# 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

### 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 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 4: Home stretch

VIDEO
4:02 minutes

Evaluating the third surface integral and coming to the final answer