| Lec # | topics | key dates |
|---|---|---|
| I. Vectors and Matrices | ||
| 1 | Vectors in 2- and 3-space Dot Product | |
| 2 | Determinants of Orders 2 and 3 Cross Product | |
| 3 | Matrices; Inverse Matrices | |
| 4 | Solving Systems of Linear Equations; Lines, Planes | |
| 5 | Parametric Curves; Velocity, Acceleration | Problem set 1 due |
| 6 | Kepler's Second Law | |
| Exam 1 (Covering Lectures 1-6) | Problem set 2 due | |
| II. Partial Derivatives | ||
| 7 | Level Curves, Partial Derivatives, Tangent Plane | |
| 8 | Max-Min Problems Least Squares Approximation | |
| 9 | 2nd Derivative Test; Boundaries and Infinity | Problem set 3 due |
| 10 | Differentials; Chain Rule | |
| 11 | Gradient, Directional Derivative | |
| 12 | Lagrange Multipliers | Problem set 4 due |
| 13 | Non-independent Variables | |
| 14 | Partial Differential Equations Review | |
| Exam 2 (Covering Lectures 7-14) | Problem set 5 due | |
| III. Double and Triple Integrals | ||
| 15 | Double and Iterated Integrals | |
| 16 | Double Integrals in Polar Coordinates Applications | |
| 17 | Change of Variables | Problem set 6 due |
| 18 | Triple Integrals in Rectangular and Cylindrical Coordinates | |
| 19 | Spherical Coordinates Gravitational Attraction | |
| IV. Vector Calculus in 2 and 3-space | ||
| 20 | Line Integrals in the Plane | Problem set 7 due |
| 21 | Gradient Fields and Path Independence | |
| 22 | Conservative Fields and Potential Functions | |
| 23 | Green's Theorem 2-dimensional Curl (Vorticity) | Problem set 8 due |
| 24 | Simply-connected Regions Review | |
| Exam 3 (Covering Lectures 15-24, Except 18-19) | Problem set 9 due | |
| 25 | Flux Form of Green's Theorem | |
| 26 | Vector Fields in 3-space; Surface Integrals and Flux | |
| 27 | Divergence (= Gauss's) Theorem | Problem set 10 due |
| 28 | Divergence Theorem (cont.) | |
| 29 | Line Integrals in Space, Exactness, and Potentials | |
| 30 | Stokes' Theorem | Problem set 11 due |
| 31 | Understanding Curl Review | |
| Exam 4 (Covering Lectures 18-19, 25-31) | ||
| 32 | Topological Issues | Problem set 12 due |
| 33 | Conservation Laws; Heat/Diffusion Equation | |
| 34 | Course Review | |
| 35 | Course Evaluation Maxwell's Equations | |