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, crossproduct, 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 W1009 
Text(s): 
Multivariable Calculus: Concepts and Contexts. 4th edition. By James Stewart. Cengage Learning 2009. ISBN: 9780495560548.

Help: 
Office hours: By appointment:
TuTh 9:50am  10:20am and 4:00pm  4:30pm in S03091.
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 
ThreeDimensional Coordinate Systems. Vectors. 


Thu, Sep 7 
The Dot Product. 


Tue, Sep 12 
Quiz #1. The Cross Product. Triple products. 


Thu, Sep 14 
Equations of Lines and Planes. 


Tue, Sep 19 
Quiz #2. Cylindrical and Spherical Coordinates. Vector Functions and Space Curves. 


Thu, Sep 21 
Derivatives and Integrals of Vector Functions. 


Tue, Sep 26 
Quiz #3. Arc Length and Curvature. Motion in Space: Velocity and Acceleration. 


Thu, Sep 28 
Functions of Several Variables. Functions and Surfaces. 


Tue, Oct 3 
Review. Exam #1. 


Thu, Oct 5 
Parametric Surfaces. 


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. 


