Unless noted otherwise, all textbook readings are from:
Apostol, Tom M. Calculus, Vol. 2: Multi-Variable Calculus and Linear Algebra with Applications to Differential Equations and Probability. Wiley, 1969. ISBN: 9780471000075.
Additional course notes by James Raymond Munkres, Professor of Mathematics, Emeritus, are also provided.
| SES # | TOPICS | TEXTBOOK READINGS | COURSE NOTES READINGS |
|---|---|---|---|
| 1 | Linear spaces and subspaces | 1.1-1.6 | Course Notes A (A1-A6) |
| 2 | Dependence, basis, dimension | 1.7-1.8, 1.11-1.12 | Course Notes A (A7-A15) |
| 3 | Linear transformations and invertibility | 2.1-2.7 | |
| 4 | Gauss-Jordan elimination, matrices |
Course Notes A (A17-A23) Course Notes B (B1-B5) |
|
| 5 | Matrix of a transformation, Linear systems | 2.10-2.11 | Course Notes B (B6-B16) |
| 6 | Matrix inverses, determinant | Course Notes B (B25-B51) | |
| 7 | Cross product, Lines and planes |
Course Notes B (B53-B56) Course Notes A (A25-A33) Course Notes B (B18-B23) |
|
| 8 | Vector valued functions, tangency | (14.1-14.5) (Apostol Vol. I) | |
| 9 | Velocity/Acceleration, arclength | (14.6-14.12) (Apostol Vol. I) | |
| 10 | Curvature, Polar coordinates | (14.114-14.16) (Apostol Vol. I) | Course Notes B (B57-B63) |
| 11 | Planetary motion, scalar and vector fields | (14.17, 14.20), 8.1-8.5 (Apostol Vol. I) | |
| 12 | Total derivative, gradient | 8.6-8.8, 8.10-8.13 | |
| 13 | Level sets, tangent planes, derivative of vector fields | 8.15-8.17 | |
| 14 | Exam 1 | ||
| 15 | Chain rule | 8.18-8.21 | |
| 16 | Implicit differentiation, inverse functions | 9.6-9.7 | Course Notes C (C10-C21) |
| 17 | Hessian matrix, maxima, minima, saddle points | 9.9 | |
| 18 | Second derivative test, Taylor’s Formula | 9.9-9.12 | Course Notes C (C22-C27) |
| 19 | Implicit function theorem | ||
| 20 | Extreme Values, Lagrange Multipliers | 9.14 | Course Notes C (C28-C33) |
| 21 | Line integrals | 10.1-10.7 | |
| 22 | Fundamental theorem of line integrals | 10.10-10.14 | |
| 23 | Gradient fields | 10.15-10.16 | |
| 24 | Potential functions, conservation | 10.17, 10.21 | |
| 25 | Double integrals over rectangles | 11.1-11.8 | |
| 26 | Existence and Fubini’s Theorem | 11.10-11.11 | Course Notes D (D1-D17) |
| 27 | Double integrals over more general regions | 11.12-11.14 | Course Notes D (D17-D25) |
| 28 | Applications of multiple integrals | 11.16, 11.17, 11.31 | |
| 29 | Exam 2 | ||
| 30 | Green’s Theorem | 11.19-11.23 | |
| 31 | Applications | Course Notes E (E1-E22) | |
| 32 | Change of variables | 11.26-11.31 | Course Notes E (E23-E33) |
| 33 | Cylindrical and spherical coordinates | 11.32, 11.33 | |
| 34 | Parameterized surfaces | 12.1-12.5 | |
| 35 | Area, surface integrals | 12.7-12.9 | |
| 36 | Stokes’s Theorem | 12.11-12.12, 12.18 | |
| 37 | Stokes’s Theorem (cont.) | Course Notes F (F1-F5) | |
| 38 | Divergence Theorem | 12.19 | |
| 39 | Minimal Surfaces | Course Notes F (F7-F16) | |
| 40 | Final Exam |
