Contour integration

11_6_1 Contours and Tangents to Contours Part 1

A contour is simply the intersection of the curve of a function and a plane or hyperplane at a specific level. The gradient of the original function is a vector perpendicular to the tangent of the contour at a point on the contour.

From playlist Advanced Calculus / Multivariable Calculus

Complex Analysis: Double Keyhole Contour

Today, we use contour integration to integrate 1/(x*sqrt(x^2-1)) from 1 to infinity.

From playlist Contour Integration

Complex Analysis: Integral of log(x^2+1)/x^2

Today, we evaluate the integral of log(x^2+1)/x^2 from minus infinity to infinity using an interesting keyhole + semicircular contour. Original post: https://math.stackexchange.com/questions/1096507/int-0-infty-frac-log1x2x2-dx-using-contour-integration

From playlist Contour Integration

Complex Analysis: Integral of 1/(x^4+1) using Contour Integration

Today, we use contour integration and the residue theorem from complex analysis to evaluate the integral of 1/(x^4+1) over the real numbers.

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

Contour Integral on a Line - Complex Variables

Contour Integral on a Line - Complex Variables Example of contour integration on a line. First we parametrize the line and then use the formula to integration.

From playlist Complex Analysis

Complex Analysis: Integral of x^(n-2)/(x^n+1) using Contour Integration

Today, we using complex analysis to evaluate the integral of 0 to infinity of x^(n-2)/(x^n+1). Note that our "n" can be any real number so long as it is greater than or equal to 2. Otherwise we would have a negative power on the numerator and the integral would diverge!

From playlist Contour Integration

Complex Analysis 07: Contour Integration

A few simple examples of contour integration

From playlist MATH2069 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

ME565 Lecture 5: ML Bounds and examples of complex integration

ME565 Lecture 1 Engineering Mathematics at the University of Washington ML Bounds and examples of complex integration Notes: http://faculty.washington.edu/sbrunton/me565/pdf/L05.pdf Course Website: http://faculty.washington.edu/sbrunton/me565/ http://faculty.washington.edu/sbrunton/

From playlist Engineering Mathematics (UW ME564 and ME565)

[Lesson 28] QED Prerequisites Scattering 5

In this lesson we discover the integral representation of the Hankel function. We are doing this in preparation of executing the Method of Steepest Descents/Saddle Point Method to determine its asymptotic form. Please consider supporting this channel on Patreon: https://www.patreon.com/X

From playlist QED- Prerequisite Topics

[Lesson 27.5 optional] QED Prerequisites Scattering 4.5 An application of Cauchy's Theorem

THis is a supplemental lecture to Scattering 4. In this lesson we practice using complex contour integration to evaluate one of the standard integrals used in the development of the formula of stationary phase. This lesson exercises the use of Cauchy's Theorem and Jordan's Lemma. Note: th

From playlist QED- Prerequisite Topics

ME565 Lecture 4: Cauchy Integral Formula

ME565 Lecture 4 Engineering Mathematics at the University of Washington Cauchy Integral Formula Notes: http://faculty.washington.edu/sbrunton/me565/pdf/L04.pdf Course Website: http://faculty.washington.edu/sbrunton/me565/ http://faculty.washington.edu/sbrunton/

From playlist Engineering Mathematics (UW ME564 and ME565)

QED Prerequisites Scattering 6

In this lesson we review some critical mathematics associated with complex analysis. In particular, the nature of an analytic function, the Cauchy Integral Theorem, and the maximum modulus theorem. After this review we turn back to the dark art of asymptotic analysis and study the very cle

From playlist QED- Prerequisite Topics

Complex Analysis L08: Integrals in the Complex Plane

This video explores contour integration of functions in the complex plane. @eigensteve on Twitter eigensteve.com databookuw.com

From playlist Engineering Math: Crash Course in Complex Analysis

The computational theory of Riemann–Hilbert problems (Lecture 3) by Thomas Trogdon

Program : Integrable​ ​systems​ ​in​ ​Mathematics,​ ​Condensed​ ​Matter​ ​and​ ​Statistical​ ​Physics ORGANIZERS : Alexander Abanov, Rukmini Dey, Fabian Essler, Manas Kulkarni, Joel Moore, Vishal Vasan and Paul Wiegmann DATE & TIME : 16 July 2018 to 10 August 2018 VENUE : Ramanujan L

From playlist Integrable​ ​systems​ ​in​ ​Mathematics,​ ​Condensed​ ​Matter​ ​and​ ​Statistical​ ​Physics

D-instanton Contribution to String Amplitudes by Ashoke Sen

ICTS In-house 2022 Organizers: Chandramouli, Omkar, Priyadarshi, Tuneer Date and Time: 20th to 22nd April, 2022 Venue: Ramanujan Hall inhouse@icts.res.in An exclusive three-day event to exchange ideas and research topics amongst members of ICTS.

From playlist ICTS In-house 2022

Complex Analysis L13: Bromwich Integrals and the Inverse Laplace Transform

This video is a culmination of this series on complex analysis, where we show how to compute the Bromwich integral used in the inverse Laplace transform. @eigensteve on Twitter eigensteve.com databookuw.com

From playlist Engineering Math: Crash Course in Complex Analysis

Complex Analysis: Integral of cos(x)/(x^2+1) using Contour Integration

Today, we evaluate a very nice integral using complex analysis. Videos on integral of x*sin(x)/(x^2+1): Complex Analysis Method: https://www.youtube.com/watch?v=O0NEtZ1Yqhs&t=9s Laplace Transform Method: https://www.youtube.com/watch?v=bF7eIV5jl84

From playlist Contour Integration