Calculus 3, Spring 2020, Practice final exam solutions

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Note: This practice final was to help for a final exam administered online and so had a different format from traditional final exams.

0:00 Intro
2:51 Rewrite integral using Green's Theorem
6:34 Line integral (conservative)
9:54 Divergence Theorem application
14:39 Stokes' Theorem (Bring Your Own Surface)
20:21 Directional derivatives and angle between vectors
25:35 Changing regions when changing variables
30:49 Going from Cartesian to spherical coordinates
33:27 Classifying critical points
35:32 Lagrange multipliers
40:08 Tangent plant to implicit surface
47:40 Properties of the gradient (max increase)
49:53 Tangent plane to implicit surface
53:41 Finding position from acceleration
58:47 Identifying quadric surface
1:00:53 Implicit partial differentiation
1:04:53 Mass of polar region
1:11:06 Changing order of integration
1:14:38 Basic properties of integration
1:20:27 Properties of the cross product
1:22:49 Projection of one vector onto another
1:25:16 Second order Taylor polynomial approximation
1:34:39 Linear approximation to function
1:38:26 Mass of wire (1D)
1:40:25 Finding flux through a surface