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 R^{2} and R^{3} |
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 R^{n} |