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Complex Analysis Complex Function Theory
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Complex Analysis Complex Function Theory
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File Type :PDF
Number of Pages :109

Description
The note covers an introductory undergraduate-level sequence in complex analysis, starting from basics notions and working up to such results as the Riemann mapping theorem or the prime number theorem. Topics covered includes: Riemann Sphere, Complex-Differentiability, and Convergence, Power Series and Cauchy-Riemann Equations, The Closed Curve Theorem and Cauchy’s Integral Formula, Applications of Cauchy’s Integral Formula, Liouville Theorem, Mean Value Theorem, Mean Value Theorem and Maximum Modulus Principle, Generalized Closed Curve Theorem and Morera’s Theorem, Morera’s Theorem, Singularities, and Laurent Expansions, Meromorphic Functions and Residues , Winding Numbers and Cauchy’s Integral Theorem, The Argument Principle, Fourier Transform and Schwarz Reflection Principle, Riemann Mapping Theorem, Analytic Continuation of Gamma and Zeta, Zeta function and Prime Number Theorem, Prime Number Theorem, Elliptic Functions, Weierstrass’s Elliptic Function and an Overview of Elliptic Invariants and Moduli Spaces.
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