Course Meeting Times
Lectures: 3 sessions / week, 1 hour / session
Prerequisites
18.01 Single Variable Calculus
Description
This is a variation on 18.02 Multivariable Calculus. It covers the same topics as in 18.02, but with more focus on mathematical concepts. Topics include:
- Vector algebra, dot product, matrices, determinant.
- Functions of several variables, continuity, differentiability, derivative.
- Parametrized curves, arc length, curvature, torsion.
- Vector fields, gradient, curl, divergence.
- Multiple integrals, change of variables, line integrals, surface integrals.
- Stokes’ theorem in one, two, and three dimensions.
Textbook
Colley, Susan Jane. Vector Calculus. 3rd ed. Upper Saddle River, NJ: Pearson Prentice Hall, 2006. ISBN: 9780131858749.
Assignments
Homework assignments are due on the second day of class every week. Late problem sets are not accepted, however the lowest problem set score will be dropped.
Grading
| ACTIVITIES | PERCENTAGES |
|---|---|
| Assignments | 25% |
| Hour exams | 45% |
| Final exam | 30% |
Calendar
| LEC # | TOPICS |
|---|---|
| 1 | Vectors in R2 and R3 |
| 2 | Dot product |
| 3 | Cross product |
| 4 | Planes and distances |
| 5 | n-dimensional space |
| 6 | Cylindrical and spherical coordinates |
| 7 | Functions |
| 8 | Limits |
| 9 | The Derivative |
| 10 | More about derivatives |
| 11 | Higher derivatives |
| 12 | Chain rule |
| 13 | Implicit functions |
| 14 | Parametrised curves |
| 15 | Arclength |
| 16 | Moving frames |
| 17 | Vector fields |
| 18 | Div grad curl and all that |
| 19 | Taylor polynomials |
| 20 | Maxima and minima: I |
| 21 | Maxima and minima: II |
| 22 | Double integrals |
| 23 | Inclusion-exclusion |
| 24 | Triple integrals |
| 25 | Change of coordinates: I |
| 26 | Change of coordinates: II |
| 27 | Line integrals |
| 28 | Manifolds with boundary |
| 29 | Conservative vector fields revisited |
| 30 | Surface integrals |
| 31 | Flux |
| 32 | Stokes theorem |
| 33 | Gauss theorem |
| 34 | Forms on Rn |
