Dual basis definition and proof that it's a basis In this video, given a basis beta of a vector space V, I define the dual basis beta* of V*, and show that it's indeed a basis. We'll see many more applications of this concept later on, but this video already shows that it's straightforwar
From playlist Dual Spaces
Introduction to Spherical Coordinates
Introduction to Spherical Coordinates This is a full introduction to the spherical coordinate system. The definition is given and then the formulas for converting rectangular to spherical and spherical to rectangular. We also look at some of the key graphs in spherical coordinates. Final
From playlist Calculus 3
Definition of spherical coordinates | Lecture 33 | Vector Calculus for Engineers
We define the relationship between Cartesian coordinates and spherical coordinates; the position vector in spherical coordinates; the volume element in spherical coordinates; the unit vectors; and how to differentiate the spherical coordinate unit vectors. Join me on Coursera: https://www
From playlist Vector Calculus for Engineers
35 - Properties of bases (continued)
Algebra 1M - international Course no. 104016 Dr. Aviv Censor Technion - International school of engineering
From playlist Algebra 1M
Multivariable Calculus | Unit Vectors
We define a unit vector, the unit basis vectors, and give some associated examples. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Vectors for Multivariable Calculus
Spherical Coordinates - Denis Potapov
This video shows some basic facts about the classical spherical coordinates in vector calculus.
From playlist Dr Denis Potapov's videos
Introduction to Spherical Coordinates
This video defines spherical coordinates and explains how to convert between spherical and rectangular coordinates. http://mathispower4u.yolasite.com/
From playlist Quadric, Surfaces, Cylindrical Coordinates and Spherical Coordinates
Spherical Tensor Operators | Wigner D-Matrices | Clebsch–Gordan & Wigner–Eckart
In this video, we will explain spherical tensor operators. They are defined like this: A spherical tensor operator T^(k)_q with rank k is a collection of 2k+1 operators that are numbered by the index q, which transform under rotations in the same way as spherical harmonics do. They are als
From playlist Quantum Mechanics, Quantum Field Theory
This video defines a cylindrical surface and explains how to graph a cylindrical surface. http://mathispower4u.yolasite.com/
From playlist Quadric, Surfaces, Cylindrical Coordinates and Spherical Coordinates
Geordie Williamson: Langlands and Bezrukavnikov II Lecture 14
SMRI Seminar Series: 'Langlands correspondence and Bezrukavnikov’s equivalence' Geordie Williamson (University of Sydney) Abstract: The second part of the course focuses on affine Hecke algebras and their categorifications. Last year I discussed the local Langlands correspondence in bro
From playlist Geordie Williamson: Langlands correspondence and Bezrukavnikov’s equivalence
What is General Relativity? Lesson 37: The line element
What is General Relativity? Lesson 37: The line element This is a repost of Lesson 37 shortened and with some corrections. We introduce the origin of the "line element" and begin our exploration of spherical symmetry. Note the indexing error when I wrote down the equation for the connec
From playlist What is General Relativity?
Converting Between Spherical and Rectangular Equations
This video provides example of how to convert between rectangular equation and spherical equations and vice versa. http://mathispower4u.com
From playlist Quadric, Surfaces, Cylindrical Coordinates and Spherical Coordinates
Positive definite kernels on spheres by E K Narayanan
DISCUSSION MEETING SPHERE PACKING ORGANIZERS: Mahesh Kakde and E.K. Narayanan DATE: 31 October 2019 to 06 November 2019 VENUE: Madhava Lecture Hall, ICTS Bangalore Sphere packing is a centuries-old problem in geometry, with many connections to other branches of mathematics (number the
From playlist Sphere Packing - 2019
Virginie Ehrlacher - Multi-center decomposition of molecular densities: a mathematical perspective
Recorded 04 May 2022. Virginie Ehrlacher of the École Nationale des Ponts-et-Chaussées presents "Multi-center decomposition of molecular densities: a mathematical perspective" at IPAM's Large-Scale Certified Numerical Methods in Quantum Mechanics Workshop. Abstract: The aim of this talk is
From playlist 2022 Large-Scale Certified Numerical Methods in Quantum Mechanics
What is General Relativity? Lesson 72: Schwarzschild Solution - the Setup
What is General Relativity? Lesson 72: Schwarzschild Solution - the Setup In this lesson we are going to set up the mathematical problem we are solving and relate that problem to physics. In preparation for this we need to understand what a spherically symmetric metric must look like, and
From playlist What is General Relativity?
What is General Relativity? Lesson 7: The Glome (OPTIONAL)
What is General Relativity? Lesson 7: The Glome (OPTIONAL) : This lesson is an aside regarding the generalization of spherical coordinates to higher dimensions.
From playlist What is General Relativity?
Joel Dahne, Uppsala University
September 23, Joel Dahne, Uppsala University Rigorous computations of eigenvalues and eigenfunctions of the Laplacian
From playlist Fall 2022 Online Kolchin seminar in Differential Algebra
AlgTop15: Rational curvature of a polytope
We use our new normalization of angle called turn-angle, or "tangle" to define the curvature of a polygon P at a vertex A. This number is obtained by studying the opposite cone at the vertex A, whose faces are perpendicular to the edges of P meeting at A. A classical theorem of Harriot on
From playlist Algebraic Topology: a beginner's course - N J Wildberger
Tess Smidt - Learning how to break symmetry with symmetry-preserving neural networks - IPAM at UCLA
Recorded 26 January 2023. Tess Smidt of the Massachusetts Institute of Technology presents "Symmetry’s made to be broken: Learning how to break symmetry with symmetry-preserving neural networks" at IPAM's Learning and Emergence in Molecular Systems Workshop. Abstract: Symmetry-preserving (
From playlist 2023 Learning and Emergence in Molecular Systems
Introduction to Cylindrical Coordinates
This video introduces cylindrical coordinates and shows how to convert between cylindrical coordinates and rectangular coordinates. http://mathispower4u.yolasite.com/
From playlist Quadric, Surfaces, Cylindrical Coordinates and Spherical Coordinates