## Introduction to Complex Analysis

Start Date: 02/23/2020

 Course Type: Common Course

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This course provides an introduction to complex analysis which is the theory of complex functions of a complex variable. We will start by introducing the complex plane, along with the algebra and geometry of complex numbers, and then we will make our way via differentiation, integration, complex dynamics, power series representation and Laurent series into territories at the edge of what is known today. Each module consists of five video lectures with embedded quizzes, followed by an electronically graded homework assignment. Additionally, modules 1, 3, and 5 also contain a peer assessment. The homework assignments will require time to think through and practice the concepts discussed in the lectures. In fact, a significant amount of your learning will happen while completing the homework assignments. These assignments are not meant to be completed quickly; rather you'll need paper and pen with you to work through the questions. In total, we expect that the course will take 6-12 hours of work per module, depending on your background.

#### Course Syllabus

We’ll begin this module by briefly learning about the history of complex numbers: When and why were they invented? In particular, we’ll look at the rather surprising fact that the original need for complex numbers did not arise from the study of quadratic equations (such as solving the equation z^2+1 = 0), but rather from the study of cubic equations! Next we’ll cover some algebra and geometry in the complex plane to learn how to compute with and visualize complex numbers. To that end we’ll also learn about the polar representation of complex numbers, which will lend itself nicely to finding roots of complex numbers. We’ll finish this module by looking at some topology in the complex plane.

#### Course Introduction

Introduction to Complex Analysis This course provides an introductory overview of complex analysis, including an introduction to exponential and logistic regression models. The course is intended for people who are curious about complex analysis, who is looking for mathematical concepts and techniques to deal with complex problems, and for people who are familiar with linear algebra and programming. The course assumes some prior knowledge of programming, and it is strongly recommended that you have some programming skills already. In this course, you will learn how to use complex linear models to study complex problems. We will introduce the calculus of linear models, which allows you to solve problems using linear algebra. You will need to know the integral calculus, and it is strongly recommended that you have some programming skills already. It is strongly recommended that you have a basic knowledge of linear algebra, including calculus. The course is designed to follow the linear algebra and programming techniques introduced in Linear Algebra for Engineers, and it is strongly recommended that you have some programming skills already. This course is designed to follow the linear algebra and programming techniques introduced in Linear Algebra for Engineers, and it is strongly recommended that you have some programming skills already. The course consists of a series of lectures with online assignments, and it is highly recommended that you take the quizzes. The lectures contain a lot of mathematical information, and the online assignments will test your understanding of the material. The course is designed to follow the linear algebra and programming techniques introduced in Linear

#### Course Tag

Power Series Complex Analysis Mapping Optimizing Compiler

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