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 integral of a scalar function
5:10 – Example: Computing surface area
10:01 – Example: Computing total mass
16:46 – Surface integral of a vector function
20:51 – Example: Computing flux through a surface

#Calculus

[RajChhabraUW]

AE501: Great review of surface integrals! I liked how the example tied surface integrals to flux problems

[mazen]

AE501 - Very clear and helpful lecture. Watching it again to help with HW#5.

[JoshShort-or]

AE501: you pick great examples thanks for making it easier to learn!

[elijahleonen]

AE501: The Surface Area example was very helpful in understanding the purpose of the double integral.

[BrianaStaheli-gfjg]

AE501: really like the examples that involve real world applications of this. Great explanation

[glopez]

Enjoyed the video. The 3-D representations really help with the understanding. Great examples. (MAE501).

[alviehaider]

AE 501 Great Introduction into surface integrals and Vector Fields

[seenaaalemu]

how can vary parameters while I use Simulink? I appreciate you way of explanation on MATLAB always thanks a lot Chris

[meganmcmahon]

AE501: It helps me to see the connection between surface integrals, f=1, and surface area! What I am still trying to conceptualize, how can a *surface* have a density? How can you find the mass over this surface? I am imagining the surface infinitely thin, but I am not sure that is the correct way to think about it.

[Richard_Le]

AE501 For the parameterization of S in the fluid example, does x always have to be substituted with u or is it an arbitrary choice?

[bsgove]

AE 501

I hated mathamatica in my undergraduate math classes, but now my opinion has completely reversed. In these more advanced math classses, it decreases the tedium of this homework by a lot, not to mention that it aids my understanding greatly.