| 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 2:00pm - 3:50pm
Th 2:00pm - 3:50pm
in W-1-009 |
| 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 9:50am - 10:20am and 4:00pm - 4:30pm
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 3 and November 14
Final Exam: TBA
Quizzes: in class, almost every Tuesday
Homework: online, using WeBWorK
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| Important dates: |
Tue, Sep 12 - Add/drop period ends
Tue, Oct 3 - Exam #1
Tue, Nov 14 - Exam #2
Wed, Nov 22 - Pass/Fail Withdrawal deadline
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| Useful links: |
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Schedule:
| Tue, Sep 5 |
Three-Dimensional Coordinate Systems. Vectors. |
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| Thu, Sep 7 |
The Dot Product. |
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| Tue, Sep 12 |
The Cross Product. Triple products. |
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| Thu, Sep 14 |
Quiz #1. Equations of Lines and Planes. |
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| Tue, Sep 19 |
Cylindrical and Spherical Coordinates. |
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| Thu, Sep 21 |
Quiz #2. Vector Functions and Space Curves. |
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| Tue, Sep 26 |
Derivatives and Integrals of Vector Functions. |
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| Thu, Sep 28 |
Quiz #3. Arc Length and Curvature. Motion in Space: Velocity and Acceleration. |
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| Tue, Oct 3 |
Parametric Surfaces. Functions of Several Variables. Functions and Surfaces. |
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| Thu, Oct 5 |
Exam #1. |
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| Tue, Oct 10 |
Limits and Continuity. Partial Derivatives. |
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| Thu, Oct 12 |
Tangent Planes and Linear Approximations. |
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| Tue, Oct 17 |
Quiz #4. The Chain Rule. Directional Derivatives and the Gradient Vector. |
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| Thu, Oct 19 |
Maximum and Minimum Values. |
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| Tue, Oct 24 |
Quiz #5. Lagrange Multipliers. Double Integrals over Rectangles. |
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| Thu, Oct 26 |
Iterated Integrals. |
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| Tue, Oct 31 |
Quiz #6. Double Integrals over General Regions. Double Integrals in Polar Coordinates. Applications of Double Integrals. |
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| Thu, Nov 2 |
Triple Integrals. |
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| Tue, Nov 7 |
Quiz #7. Triple Integrals in Cylindrical and Spherical Coordinates. |
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| Thu, Nov 9 |
Change of Variables in Multiple Integrals. |
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| Tue, Nov 14 |
Review. Exam #2. |
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| Thu, Nov 16 |
Line Integrals. |
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| Tue, Nov 21 |
The Fundamental Theorem for Line Integrals. Green's Theorem. |
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| Tue, Nov 28 |
Quiz #8. Applications of Line Integrals. Smooth Parametrizations. |
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| Thu, Nov 30 |
Vector Fields. Surface Area. Surface Integrals. |
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| Tue, Dec 5 |
Quiz #9. Curl and Divergence. The Divergence Theorem. |
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| Thu, Dec 7 |
Stokes' Theorem. |
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| Tue, Dec 12 |
Review. |
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