In the mathematical fields of the calculus of variations and differential geometry, the variational vector field is a certain type of vector field defined on the tangent bundle of a differentiable manifold which gives rise to variations along a vector field in the manifold itself. Specifically, let X be a vector field on M. Then X generates a one-parameter group of local diffeomorphisms FlXt, the flow along X. The differential of FlXt gives, for each t, a mapping where TM denotes the tangent bundle of M. This is a one-parameter group of local diffeomorphisms of the tangent bundle. The variational vector field of X, denoted by T(X) is the tangent to the flow of d FlXt. (Wikipedia).
11_7_1 Potential Function of a Vector Field Part 1
The gradient of a function is a vector. n-Dimensional space can be filled up with countless vectors as values as inserted into a gradient function. This is then referred to as a vector field. Some vector fields have potential functions. In this video we start to look at how to calculat
From playlist Advanced Calculus / Multivariable Calculus
Introduction to Vector Fields This video discusses, 1) The definition of a vector field. 2) Examples of vector fields including the gradient, and various velocity fields. 3) The definition of a conservative vector field. 4) The definition of a potential function. 5) Test for conservative
From playlist Calculus 3
Ex 1: Determine the Curl of a Vector Field (2D)
This video explains how to determine the curl of a vector field in the xy-plane. The meaning of the curl is discussed and shown graphically. http://mathispower4u.com
From playlist Vector Fields, Divergence, and Curl
Multivariable Calculus | Conservative vector fields.
We prove some results involving conservative vector fields and describe a strategy for finding a potential function. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Multivariable Calculus
MATH2018 Lecture 3.2 Vector Fields
We discuss the concept of a vector field and introduce some basic tools for understanding them: divergence and curl.
From playlist MATH2018 Engineering Mathematics 2D
Multivariable Calculus | What is a vector field.
We introduce the notion of a vector field and give some graphical examples. We also define a conservative vector field with examples. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Multivariable Calculus
One prominent example of a vector field is the Gradient Vector Field. Given any scalar, multivariable function f: R^n\to R, we can get a corresponding vector field that has a precise geometrical meaning: the vectors point in the direction of maximal increase of the function. MY VECTOR CA
Worldwide Calculus: Vector Fields
Lecture on 'Vector Fields' from 'Worldwide Multivariable Calculus'. For more lecture videos and $10 digital textbooks, visit www.centerofmath.org.
From playlist Integration and Vector Fields
[Lesson 22] QED Prerequisites: The Electromagnetic Field Tensor
This is a REPOST of a lecture with video repairs and some annoying errors corrected! To reinforce our efforts to put the 4-potential at center stage we do a second development, this time founded in Lorentz invariance ala Landau and Lifshitz "Classical Theory of Fields." Then, we show how
From playlist QED- Prerequisite Topics
Gravitational radiation from post-Newtonian sources.... by Luc Blanchet (Lecture - 1)
PROGRAM SUMMER SCHOOL ON GRAVITATIONAL WAVE ASTRONOMY ORGANIZERS : Parameswaran Ajith, K. G. Arun and Bala R. Iyer DATE : 15 July 2019 to 26 July 2019 VENUE : Madhava Lecture Hall, ICTS Bangalore This school is part of the annual ICTS summer schools on gravitational-wave (GW) astronomy.
From playlist Summer School on Gravitational Wave Astronomy -2019
Noether's theorems and their growing physical relevance by Joseph Samuel
DATES: Monday 29 Aug, 2016 - Tuesday 30 Aug, 2016 VENUE: Madhava Lecture Hall, ICTS Bangalore Emmy Noether (1882-1935) is well known for her famous contributions to abstract algebra and theoretical physics. Noether’s mathematical work has been divided into three ”epochs”. In the first (
From playlist The Legacy of Emmy Noether
The thresholding scheme for mean curvature flow as minimizing movement scheme - 3
Speaker: Felix Otto (Max Planck Institute for Mathematics in the Sciences in Leipzig) International School on Extrinsic Curvature Flows | (smr 3209) 2018_06_13-14_00-smr3209
From playlist Felix Otto: "The thresholding scheme for mean curvature flow as minimizing movement scheme", ICTP, 2018
Supersymmetry and Superspace, Part 2 - Jon Bagger
Supersymmetry and Superspace, Part 2 Jon Bagger Johns Hopkins University July 20, 2010
From playlist PiTP 2010
Y. Tonegawa - Analysis on the mean curvature flow and the reaction-diffusion approximation (Part 1)
The course covers two separate but closely related topics. The first topic is the mean curvature flow in the framework of GMT due to Brakke. It is a flow of varifold moving by the generalized mean curvature. Starting from a quick review on the necessary tools and facts from GMT and the def
From playlist Ecole d'été 2015 - Théorie géométrique de la mesure et calcul des variations : théorie et applications
The thresholding scheme for mean curvature flow as minimizing movement scheme - 4
Speaker: Felix Otto (Max Planck Institute for Mathematics in the Sciences in Leipzig) International School on Extrinsic Curvature Flows | (smr 3209) 2018_06_14-10_45-smr3209
From playlist Felix Otto: "The thresholding scheme for mean curvature flow as minimizing movement scheme", ICTP, 2018
Recent advances in Geometric Analysis - 6 June 2018
http://crm.sns.it/event/435 Centro di Ricerca Matematica Ennio De Giorgi The aim of the workshop is to bring together experts working on different sides of Geometric Analysis: PDE aspects, minimal or constant mean curvature surfaces, geometric inequalities, applications to general relativ
From playlist Centro di Ricerca Matematica Ennio De Giorgi
This video explains the definition of a vector space and provides examples of vector spaces.
From playlist Vector Spaces
F. Schulze - An introduction to weak mean curvature flow 1
It has become clear in recent years that to understand mean curvature flow through singularities it is essential to work with weak solutions to mean curvature flow. We will give a brief introduction to smooth mean curvature flow and then discuss Brakke flows, their basic properties and how
From playlist Ecole d'été 2021 - Curvature Constraints and Spaces of Metrics