Multivariable Calculus (video)

This course covers vector and multi-variable calculus. It is the second semester in the freshman calculus sequence. Topics include vectors and matrices, partial derivatives, double and triple integrals, and vector calculus in 2 and 3-space.
Course Features
I. Vectors and matrices
1     Dot product
2     Determinants; cross product
3     Matrices; inverse matrices
4     Square systems; equations of planes
5     Parametric equations for lines and curves
6     Velocity, acceleration - Kepler's second law
7     Review
II. Partial derivativesh;
8     Level curves; partial derivatives; tangent plane approximation
9     Max-min problems; least squares
10     Second derivative test; boundaries and infinity
11     Differentials; chain rule
12     Gradient; directional derivative; tangent plane
13     Lagrange multipliers
14     Non-independent variables
15     Partial differential equations; review
III. Double integrals and line integrals in the plane
16     Double integrals
17     Double integrals in polar coordinates; applications
18     Change of variables
19     Vector fields and line integrals in the plane
20     Path independence and conservative fields
21     Gradient fields and potential functions
22     Green's theorem
23     Flux; normal form of Green's theorem
24     Simply connected regions; review
IV. Triple integrals and surface integrals in 3-space
25     Triple integrals in rectangular and cylindrical coordinates
26     Spherical coordinates; surface area
27     Vector fields in 3D; surface integrals and flux
28     Divergence theorem
29     Divergence theorem (cont.): applications and proof
30     Line integrals in space, curl, exactness and potentials
31     Stokes' theorem
32     Stokes' theorem (cont.); review
33     Topological considerations - Maxwell's equations
34     Final review
35     Final review (cont.)