Lie derivative pt. 2: Properties and general tensors
Part 1: https://youtu.be/vFsqbsRl_K0 Updated version with the sign error fixed (sort of). The previous version of this video contained an ugly sign error as pointed out by Magist. It should now be clear what the correct sign is. Unfortunately, I also had to cut out part of the video becau
From playlist Lie derivative
Lie derivative of a vector field (flow and pushforward)
Part 2: https://youtu.be/roFNj3k4Lmc In this video I show you how you can derive the Lie derivative of a vector field. First, we look at a vector field on a manifold and develop the notion of an integral curve followed by the flow of the vector field. We can then move another vector along
From playlist Lie derivative
Lie derivatives of differential forms
Introduces the lie derivative, and its action on differential forms. This is applied to symplectic geometry, with proof that the lie derivative of the symplectic form along a Hamiltonian vector field is zero. This is really an application of the wonderfully named "Cartan's magic formula"
From playlist Symplectic geometry and mechanics
Derivatives are the main object of study in differential calculus. They describe rates of change of functions. That makes them incredibly useful in all of science, as many models can be expressed by describing the changes over time (e.g. of physical quantities). However, the abstract defin
From playlist Summer of Math Exposition Youtube Videos
Calculus - What is a Derivative? (1 of 8) Overview
Visit http://ilectureonline.com for more math and science lectures! In this video I will give a general overview and the definition of “What is a derivative?”
From playlist CALCULUS 1 CH 2 WHAT IS A DERIVATIVE?
This lecture is part of an online graduate course on Lie groups. We define the Lie algebra of a Lie group in two ways, and show that it satisfied the Jacobi identity. The we calculate the Lie algebras of a few Lie groups. For the other lectures in the course see https://www.youtube.co
From playlist Lie groups
Calculus - What is a Derivative? (7 of 8) A Function Describing a Change (In a Function)
Visit http://ilectureonline.com for more math and science lectures! In this video I will describe the physical meaning of a derivative.
From playlist CALCULUS 1 CH 2 WHAT IS A DERIVATIVE?
Definition of derivative in terms of a limit, (def 1)
Definition of derivative, calculus 1 homework solution. #calculus Check out my 100 derivatives: https://youtu.be/AegzQ_dip8k
From playlist Sect 2.7, Definition of Derivative
Lie Groups and Lie Algebras: Lesson 22 - Lie Group Generators
Lie Groups and Lie Algebras: Lesson 22 - Lie Group Generators A Lie group can always be considered as a group of transformations because any group can transform itself! In this lecture we replace the "geometric space" with the Lie group itself to create a new collection of generators. P
From playlist Lie Groups and Lie Algebras
Lie Groups and Lie Algebras: Lesson 25 - the commutator and the Lie Algebra
Lie Groups and Lie Algebras: Lesson 25 - the commutator In this lecture we discover how to represent an infinitesimal commutator of the Lie group using a member of the Lie algebra. We promote the vector space spawned by the group generators to an algebra. Please consider supporting this
From playlist Lie Groups and Lie Algebras
Math 131 Fall 2018 102418 Taylor's Theorem; Introduction to Sequences
Sketch of proof of L'Hopital's Rule. Taylor's theorem: definition of Taylor polynomial. Proof of Taylor's theorem. Introduction to sequences. Definition of convergence of a sequence (in a metric space). Example. Implications of convergence to a point: every neighborhood of the point
From playlist Course 7: (Rudin's) Principles of Mathematical Analysis (Fall 2018)
Tensor Calculus Lecture 8: Embedded Surfaces and the Curvature Tensor
This course will eventually continue on Patreon at http://bit.ly/PavelPatreon Textbook: http://bit.ly/ITCYTNew Errata: http://bit.ly/ITAErrata McConnell's classic: http://bit.ly/MCTensors Table of Contents of http://bit.ly/ITCYTNew Rules of the Game Coordinate Systems and the Role of Te
From playlist Introduction to Tensor Calculus
Calculus 1: What is a Derivative? (1 of 9) Basic Definitions
Visit http://ilectureonline.com for more math and science lectures! In this video I will introduce the basic definitions of what is a derivative. Next video in the series can be seen at: http://youtu.be/29Px0qXE1BU
From playlist CALCULUS 1 CH 2 WHAT IS A DERIVATIVE?
Title: Rational Matrix Differential Operators and Integral Systems of PDEs
From playlist Fall 2017
Lie Groups and Lie Algebras: Lesson 19 - Infinitesimal transformation example
Lie Groups and Lie Algebras: Lesson 19 - Infinitesimal transformation example In this lecture we demonstrate how a transformation group generator can transform a function on the geometric space when the transformation is infinitesimal. For this we use Gilmores 2-parameter scale/shift exa
From playlist Lie Groups and Lie Algebras
Differential Equations 1: Oxford Mathematics 2nd Year Student Lecture
We continue with our series of Student Lectures with this first lecture in the 2nd year Course on Differential Equations. Professor Philip Maini begins with a recap of the previous year's work before moving on to give examples of ordinary differential equations which exhibit either unique,
From playlist Oxford Mathematics Student Lectures - Differential Equations
Lie Groups and Lie Algebras: Lesson 20 - Finite transformation example
Lie Groups and Lie Algebras: Lesson 20 - Finite transformation example A finite transformation is simply a lot of infinitesimal transformations! A Lie group, we have already show is a connected topological space and we know that any finite transformation can be built from a large product
From playlist Lie Groups and Lie Algebras
Nina Snaith: Zeros, moments and determinants
For 20 years we have known that average values of characteristic polynomials of random unitary matrices provide a good model for moments of the Riemann zeta function. Now we consider mixed moments of characteristic polynomials and their derivatives, calculations which are motivated by ques
From playlist Probability and Statistics
In this video, we are going to visualize the concept of FRACTIONAL DERIVATIVE in a new geometric way.
From playlist Summer of Math Exposition Youtube Videos