| 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: |
MoTuWeTh 10:00am - 11:45am in Y-04-4180 |
| Text(s): |
Multivariable Calculus: Concepts and Contexts. 4th edition. By James Stewart. Cengage Learning 2009. ISBN: 978-0495560548.
Multivariable Calculus - Lecture notes. Provided by instructor.
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| Help: |
Office hours: By appointment, MoTuWeTh 7:30 - 8:00 and 12:30 - 13:30 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, August 8 and August 25
Quizzes: in class, Jul 25, Aug 1, Aug 15, Aug 22
Homework: online, using WeBWorK
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| Important dates: |
Mon, Jul 18 - First day of class
Mon, Jul 25 - Quiz #1
Mon, Aug 1 - Quiz #2
Mon, Aug 8 - Exam #1
Mon, Aug 15 - Quiz #3
Mon, Aug 22 - Quiz #4
Thu, Aug 25 - Exam #2; Last day of class
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| Useful links: |
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Schedule:
| Mon, Jul 18 |
Three-Dimensional Coordinate Systems. Vectors. |
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| Tue, Jul 19 |
The Dot Product. The Cross Product. |
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| Wed, Jul 20 |
Equations of Lines and Planes. |
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| Thu, Jul 21 |
Cylindrical and Spherical Coordinates. |
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| Mon, Jul 25 |
Quiz #1. Functions of Several Variables. Functions and Surfaces. Parametric Surfaces. Vector Fields. |
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| Tue, Jul 26 |
Vector Functions and Space Curves. Derivatives and Integrals of Vector Functions. |
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| Wed, Jul 27 |
Arc Length and Curvature. Motion in Space: Velocity and Acceleration. |
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| Thu, Jul 28 |
Limits and Continuity. Partial Derivatives. |
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| Mon, Aug 1 |
Quiz #2. Tangent Planes and Linear Approximations. |
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| Tue, Aug 2 |
The Chain Rule. Directional Derivatives and the Gradient Vector. |
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| Wed, Aug 3 |
Maximum and Minimum Values. |
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| Thu, Aug 4 |
Lagrange Multipliers. |
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| Mon, Aug 8 |
Exam #1. |
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| Tue, Aug 9 |
Double Integrals over Rectangles. Iterated Integrals. |
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| Wed, Aug 10 |
Double Integrals over General Regions. Triple Integrals. |
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| Thu, Aug 11 |
Double Integrals in Polar Coordinates. Applications of Double Integrals. |
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| Mon, Aug 15 |
Quiz #3. Triple Integrals in Cylindrical and Spherical Coordinates. Change of Variables in Multiple Integrals. |
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| Tue, Aug 16 |
Line Integrals. |
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| Wed, Aug 17 |
The Fundamental Theorem for Line Integrals. Green's Theorem. Curl and Divergence. |
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| Thu, Aug 18 |
Surface Area. Surface Integrals. |
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| Mon, Aug 22 |
Quiz #4. The Divergence Theorem. |
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| Tue, Aug 23 |
Stokes' Theorem. |
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| Wed, Aug 24 |
Review. |
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| Thu, Aug 25 |
Exam #2. |
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