| 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: |
Tu 1:00pm - 3:15pm
Th 2:00pm - 3:15pm
in W-01-044 |
| Text(s): |
Multivariable Calculus: Concepts and Contexts. 4th edition. By James Stewart. Cengage Learning 2009. ISBN: 978-0495560548.
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| Help: |
Office hours: By appointment
TuTh 11:00 - 12:00 and 15:30 - 16:30
in S-03-091.
Please follow this link
to schedule a 10 or 20 minute appointment, at least 2 hours in advance. You can stop by my office without a confirmed appointment, but I may be unavailable.
Piazza: Instead of sending questions by email, please use the discussion boards available at piazza.com to post questions and provide answers. |
| Assignments: |
Exams: in class, October 4 and November 15
Final Exam: December 20, 3:00pm - 6:00pm
Quizzes: in class, almost every Tuesday
Homework: online, using WeBWorK
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| Important dates: |
Tue, Sep 13 - Add/drop period ends
Tue, Oct 4 - Exam #1
Tue, Nov 15 - Exam #2
Wed, Nov 23 - Pass/Fail Withdrawal deadline
Tue, Dec 20 - Final Exam
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| Useful links: |
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Schedule:
| Tue, Sep 6 |
Three-Dimensional Coordinate Systems. Vectors. |
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| Thu, Sep 8 |
The Dot Product. |
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| Tue, Sep 13 |
Quiz #1. The Cross Product. Triple products. |
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| Thu, Sep 15 |
Equations of Lines and Planes. |
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| Tue, Sep 20 |
Quiz #2. Cylindrical and Spherical Coordinates. Vector Functions and Space Curves. |
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| Thu, Sep 22 |
Derivatives and Integrals of Vector Functions. |
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| Tue, Sep 27 |
Quiz #3. Arc Length and Curvature. |
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| Thu, Sep 29 |
Motion in Space: Velocity and Acceleration. Functions of Several Variables. Functions and Surfaces. |
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| Tue, Oct 4 |
Review. Exam #1. |
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| Thu, Oct 6 |
Parametric Surfaces. |
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| Tue, Oct 11 |
Limits and Continuity. Partial Derivatives. |
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| Thu, Oct 13 |
Tangent Planes and Linear Approximations. |
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| Tue, Oct 18 |
Quiz #4. The Chain Rule. Directional Derivatives and the Gradient Vector. |
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| Thu, Oct 20 |
Maximum and Minimum Values. |
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| Tue, Oct 25 |
Quiz #5. Lagrange Multipliers. Double Integrals over Rectangles. |
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| Thu, Oct 27 |
Iterated Integrals. |
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| Tue, Nov 1 |
Quiz #6. Double Integrals over General Regions. Double Integrals in Polar Coordinates. |
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| Thu, Nov 3 |
Applications of Double Integrals. Triple Integrals. |
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| Tue, Nov 8 |
Quiz #7. Triple Integrals in Cylindrical and Spherical Coordinates. |
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| Thu, Nov 10 |
Change of Variables in Multiple Integrals. |
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| Tue, Nov 15 |
Review. Exam #2. |
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| Thu, Nov 17 |
Line Integrals. |
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| Tue, Nov 22 |
The Fundamental Theorem for Line Integrals. Green's Theorem. |
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| Tue, Nov 29 |
Quiz #8. Applications of Line Integrals. Smooth Parametrizations. |
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| Thu, Dec 1 |
Surface Area. Surface Integrals. |
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| Tue, Dec 6 |
Quiz #9. Curl and Divergence. The Divergence Theorem. |
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| Thu, Dec 8 |
Stokes' Theorem. |
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| Tue, Dec 13 |
Review. |
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| Tue, Dec 20 |
Final Exam. |
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