Math 402 (spring 2020): The Divergence Theorem

Math 402 (spring 2020): Stokes' Theorem

Math 402 (spring 2020): Surface Integrals

Here are parameterizations of the cone written out in detail. (The double-bar for vector magnitude was the notation we were using when I first wrote this up. Stewart uses single-bar notation, like absolute value bars.) As you can see, the video illustrates the second approach.

Math 402 (spring 2020): Green's Theorem

The solutions below demonstrate different solutions to the problem solved in the video. Note that Green's Theorem can be used only when the field F is planar and the path C is closed. As you can see, different solutions may work just fine, but this is an example where simply doing the line integral (and skipping Green's Theorem) is not recommended.

Math 402 (spring 2020): The Fundamental Theorem of Calculus for Line Integrals

Math 402 (spring 2020): The divergence and curl of a vector field

Math 402 (spring 2020): An introduction to line integrals

Math 402 (spring 2020): Vector fields and gravity

Math 402 (spring 2020): Triple integration in spherical coordinates

Math 402 (spring 2020): Multiple integrals in rectangular and cylindrical coordinates

Math 402 (spring 2020): Applications of double integrals

Math 402 (spring 2020): Double integration with polar coordinates

Math 402 (spring 2020): Double Integration for nonrectangular regions

Math 402 (spring 2020): Double Integration

Math 402 (spring 2020): Lagrange Multipliers

Note: If two vectors are multiples of each other (i.e., parallel), it's completely arbitrary which side of the equation gets the scalar coefficient: λ∇f = ∇g is just as good as ∇f = λ∇g.

Math 402 (spring 2020): Optimizing f(x, y)

Math 402 (spring 2020): Directional Derivatives & Gradient Vectors