Complex analysis: Residue calculus
This lecture is part of an online undergraduate course on complex analysis. We describe the residue calculus, and show how to use it to evaluate some integrals. For the other lectures in the course see https://www.youtube.com/playlist?list=PL8yHsr3EFj537_iYA5QrvwhvMlpkJ1yGN
From playlist 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
Math 135 Complex Analysis Lecture 22 041615: Calculus of Residues
Calculus of residues: examples of integrating a function with simple poles on the real axis; integrating a function with a branch cut; integrating along a branch cut.
From playlist Course 8: Complex Analysis
Complex Analysis: Residue At Infinity
Today, we take a look an interesting concept called the residue at infinity.
From playlist Contour Integration
Math 135 Complex Analysis Lecture 19 040715: Calculus of Residues, introduction
Calculus of residues: Cauchy residue theorem; Residue at infinity (error: missing minus sign); residues at simple poles; residues at poles of known order.
From playlist Course 8: Complex Analysis
Complex Analysis 14: Residues part 2, poles
Residues: part 2 (poles)
From playlist MATH2069 Complex Analysis
Complex Analysis 16: An application of Residues
Using residues to find a real integral
From playlist MATH2069 Complex Analysis
Complex analysis: Using the Residue Theorem, we show that the improper integral of 1/(1+x^4) over the real line equals pi sqrt(2)/2. Key steps include computing residues and estimates on integrals.
From playlist Complex Analysis
Complex Analysis 15: The Residue Theorem
The Residue Theorem and some examples of its use.
From playlist MATH2069 Complex Analysis
Complex Analysis - Part 35 - Application of the Residue Theorem
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From playlist Complex Analysis
Complex Analysis - Part 32 - Residue
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From playlist Complex Analysis
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 - Part 34 - Residue Theorem
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From playlist Complex Analysis
Complex Analysis - Part 33 - Residue for Poles
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From playlist Complex Analysis
Complex analysis: Summing series
This lecture is part of an online undergraduate course on complex analysis. This is a replacement for a previous video, correcting some minor typos. We show how to use the residue calculus to sum series, such as Euler's series 1/1^2 + 1/2^2+ ... Solution to exercise in rot 13: cv phorq
From playlist Complex analysis
Complex Analysis: Nasty Integral with Elegant Solution
Today, we evaluate a very difficult-looking integral (at least for real methods) using complex analysis. Original Question: https://math.stackexchange.com/questions/2174693/int-0-infty-frac1xe-ln2x-4-pi2-dx-keyhole-contour-o?rq=1
From playlist Contour Integration
Complex Analysis: Integral of 1/(x^2+1) using Contour Integration
Today, we use complex analysis to evaluate the improper integral on the real numbers of the integral of 1/(x^2+1).
From playlist Contour Integration
Complex Analysis L09: Complex Residues
This video discusses the residue theorem in complex analysis and how to compute complex contour integrals around singular points. This culminates in the integral of the function f(z)=1/z. @eigensteve on Twitter eigensteve.com databookuw.com
From playlist Engineering Math: Crash Course in 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