In this course, we extend mathematical analysis on single variable functions to multivariable functions. We will learn key concepts on multivariable functions such as partial derivatives, multiple integrals, and their applications.
Colley, Vector Calculus
Susan J. Colley, Vector Calculus
The final grade is determined based on the following scheme.
| Grade | Score | Grade | Score |
|---|---|---|---|
| A+ | 90-100 | C+ | 40-49 |
| A0 | 80-89 | C0 | 30-39 |
| A- | 75-79 | C- | 25-29 |
| B+ | 65-74 | D+ | 15-24 |
| B0 | 55-64 | D0 | 5-14 |
| B- | 50-54 | D- | 1-4 |
| F | 0 |
| Week | Topics | Chapters |
|---|---|---|
| 1 | Dot and cross product, equation of planes, and coordinate systems | 1.1-1.7 |
| 2 | Graphing surface, limits | 2.1-2.2 |
| 3 | The derivatives and partial derivatives | 2.3-2.4 |
| 4 | The chain rule, directional derivatives, and the gradient | 2.5-2.6 |
| 5 | Parametrized curves, Kepler’s laws, arclength, and Differential Geometry | 3.1-3.2 |
| 6 | Vector fields, gradient, divergence, curl, and the del operator | 3.3-3.4 |
| 7 | Differentials and Taylor’s theorem, extrema of functions | 4.1-4.2 |
| 8 | Midterm | |
| 9 | Lagrange multiplier | 4.3-4.4 |
| 10 | Areas, volumes, and double integrals | 5.1-5.2 |
| 11 | Changing the order of integration, triple integrals, and change of variables | 5.3-5.5 |
| 12 | Application of integration, Line integrals | 5.6-6.1 |
| 13 | Green’s theorem, conservative vector fields | 6.2-6.3 |
| 14 | Parametrized surfaces, surface integrals | 7.1-7.2 |
| 15 | Stokes’s and Gauss’s theorem, differential forms | 7.3 |
| 16 | Final |