Theorems in topology | Differential topology
In mathematics, the discussion of vector fields on spheres was a classical problem of differential topology, beginning with the hairy ball theorem, and early work on the classification of division algebras. Specifically, the question is how many linearly independent smooth nowhere-zero vector fields can be constructed on a sphere in N-dimensional Euclidean space. A definitive answer was provided in 1962 by Frank Adams. It was already known, by direct construction using Clifford algebras, that there were at least ρ(N)-1 such fields (see definition below). Adams applied homotopy theory and topological K-theory to prove that no more independent vector fields could be found. Hence ρ(N)-1 is the exact number of pointwise linearly independent vector fields that exist on an (N-1)-dimensional sphere. (Wikipedia).
Intro to VECTOR FIELDS // Sketching by hand & with computers
Vector Fields are extremely important in math, physics, engineering, and many other fields. Gravitational fields, electric fields, magnetic fields, velocity fields, these are all examples of vector fields. In this video we will define the concept of a vector field, talk about some basic te
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
Free ebook http://tinyurl.com/EngMathYT A basic introduction to vector fields discussing the need for vector fields and some of the basic mathematics associated with them.
From playlist Engineering Mathematics
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
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
This video explains the definition of a vector space and provides examples of vector spaces.
From playlist Vector Spaces
From playlist Drawing a sphere
The video explains how to determine the center and radius of a sphere. http://mathispower4u.yolasite.com/
From playlist Vectors
Lec 27: Vector fields in 3D; surface integrals & flux | MIT 18.02 Multivariable Calculus, Fall 2007
Lecture 27: Vector fields in 3D; surface integrals and flux. 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
From playlist Problems | Charges, Forces, and Fields
Mod-02 Lec-08 Electric Field and Potential
Electromagnetic Theory by Prof. D.K. Ghosh,Department of Physics,IIT Bombay.For more details on NPTEL visit http://nptel.ac.in
From playlist IIT Bombay: Electromagnetic Theory
8.02x - Lect 3 - Electric Flux, Gauss' Law, Examples
Electric Flux, Gauss's Law, Examples Assignments Lecture 1, 2, 3, 4 and 5: http://freepdfhosting.com/2cb4aad955.pdf Solutions Lecture 1, 2, 3, 4 and 5: http://freepdfhosting.com/75b96693f2.pdf
From playlist 8.02x - MIT Physics II: Electricity and Magnetism
Surface Integral of a Vector Field | Lecture 41 | Vector Calculus for Engineers
How to compute the surface integral of a vector field. Join me on Coursera: https://www.coursera.org/learn/vector-calculus-engineers Lecture notes at http://www.math.ust.hk/~machas/vector-calculus-for-engineers.pdf Subscribe to my channel: http://www.youtube.com/user/jchasnov?sub_confir
From playlist Vector Calculus for Engineers
Electric Flux and Gauss' Law - Review for AP Physics C: Electricity and Magnetism
AP Physics C: Electricity and Magnetism review of Electric Flux and Gauss’ Law including: Electric flux for a constant electric field, an example of the flux through a closed rectangular box, the electric flux from a point charge, a basic introduction to Gauss’ law, an example of Gauss’ la
From playlist AP Physics C: Electricity & Magnetism Review
For more information about Professor Shankar's book based on the lectures from this course, Fundamentals of Physics: Mechanics, Relativity, and Thermodynamics, visit http://bit.ly/1jFIqNu. Fundamentals of Physics, II (PHYS 201) The electric field is discussed in greater detail and field
From playlist Fundamentals of Physics II with Ramamurti Shankar
The Math You Didn't Learn | #SoME2
Sometimes people wonder what actual mathematicians do. Do they crunch large numbers? Participate in competitions with each other? (They actually did a lot of that in the Middle Ages). Are they geniuses whose activites are unfathomable for us normal people? Math is a very large field, but m
From playlist Summer of Math Exposition 2 videos
Deriving Gauss's Law for Electric Flux via the Divergence Theorem from Vector Calculus
I love this application of vector calculus. We are going to derive one of the foundational laws in electricity and magnitism called Gauss' Law, which is one of Maxwell's four equations that govern E&M. This is a property of the divergence theorem, which we studied in the previous video in
Einstein's General Theory of Relativity | Lecture 2
In this lecture, Professor Leonard Susskind of the Stanford University Physic's Department discusses dark energy, the tendency of it to tear atoms apart, and Gauss's Law. Einstein's Theory (PHY 27) discusses the different applications of Einstein's Theory of Relativity in particle phy
From playlist Lecture Collection | Modern Physics: Einstein's Theory