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Surface integrals

14 videos
Finding line integrals to be a bit boring? Well, this tutorial will add new dimension to your life by explore what surface integrals are and how we can calculate them.

Partial derivatives of vector-valued functions

VIDEO 10:07 minutes
Partial Derivatives of Vector-Valued Functions

Introduction to the surface integral

VIDEO 22:14 minutes
Introduction to the surface integral

Example of calculating a surface integral part 1

VIDEO 10:45 minutes
Example of calculating a surface integral part 1

Example of calculating a surface integral part 2

VIDEO 10:29 minutes
Example of calculating a surface integral part 2

Example of calculating a surface integral part 3

VIDEO 9:54 minutes
Example of calculating a surface integral part 3

Surface integral example part 1: Parameterizing the unit sphere

VIDEO 11:05 minutes
Visualizing a suitable parameterization

Surface integral example part 2: Calculating the surface differential

VIDEO 12:51 minutes
Taking the cross product to calculate the surface differential in terms of the parameters

Surface integral example part 3: The home stretch

VIDEO 12:39 minutes
Using a few trigonometric identities to finally calculate the value of the surface integral

Surface integral ex2 part 1: Parameterizing the surface

VIDEO 5:10 minutes
Parametrizing a surface that can be explictly made a function of x and y.

Surface integral ex2 part 2: Evaluating integral

VIDEO 9:51 minutes
Evaluating the surface integral

Surface integral ex3 part 1: Parameterizing the outside surface

VIDEO 9:00 minutes
Breaking apart a larger surface into its components

Surface integral ex3 part 2: Evaluating the outside surface

VIDEO 9:10 minutes
Evaluating the surface integral over the outside of the chopped cylinder

Surface integral ex3 part 3: Top surface

VIDEO 12:41 minutes
Parametrizing the top surface

Surface integral ex3 part 4: Home stretch

VIDEO 4:02 minutes
Evaluating the third surface integral and coming to the final answer