Surfaces | Area | Multivariable calculus

Surface integral

In mathematics, particularly multivariable calculus, a surface integral is a generalization of multiple integrals to integration over surfaces. It can be thought of as the double integral analogue of the line integral. Given a surface, one may integrate a scalar field (that is, a function of position which returns a scalar as a value) over the surface, or a vector field (that is, a function which returns a vector as value). If a region R is not flat, then it is called a surface as shown in the illustration. Surface integrals have applications in physics, particularly with the theories of classical electromagnetism. (Wikipedia).

Surface integral
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Surface Integral of a Vector Field - Part 2

http://mathispower4u.wordpress.com/

From playlist Surface Integrals

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What is a Surface Integral?

Surface Integral In this video, I give an example of how to calculate a surface integral, which is a way of calculating the integral under a function, but over a surface. The key to this is to parametrize the surface and turn this integral into an ordinary double integral. Lots of beautif

From playlist Vector Calculus

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Surface Integrals with Parameterized Surface - Part 2

The video explains how to evaluate a surface integral when the surface is given parametrically. http://mathispower4u.wordpress.com/

From playlist Surface Integrals

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More on surface integrals. Chris Tisdell UNSW

This lecture continues discussing "surface integrals" and further illustrates how to integral functions over surfaces. The idea is a generalization of double integrals in the plane. The concept of surface integral has a number of important applications in the field of engineering, fo

From playlist Vector Calculus @ UNSW Sydney. Dr Chris Tisdell

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Surface Integral of a Vector Field - Part 1

http://mathispower4u.wordpress.com/

From playlist Surface Integrals

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Calculus 16.7 Surface Integrals

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

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23: Scalar and Vector Field Surface Integrals - Valuable Vector Calculus

Video on scalar field line integrals: https://youtu.be/WVQgEeZY_l0 Vector field line integrals: https://youtu.be/0TC4QEE56oc Video on double integrals: https://youtu.be/9AHXnRpF0n8 An explanation of how to calculate surface integrals in scalar and vector fields. We go over where the form

From playlist Valuable Vector Calculus

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Surface Integrals of Scalar and Vector Fields/Functions

In this video we show how to calculate a surface integral of both scalar and vector functions. A surface integral can be used to compute parameters such as the surface area, total mass, volumetric flow rate, and other quantities. Topics and timestamps: 0:00 – Introduction 1:32 – Surface

From playlist Calculus

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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

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Surface integral over a curve

Have you ever wondered why the divergence theorem doesn't apply to line integrals? That's because the definition of the line integral is somewhat flawed! In this video, I generalize the notion of a surface integral so that it can be applied to line integrals (I call this a line-surface i

From playlist Multivariable Calculus

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27: Stokes' Theorem - Valuable Vector Calculus

Video explaining the curl formula: https://youtu.be/b5VJVa5q3Oc Video on surface integrals: https://youtu.be/hVBoEEJlNuI It's possible for the boundary of a surface to have multiple separate parts. It turns out that, in general, if a surface has a boundary, then that boundary is made up

From playlist Valuable Vector Calculus

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Mod-01 Lec-03 Divergence and Curl of Vector Fields

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

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Lec 32: Stokes' theorem (cont.); review | MIT 18.02 Multivariable Calculus, Fall 2007

Lecture 32: Stokes' theorem (cont.); review. 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

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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

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