Argument (complex analysis)

What are complex numbers? | Essence of complex analysis #2

A complete guide to the basics of complex numbers. Feel free to pause and catch a breath if you feel like it - it's meant to be a crash course! Complex numbers are useful in basically all sorts of applications, because even in the real world, making things complex sometimes, oxymoronicall

From playlist Essence of complex analysis

Why care about complex analysis? | Essence of complex analysis #1

Complex analysis is an incredibly powerful tool used in many applications, specifically in solving differential equations (Laplace's and others via inverse Fourier / Laplace transforms), and of course, fundamental theorem of algebra, Riemann hypothesis, as well as solving complicated integ

From playlist Essence of complex analysis

Complex Analysis Overview

In this video, I give a general (and non-technical) overview of the topics covered in an elementary complex analysis course, which includes complex numbers, complex functions, the Cauchy-Riemann equations, Cauchy’s integral formula, residues and poles, and many more! Watch this video if yo

From playlist Complex Analysis

Complex analysis: Integration

This lecture is part of an online undergraduate course on complex analysis. We define integration of a complex function along a path as the limit of a sum, and give its basic properties. We finish by calculating the integral of z^n around a circle. For the other lectures in the course s

From playlist Complex analysis

Complex Analysis Introduction

From playlist Complex Analysis Made Simple

Complex analysis: Classification of elliptic functions

This lecture is part of an online undergraduate course on complex analysis. We give 3 description of elliptic functions: as rational functions of P and its derivative, or in terms of their zeros and poles, or in terms of their singularities. We end by giving a brief description of the a

From playlist Complex analysis

Complex analysis: Introduction

This lecture is part of an online undergraduate course on complex analysis. This is the first lecture, and gives a quick overview of some of the topics that might be covered, such as Cauchy's theorem, analytic continuation, the Riemann zeta function, and the Mandelbrot set. For the oth

From playlist Complex analysis

Complex analysis: Arithmetic

This lecture is part of an online undergraduate course on complex analysis. We review the basic arithmetic of complex numbers, and given some applications to some problems in number theory related to sums of two squares. At the end we briefly cover the quaternions. For the other lecture

From playlist Complex analysis

Complex analysis: Singularities

This lecture is part of an online undergraduate course on complex analysis. We discuss the different sorts of singularities of a holomorphic function (removable singularities, poles, essential singularities, branch-points, limits of singularities, natural boundaries) and give examples of

From playlist Complex analysis

Complex Analysis Episode 7: Multiplying and Dividing in Polar Form

Some of the links below are affiliate links. As an Amazon Associate I earn from qualifying purchases. If you purchase through these links, it won't cost you any additional cash, but it will help to support my channel. Thank you! Complex Analysis Textbook https://amzn.to/2u5fgl4 (affiliate

From playlist Complex Analysis

How to Compute sqrt(i) - Complex Analysis with the Math Sorcerer

How to Compute sqrt(i) - Complex Analysis with the Math Sorcerer In this video we compute the square root of i (sqrt(i)) using basic math that is learned in a typical undergraduate complex analysis course.

From playlist Complex Analysis

Complex Analysis Episode 6: Polar Form of Complex Numbers

Some of the links below are affiliate links. As an Amazon Associate I earn from qualifying purchases. If you purchase through these links, it won't cost you any additional cash, but it will help to support my channel. Thank you! Complex Analysis Textbook https://amzn.to/2u5fgl4 (affiliate

From playlist Complex Analysis

What are Conformal Mappings? | Nathan Dalaklis

Conformal Mappings are a gem of Complex analysis that play a big role in both the theory behind the analysis of functions of a complex variable as well as studying fluid dynamics and electrostatics in physics, along with general relativity. In this video, a brief introduction to these maps

From playlist The First CHALKboard

How to maintain analytical complexity in the face of the experimental turn by Andreas Wimmer

Program Summer Research Program on Dynamics of Complex Systems ORGANIZERS: Amit Apte, Soumitro Banerjee, Pranay Goel, Partha Guha, Neelima Gupte, Govindan Rangarajan and Somdatta Sinha DATE : 15 May 2019 to 12 July 2019 VENUE : Madhava hall for Summer School & Ramanujan hall f

From playlist Summer Research Program On Dynamics Of Complex Systems 2019

Complex Analysis Episode: 9 Roots of Complex Numbers

Some of the links below are affiliate links. As an Amazon Associate I earn from qualifying purchases. If you purchase through these links, it won't cost you any additional cash, but it will help to support my channel. Thank you! Complex Analysis Textbook https://amzn.to/2u5fgl4 (affiliate

From playlist Complex Analysis

i^i using Complex Analysis

i^i using Complex Analysis In this video we compute i^i using math from the field of complex analysis. This is a good example of how complex^complex = real.

From playlist Complex Analysis

Complex Analysis Episode 8: De Moivre's Formula and Powers of Complex Numbers

Some of the links below are affiliate links. As an Amazon Associate I earn from qualifying purchases. If you purchase through these links, it won't cost you any additional cash, but it will help to support my channel. Thank you! Complex Analysis Textbook https://amzn.to/2u5fgl4 (affiliate

From playlist Complex Analysis

Complex analysis: Elliptic functions

This lecture is part of an online undergraduate course on complex analysis. We start the study of elliptic (doubly periodic) functions by constructing some examples, and finding some conditions that their poles and zeros must satisfy. For the other lectures in the course see https://www

From playlist Complex analysis

Math 135 Complex Analysis Lecture 03 0127151: Basic Topological Concepts part 1

Basic topology review: open sets, open sets and set operations, limits, uniqueness of limits, limits and arithmetic, continuity.

From playlist Course 8: Complex Analysis