Fundamental of Complex Analysis (Solutions of Some Exercises)

Complex analysis is the study of functions that exist in the complex plane, that is, functions with complex arguments and complex outputs. With roots in the 18th century and the years just before, it is one of the classical branches of mathematics. In the 20th century, significant figures in mathematics who are connected to complex numbers include Euler, Gauss, Riemann, Cauchy, Gösta Mittag-Leffler, Weierstrass, and many others.

Studying complex functions and their characteristics, such as continuity, differentiability, analyticality, singularities, power series representation, and others, is the primary objective of complex analysis1. Engineering and physics both use complex analysis extensively.

Solutions of some exercises from Fundamental of Complex Analysis written by Dr. M. Iqbal and published by Ilmi Kitab Khana, Lahore- PAKISTAN. These are handwritten notes by Prof.(Rtd) Muhammad Saleem.

This book covers most of the fundamental topics on complex analysis. But this book has wide readers in Pakistan. This book contains lot of questions and this is a reason that many teachers consider it to make question paper from this book specially for annual system examination.

This book covers many notions but we are mentioning here the most important ones.

• Basic concepts and complex numbers.
• Limit, continuity and differentiability of complex functions.
• Uniform continuity.
• Analytic or regular or holomorphic functions.
• Harmonic functions.
• Laplace equation in polar form.
• Elementary functions.
• Complex Integration.
• Power series and related theorems.
• Taylor's' theorem
• Mauritians' series
• Laurent's' theorem
• Singularities and calculus of residues
• Zero of a function
• Residue at pole

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• Real Analysis Notes by Prof Syed Gul Shah