In vector calculus, the divergence theorem, also known as Gauss's theorem or Ostrogradsky's theorem, is a theorem which relates the flux of a vector field through a closed surface to the divergence of the field in the volume enclosed. More precisely, the divergence theorem states that the surface integral of a vector field over a closed surface, which is called the "flux" through the surface, is equal to the volume integral of the divergence over the region inside the surface. Intuitively, it states that "the sum of all sources of the field in a region (with sinks regarded as negative sources) gives the net flux out of the region". The divergence theorem is an important result for the mathematics of physics and engineering, particularly in electrostatics and fluid dynamics. In these fields, it is usually applied in three dimensions. However, it generalizes to any number of dimensions. In one dimension, it is equivalent to integration by parts. In two dimensions, it is equivalent to Green's theorem. (Wikipedia).
Divergence Theorem. In this video, I give an example of the divergence theorem, also known as the Gauss-Green theorem, which helps us simplify surface integrals tremendously. It's, in my opinion, the most important theorem in multivariable calculus. It is also extremely useful in physics,
From playlist Vector Calculus
26: Divergence Theorem - Valuable Vector Calculus
Video explaining the definition of divergence: https://youtu.be/UEU9dLgmBH4 Video on surface integrals: https://youtu.be/hVBoEEJlNuI The divergence theorem, also called Gauss's theorem, is a natural consequence of the definition of divergence. In this video, we'll see an intuitive explana
From playlist Valuable Vector Calculus
24: Divergence - Valuable Vector Calculus
In-depth explanation of divergence formula: https://youtu.be/W--29EqUSl0 Explanation of the definition of divergence of a vector field. What does divergence mean? How do we calculate divergence? We'll also talk about some geometric meaning to the formula for divergence. Full Valuable Vec
From playlist Valuable Vector Calculus
Free ebook http://tinyurl.com/EngMathYT A basic introduction to the divergence of a vector field - one of the basic operations of vector calculus. I discuss how to calculate the divergence and its physical connection with flux density. Plenty of examples are discussed.
From playlist Engineering Mathematics
Free ebook http://tinyurl.com/EngMath A short tutorial on how to apply Gauss' Divergence Theorem, which is one of the fundamental results of vector calculus. The theorem is stated and we apply it to a simple example.
From playlist Several Variable Calculus / Vector Calculus
Divergence of a vector field: Vector Calculus
Free ebook http://tinyurl.com/EngMathYT I present a simple example where I compute the divergence of a given vector field. I give a rough interpretation of the physical meaning of divergence. Such an example is seen in 2nd year university mathematics courses.
From playlist Engineering Mathematics
Divergence of series -- Calculus II
This lecture is on Calculus II. It follows Part II of the book Calculus Illustrated by Peter Saveliev. The text of the book can be found at http://calculus123.com.
From playlist Calculus II
Download the free PDF http://tinyurl.com/EngMathYT A basic lecture discussing the divergence of a vector field. I show how to calculate the divergence and present some geometric explanation of what the divergence represents. Several examples are discussed. Such ideas have important appl
From playlist Engineering Mathematics
Calculus 3: Divergence and Curl (6 of 32) What is the Divergence? Part 4
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain what is the divergence using a non-linear example where F=(x^2)i. Next video in the series can be seen at: https://youtu.be/dyWeTKHFlg8
From playlist CALCULUS 3 CH 8 DIVERGENCE AND CURL
The Divergence Theorem // Geometric Intuition & Statement // Vector Calculus
In this video we get to the last major theorem in our playlist on vector calculus: The Divergence Theorem. We've actually already seen the two-dimensional analog when we studied the Divergence or Flux form of Green's Theorem. Now we upgrade to the three-dimensional situation where we have
Gauss's Divergence theorem is one of the most powerful tools in all of mathematical physics. It is the primary building block of how we derive conservation laws from physics and translate them into partial differential equations. @eigensteve on Twitter eigensteve.com databookuw.com %%
From playlist Engineering Math: Vector Calculus and Partial Differential Equations
A unified view of Vector Calculus (Stoke's Theorem, Divergence Theorem & Green's Theorem)
In the final video of my vector calculus playlist (congrats to everyone for making it to the end!!!) I want to do a bit of an overview of the major theorems we have seen in this course - Stokes' Theorem, Divergence Theorem, Green's Theorem - all are part of a unified framework. Loosely, in
Worldwide Calculus: The Divergence Theorem
Lecture on 'The Divergence Theorem' from 'Worldwide Multivariable Calculus'. For more lecture videos and $10 digital textbooks, visit www.centerofmath.org.
From playlist Integration and Vector Fields
The Divergence Theorem, a visual explanation
This video talks about the divergence theorem, one of the fundamental theorems of multivariable calculus. The divergence theorem relates a flux integral to a triple integral. Green's Theorem: https://youtu.be/8SwKD5_VL5o Line Integrals: https://youtu.be/dnGDmZynvYY Follow Me! https://i
From playlist Multivariable Calculus
Jason Behrstock: Random graphs and applications to Coxeter groups
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Algebra
Tensor Calculus Lecture 13b: Integration - The Divergence Theorem
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
Converting Maxwells Equations from Differential to Integral Form
In this video I show how to make use of Stokes and Divergence Theorem in order to convert between Differential and Integral form of Maxwell's equations. I also try to explain their connection to fluid dynamics, as well as motivation for each form.
From playlist Math/Derivation Videos
Calculus 16.9 The Divergence Theorem
My notes are available at http://asherbroberts.com/ (so you can write along with me). Calculus: Early Transcendentals 8th Edition by James Stewart
From playlist Calculus
Extended Gauss' Theorem | MIT 18.02SC Multivariable Calculus, Fall 2010
Extended Gauss' Theorem Instructor: Joel Lewis View the complete course: 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 18.02SC: Homework Help for Multivariable Calculus
Ex 2: Determine the Divergence of a Vector Field
This video explains how to find the divergence of a vector field. The meaning is discussed and shown graphically. http://mathispower4u.com
From playlist Vector Fields, Divergence, and Curl