Incompressible fluid flow example
From playlist Divergence
Adjoint Equation of a Linear System of Equations - by implicit derivative
Automatic Differentiation allows for easily propagating derivatives through explicit relations. The adjoint method also enables efficient derivatives over implicit relations like linear systems, which enables the computation of sensitivities. Here are the notes: https://raw.githubuserconte
From playlist Summer of Math Exposition Youtube Videos
11_3_1 The Gradient of a Multivariable Function
Using the partial derivatives of a multivariable function to construct its gradient vector.
From playlist Advanced Calculus / Multivariable Calculus
11_4_2 The Derivative of the Composition of Functions
A further look at the derivative of the composition of a multivariable function and a vector function. There are two methods to calculate such a derivative.
From playlist Advanced Calculus / Multivariable Calculus
Matrix methods for systems of differential equations
Free ebook http://tinyurl.com/EngMathYT I show how to use matrix methods to solve first order systems of differential equations. The ideas involve diagonalization and basic linear ODEs. The example shown involves symmetric matrices.
From playlist Engineering Mathematics
Quantitative estimates for Advective Equation with degenerate constraint – P.-E. Jabin – ICM2018
Mathematics in Science and Technology | Partial Differential Equations Invited Lecture 17.9 | 10.8 Quantitative estimates for Advective Equation with degenerate anelastic constraint Pierre-Emmanuel Jabin Abstract: In these proceedings we are interested in quantitative estimates for advec
From playlist Partial Differential Equations
C17 Non homogeneous higher order linear ODEs with constant coefficients
Explanation of the methods involved in solving a non-homogeneous, linear, ODE, with constant coefficients.
From playlist Differential Equations
Differential Equations with Forcing: Method of Variation of Parameters
This video solves externally forced linear differential equations with the method of variation of parameters. This approach is extremely powerful. The idea is to solve the unforced, or "homogeneous" system, and then to replace the unknown coefficients c_k with unknown functions of time c
From playlist Engineering Math: Differential Equations and Dynamical Systems
C07 Homogeneous linear differential equations with constant coefficients
An explanation of the method that will be used to solve for higher-order, linear, homogeneous ODE's with constant coefficients. Using the auxiliary equation and its roots.
From playlist Differential Equations
Seminar In the Analysis and Methods of PDE (SIAM PDE): Benoit Perthame
The COVID-19 pandemic and consequent social distancing call for online venues of research dissemination. This webinar will serve as a way to recognize achievements in our area, and it will be expected to help promoting the standing of both SIMA and APDE. Further, these webinars should be b
From playlist Seminar In the Analysis and Methods of PDE (SIAM PDE)
Lecture Laurent Desvillettes: Coupling kinetic and fluid equations in the theory of sprays I
The lecture was held within the of the Hausdorff Trimester Program: Kinetic Theory Abstract: In the first lecture, typical systems of equations for the sprays are presented, including the mesoscopic description in which a kinetic equation for the droplets is coupled with a fluid equation
From playlist Summer School: Trails in kinetic theory: foundational aspects and numerical methods
Rupert Klein: Internal wave dynamics in the atmosphere - Lecture 2
Earth’s atmosphere hosts a rich spectrum of phenomena that involve interactions of a variety of processes across many length and time scales. A systematic approach to analyzing these scale dependent processes is a core task of theoretical meteorology and a prerequi- site to constructing re
From playlist Mathematical Physics
Euler's method for estimating solution to non-separable first-order differential equations.
From playlist Advanced Calculus / Multivariable Calculus
Dual cascade, dissipation mechanisms and finite temperature effects by Marc Brachet
Turbulence from Angstroms to light years DATE:20 January 2018 to 25 January 2018 VENUE:Ramanujan Lecture Hall, ICTS, Bangalore The study of turbulent fluid flow has always been of immense scientific appeal to engineers, physicists and mathematicians because it plays an important role acr
From playlist Turbulence from Angstroms to light years
17 - How to write an Eulerian fluid simulator with 200 lines of code.
For the source html code, demo and all other tutorials see https://matthias-research.github.io/pages/tenMinutePhysics/index.html There is also a discord server to discuss all videos here: https://discord.gg/TvqBcyfHJN In this tutorial I explain the basics of Eulerian, grid-based fluid sim
From playlist Fluid Simulation
Hydrodynamics, variational principles and integrability (Pedagogical Lecture 1) by Alexander Abanov
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 : 16 July 2018 to 10 August 2018 VENUE: Ramanujan Lecture Hall, ICTS Bangalore
From playlist Integrable systems in Mathematics, Condensed Matter and Statistical Physics
Machine Learning for Computational Fluid Dynamics
Machine learning is rapidly becoming a core technology for scientific computing, with numerous opportunities to advance the field of computational fluid dynamics. This paper highlights some of the areas of highest potential impact, including to accelerate direct numerical simulations, to i
From playlist Data Driven Fluid Dynamics
Michael Atiyah: Poincaré conjecture, Hodge conjecture, Yang-Mills, Navier-Stokes [2000]
Millennium Meeting These videos document the Institute's landmark Paris millennium event which took place on May 24-25, 2000, at the Collège de France. On this occasion, CMI unveiled the "Millennium Prize Problems," seven mathematical quandaries that have long resisted solution. The announ
From playlist Number Theory
Lec 29: Divergence theorem (cont.): applications & proof | MIT 18.02 Multivariable Calculus, Fall 07
Lecture 29: Divergence theorem (cont.): applications and proof. View the complete course at: http://ocw.mit.edu/18-02SCF10 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT 18.02 Multivariable Calculus, Fall 2007
Approximating the Jacobian: Finite Difference Method for Systems of Nonlinear Equations
Generalized Finite Difference Method for Simultaneous Nonlinear Systems by approximating the Jacobian using the limit of partial derivatives with the forward finite difference. Example code on GitHub https://www.github.com/osveliz/numerical-veliz Chapters 0:00 Intro 0:13 Prerequisites 0:3
From playlist Solving Systems of Nonlinear Equations