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UMass Boston
Fall 2017 (Sep 5 - Dec 13)
MATH 242 - Multivariable and Vector Calculus -- Section 003
 
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.
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
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
Useful links: Piazza - CMS - Message boards
WeBWorK - Online homework
Schedule:
Tue, Sep 5   Three-Dimensional Coordinate Systems. Vectors.
Thu, Sep 7   The Dot Product.
Tue, Sep 12   The Cross Product. Triple products.
Thu, Sep 14   Quiz #1. Equations of Lines and Planes.
Tue, Sep 19   Cylindrical and Spherical Coordinates.
Thu, Sep 21   Quiz #2. Vector Functions and Space Curves.
Tue, Sep 26   Derivatives and Integrals of Vector Functions.
Thu, Sep 28   Quiz #3. Arc Length and Curvature. Motion in Space: Velocity and Acceleration.
Tue, Oct 3   Parametric Surfaces. Functions of Several Variables. Functions and Surfaces.
Thu, Oct 5   Exam #1.
Tue, Oct 10   Limits and Continuity. Partial Derivatives.
Thu, Oct 12   Tangent Planes and Linear Approximations.
Tue, Oct 17   Quiz #4. The Chain Rule. Directional Derivatives and the Gradient Vector.
Thu, Oct 19   Maximum and Minimum Values.
Tue, Oct 24   Quiz #5. Lagrange Multipliers. Double Integrals over Rectangles.
Thu, Oct 26   Iterated Integrals.
Tue, Oct 31   Quiz #6. Double Integrals over General Regions. Double Integrals in Polar Coordinates. Applications of Double Integrals.
Thu, Nov 2   Triple Integrals.
Tue, Nov 7   Quiz #7. Triple Integrals in Cylindrical and Spherical Coordinates.
Thu, Nov 9   Change of Variables in Multiple Integrals.
Tue, Nov 14   Review. Exam #2.
Thu, Nov 16   Line Integrals.
Tue, Nov 21   The Fundamental Theorem for Line Integrals. Green's Theorem.
Tue, Nov 28   Quiz #8. Applications of Line Integrals. Smooth Parametrizations.
Thu, Nov 30   Vector Fields. Surface Area. Surface Integrals.
Tue, Dec 5   Quiz #9. Curl and Divergence. The Divergence Theorem.
Thu, Dec 7   Stokes' Theorem.
Tue, Dec 12   Review.