| Course Description: |
Differential and integral calculus of functions of several variables and of vector fields. Topics include Euclidean, polar, cylindrical, and spherical coordinates; dot product, cross-product, equations of lines and planes; continuity, partial derivatives, directional derivatives, optimization in several variables; multiple integrals, iterated integrals, change of coordinates, Jacobians, general substitution rule; curves and surfaces, parametrizations, line integrals, surface integrals; gradient, circulation, flux, divergence; conservative, solenoidal vector fields; scalar, vector potential; Green, Gauss, and Stokes theorems. |
| Syllabus: |
Syllabus (PDF file) |
| Schedule: |
TuTh 12:30pm - 1:45pm
Th 2:00pm - 2:50pm
in W01-0041 |
| Text(s): |
|
| Help: |
Office hours: Tu 2:00pm - 2:50pm in W03-154-15
additional times by arrangement.
Blackboard: Instead of sending questions by email, please use the discussion boards available at [...] to post questions and provide answers. |
| Assignments: |
Exams: in class, October 4
and November 15
Final Exam: TBA
Quizzes: in class, almost every Thursday
Homework: online, using WeBWorK
|
| Important dates: |
Tue, Oct 4 - Exam #1
Tue, Nov 15 - Exam #2
|
| Useful links: |
|
|
Schedule:
| Tue, Sep 6 |
Three-Dimensional Coordinate Systems. Vectors. |
|
|
| Thu, Sep 8 |
The Dot Product. |
|
|
| Tue, Sep 13 |
The Cross Product. Triple products. |
|
|
| Thu, Sep 15 |
Quiz #1. Equations of Lines and Planes. |
|
|
| Tue, Sep 20 |
Cylindrical and Spherical Coordinates. |
|
|
| Thu, Sep 22 |
Quiz #2. Vector Functions and Space Curves. |
|
|
| Tue, Sep 27 |
Derivatives and Integrals of Vector Functions. |
|
|
| Thu, Sep 29 |
Quiz #3. Arc Length and Curvature. Motion in Space: Velocity and Acceleration. |
|
|
| Tue, Oct 4 |
Parametric Surfaces. Functions of Several Variables. Functions and Surfaces. |
|
|
| Thu, Oct 6 |
Exam #1. |
|
|
| Tue, Oct 11 |
Limits and Continuity. Partial Derivatives. |
|
|
| Thu, Oct 13 |
Tangent Planes and Linear Approximations. |
|
|
| Tue, Oct 18 |
Quiz #4. The Chain Rule. Directional Derivatives and the Gradient Vector. |
|
|
| Thu, Oct 20 |
Maximum and Minimum Values. |
|
|
| Tue, Oct 25 |
Quiz #5. Lagrange Multipliers. Double Integrals over Rectangles. |
|
|
| Thu, Oct 27 |
Iterated Integrals. |
|
|
| Tue, Nov 1 |
Quiz #6. Double Integrals over General Regions. Double Integrals in Polar Coordinates. Applications of Double Integrals. |
|
|
| Thu, Nov 3 |
Triple Integrals. |
|
|
| Tue, Nov 8 |
Quiz #7. Triple Integrals in Cylindrical and Spherical Coordinates. |
|
|
| Thu, Nov 10 |
Change of Variables in Multiple Integrals. |
|
|
| Tue, Nov 15 |
Review. Exam #2. |
|
|
| Thu, Nov 17 |
Line Integrals. |
|
|
| Tue, Nov 22 |
The Fundamental Theorem for Line Integrals. Green's Theorem. |
|
|
| Tue, Nov 29 |
Quiz #8. Applications of Line Integrals. Smooth Parametrizations. |
|
|
| Thu, Dec 1 |
Vector Fields. Surface Area. Surface Integrals. |
|
|
| Tue, Dec 6 |
Quiz #9. Curl and Divergence. The Divergence Theorem. |
|
|
| Thu, Dec 8 |
Stokes' Theorem. |
|
|
| Tue, Dec 13 |
Review. |
|
|
|