Denis Auroux

Lecture 01: Dot product

Lecture 02: Determinants; cross product

Lecture 08: Level curves; partial derivatives; tangent plane approximation

Lecture 05: Parametric equations for lines and curves

Lecture 04: Square systems; equations of planes

Lecture 03: Matrices; inverse matrices

Lecture 09: Max-min problems; least squares

Lecture 13: Lagrange multipliers

Lecture 11: Differentials; chain rule

Lecture 16: Double integrals

Lecture 12: Gradient; directional derivative; tangent plane

Lecture 19: Vector fields and line integrals in the plane

Lecture 10: Second derivative test; boundaries and infinity

Lecture 06: Velocity, acceleration; Kepler's second law

Lecture 17: Double integrals in polar coordinates; applications

Lecture 18: Change of variables

Lecture 22: Green's theorem

Lecture 07: Review

Lecture 14: Non-independent variables

Lecture 28: Divergence theorem

Lecture 27: Vector fields in 3D; surface integrals and flux

Lecture 15: Partial differential equations; review

Lecture 21: Gradient fields and potential functions

Lecture 25: Triple integrals in rectangular and cylindrical coordinates

Lecture 20: Path independence and conservative fields

Lecture 26: Spherical coordinates; surface area

Lecture 31: Stokes' theorem

Lecture 23: Flux; normal form of Green's theorem

Lecture 35: Final review (cont.)

Lecture 33: Topological considerations; Maxwell's equations

Lecture 29: Divergence theorem (cont.): applications and proof

Lecture 24: Simply connected regions; review

Lecture 32: Stokes' theorem (cont.); review

Lecture 34: Final review

Chopin - Etude Op 10 No 1

1 - Dot Product

Debussy - Pour le Piano - Prel

Rachmaninov - Prelude Op 23 No

2 - Determinants; Cross Product

Rachmaninov, Prelude Op 23 No 4

Lecture 12 - Partial derivatives - Gradient; directional derivative; tangent plane

3 - Matrices; Inverse Matrices

4 - Square Systems; Equations of Planes