Fundamentals Of Complex Variables Analysis

An Introduction

What you'll learn
Analyticity
Complex Integration
Complex Power Series
Requirements
Basics of Engineering Mathematicsematics
Description
Complex Variables Analysis is the branch of mathematics that lies at the intersection point of several areas of mathematics that are both pure and applied in nature. The study of complex variable analysis generally deals with numerical, harmonic, and asymptotic analysis. Complex Variable Analysis finds a large number of applications to the solution of physical problems. The development of complex variable analysis is driven by applications in engineering, medicine, and biology. In the real world, the application of complex variable analysis includes the study of the propagation of acoustic waves for designing jet engines, boundary problems in fluid mechanics and heat transfer, and as well as conformal geometry in shape analysis, imaging, and computer vision.The present Massive Open Online Course is divided into two sections. First section deals with the study of Analytic functions, harmonic functions, and some important theorems along with some numerical problems which will make the learners grasp the whole concept. The second section deals with the study of Complex Integration and it further deals with the study of theorems such as Complex Integral Theorem and Complex Integral Function with some numerical examples.Students enrolling in this course should have a basic understanding of engineering mathematics and most importantly should be familiar with Calculus.

Overview

Section 1: Analyticity

Lecture 1 Complex Number

Lecture 2 Complex Variable and Complex Function

Lecture 3 Neighborhood of a point and Analytic Function

Lecture 4 Theorem

Lecture 5 Numericals

Lecture 6 Harmonic Function

Section 2: Complex Integration

Lecture 7 Introduction

Lecture 8 Types of Curves and Regions

Lecture 0 Theorems

Beginner in Complex Variables