Analytic Functions|| Examples of Cauchy's Riemann(C.R) Equations|| Complex Analysis

COURSE: COMPLEX ANALYSIS CHAPTER # 2 Analytic Functions. Topic: In this lecture I shall discuss some important examples related to Cauchy's Riemann(C.R) Equations ------------------------------------------------------------------------------------------------------------------------------------------------------- To watch complete course of complex Analysis click    • COMPLEX ANALYSIS|| HIGHER MATHMATICS|| PRO...   ------------------------------------------------------------------------------------------------------------------------------------------------------- FOLLOWING ARE THE CONTENTS OF COMPLEX ANALYSIS 1. Complex numbers, complex planes, complex functions 2. Analytic functions 3. Entire functions 4. Harmonic functions 5. Elementary functions: complex exponential, logarithmic and hyperbolic functions 6. Infinite Series 7. Power series, derived series, radius of convergence 8. Taylor series and Laurent series 9. Conformal Representation 10. Transformation, conformal transformation 11. Linear transformation 12. Möbius transformations 13. Complex Integration 14. Complex integrals 15. Cauchy-Goursat theorem 16. Cauchy’s integral formula and their consequences 17. Liouville’s theorem 18. Morera’s theorem 19. Derivative of an analytic function Singularity and Poles  Review of Laurent series  Zeros, singularities  Poles and residues Contour Integration  Cauchy’s residue theorem  Applications of Cauchy’s residue theorem Expansion of Functions and Analytic Continuation  Mittag-Leffler theorem  Weierstrass’s factorization theorem  Analytic continuation Elliptic Functions  Periodic functions  Elliptic functions and its properties  Weierstrass function  (z)  Differential equation satisfied by  (z)  Integral formula for  (z)  Addition theorem for  (z)  Duplication formula for  (z)  Elliptic functions in terms of Weierstrass function with the same periods  Quasi periodic functions: The zeta and sigma functions of Weierstrass  Jacobian elliptic functions and its properties ------------------------------------------------------------------------------------------------------------------------------------------------------- #ComplexAnalysis #AnalyticFunctions #CauchyRiemann #HolomorphicFunctions #ComplexCalculus #Analyticity #ComplexVariables #EntireFunctions #PoleAnalysis #ComplexIntegration #HarmonicFunctions #Singularities #ComplexDifferentialEquations #ComplexFunctionTheory #AnalyticContinuation ------------------------------------------------------------------------------------------------------------------------------------------------------- #highermathematics #Maths4U. #professorazmatali #complexanalysis ‪@azmatali006‬