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UMass Boston
Summer II 2016 (Jul 18 - Aug 25)
MATH 242 - Multivariable and Vector Calculus -- Section 01B
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.
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
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
Useful links: Piazza - CMS - Message boards
WeBWorK - Online homework
Mon, Jul 18   Three-Dimensional Coordinate Systems. Vectors.
Tue, Jul 19   The Dot Product. The Cross Product.
Wed, Jul 20   Equations of Lines and Planes.
Thu, Jul 21   Cylindrical and Spherical Coordinates.
Mon, Jul 25   Quiz #1. Functions of Several Variables. Functions and Surfaces. Parametric Surfaces. Vector Fields.
Tue, Jul 26   Vector Functions and Space Curves. Derivatives and Integrals of Vector Functions.
Wed, Jul 27   Arc Length and Curvature. Motion in Space: Velocity and Acceleration.
Thu, Jul 28   Limits and Continuity. Partial Derivatives.
Mon, Aug 1   Quiz #2. Tangent Planes and Linear Approximations.
Tue, Aug 2   The Chain Rule. Directional Derivatives and the Gradient Vector.
Wed, Aug 3   Maximum and Minimum Values.
Thu, Aug 4   Lagrange Multipliers.
Mon, Aug 8   Exam #1.
Tue, Aug 9   Double Integrals over Rectangles. Iterated Integrals.
Wed, Aug 10   Double Integrals over General Regions. Triple Integrals.
Thu, Aug 11   Double Integrals in Polar Coordinates. Applications of Double Integrals.
Mon, Aug 15   Quiz #3. Triple Integrals in Cylindrical and Spherical Coordinates. Change of Variables in Multiple Integrals.
Tue, Aug 16   Line Integrals.
Wed, Aug 17   The Fundamental Theorem for Line Integrals. Green's Theorem. Curl and Divergence.
Thu, Aug 18   Surface Area. Surface Integrals.
Mon, Aug 22   Quiz #4. The Divergence Theorem.
Tue, Aug 23   Stokes' Theorem.
Wed, Aug 24   Review.
Thu, Aug 25   Exam #2.