauchyRiemann equations, Harmonic functions, necessary and sufficient conditions for differentiability. Analyticity and zeros of exponential, trigonometric and logarithmic functions. | |
| 3 | Complex integration, Green’s theorem, Anti-derivative theorem, CauchyGoursat theorem, Cauchy integral formula, Cauchy’s inequality, Derivative of analytic function. | |
| 4 | Liouville’s theorem, Fundamental theorem of algebra, Maximum modulus theorem and its
consequences. Sequences, series and their convergence, Taylor series and Laurent series of analytic functions. |
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