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
Complex Analysis Episode 12: The Complex Exponential Function
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
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
Graph the Direct Image of a Set Under the Complex Exponential Function Example
Graph the Direct Image of a Set Under the Complex Exponential Function Example
From playlist Complex Analysis
The 5 ways to visualize complex functions | Essence of complex analysis #3
Complex functions are 4-dimensional: its input and output are complex numbers, and so represented in 2 dimensions each, so how do we visualize complex functions if we are living in a 3D world? There are actually 5 different ways to visualize a complex function, and this video is going to e
From playlist Essence of complex analysis
Represent a Discrete Function Using Ordered Pairs, a Table, and Function Notation
This video explains how to represent a discrete function given as points as ordered pairs, a table, and using function notation. http://mathispower4u.com
From playlist Introduction to Functions: Function Basics
Complex analysis: Holomorphic functions
This lecture is part of an online undergraduate course on complex analysis. We define holomorphic (complex differentiable) functions, and discuss their basic properties, in particular the Cauchy-Riemann equations. For the other lectures in the course see https://www.youtube.com/playlist
From playlist Complex analysis
Terence Tao: The circle method from the perspective of higher order Fourier analysis
Higher order Fourier analysis is a collection of results and methods that can be used to control multilinear averages (such as counts for the number of four-term progressions in a set) that are out of reach of conventional linear Fourier analysis methods (i.e., out of reach of the circle m
From playlist Harmonic Analysis and Analytic Number Theory
Areejit Samal (7/25/22): Forman-Ricci curvature: A geometry-inspired measure with wide applications
Abstract: In the last few years, we have been active in the development of geometry-inspired measures for the edge-based characterization of real-world complex networks. In particular, we were first to introduce a discretization of the classical Ricci curvature proposed by R. Forman to the
From playlist Applied Geometry for Data Sciences 2022
Lecture 8, Continuous-Time Fourier Transform | MIT RES.6.007 Signals and Systems, Spring 2011
Lecture 8, Continuous-Time Fourier Transform Instructor: Alan V. Oppenheim View the complete course: http://ocw.mit.edu/RES-6.007S11 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT RES.6.007 Signals and Systems, 1987
The Monge - Ampère equations, the Bergman kernel, (Lecture 4) by Kengo Hirachi
PROGRAM CAUCHY-RIEMANN EQUATIONS IN HIGHER DIMENSIONS ORGANIZERS: Sivaguru, Diganta Borah and Debraj Chakrabarti DATE: 15 July 2019 to 02 August 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Complex analysis is one of the central areas of modern mathematics, and deals with holomo
From playlist Cauchy-Riemann Equations in Higher Dimensions 2019
Konstantin Mischaikow (8/28/21): Solving systems of ODEs via combinatorial homological algebra
Using the simplest possible nontrivial model system (2-dimensional with continuous piecewise linear nonlinearities, but a high dimensional parameter space) and as many pictures as possible I will outline how one can efficiently compute a homological representation of dynamics and then demo
From playlist Beyond TDA - Persistent functions and its applications in data sciences, 2021
Lecture 15, Discrete-Time Modulation | MIT RES.6.007 Signals and Systems, Spring 2011
Lecture 15, Discrete-Time Modulation Instructor: Alan V. Oppenheim View the complete course: http://ocw.mit.edu/RES-6.007S11 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT RES.6.007 Signals and Systems, 1987
Lecture 12: Lebesgue Integrable Functions, the Lebesgue Integral and the Dominated Convergence...
MIT 18.102 Introduction to Functional Analysis, Spring 2021 Instructor: Dr. Casey Rodriguez View the complete course: https://ocw.mit.edu/courses/18-102-introduction-to-functional-analysis-spring-2021/ YouTube Playlist: https://www.youtube.com/watch?v=W2pw1JWc9k4&list=PLUl4u3cNGP63micsJp_
From playlist MIT 18.102 Introduction to Functional Analysis, Spring 2021
Overview of various methods for sensitivity analysis in the UQ of subsurface systems
From playlist Uncertainty Quantification
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
Thierry Fack: Non-commutative Geometry and Morse Theory for Foliation
We show how to develop a Morse theory along the leaves of a measured foliation. In particular, we prove Morse inequalities for foliations and show how to compute the L^2-cohomology of a foliation from the singularities of a leafwise Morse function. The lecture was held within the framewor
From playlist HIM Lectures: Trimester Program "Non-commutative Geometry and its Applications"