Math 268: Multidimensional Calculus
Fall 2015

Instructor Gautam Iyer.   WEH 6121.
Lectures MWF 3:30--4:20 in WEH 5312.
Office Hours (instructor) Mon 11:30--12:20, Fri 10:30--11:20
TA Son Van.  WEH 8205.
Office Hours (TA) Tue 10:00--11:15 and 2:30--3:20
Recitation Tu 3:30-4:20 in WEH 5320.
Homework due Wednesdays, at the beginning of class. Late homework will not be accepted
Midterm 1 Wed, Sep 30 (in class)
Midterm 2 Wed, Nov 4 (in class)
Final Sun, Dec 20, 1:00PM-4:00PM (WEH 5415)
Mailing list math-268 (for course announcements and discussion. Please subscribe to this list.)

Course Description

This course is a serious introduction to multidimensional calculus that makes use of matrices and linear transformations. Students will be expected to write proofs; however, some of the deeper results will be presented without proofs.

Tentative Syllabus

  • Functions of several variables, regions and domains, limits and continuity.
  • Partial derivatives, linearization, Jacobian.
  • Chain rule, inverse and implicit functions and geometric applications.
  • Higher derivatives, Taylor’s theorem, optimization, vector fields.
  • Multiple integrals and change of variables, Leibnitz’s rule.
  • Line integrals, Green’s theorem.
  • Path independence and connectedness, conservative vector fields.
  • Surfaces and orientability, surface integrals.
  • Divergence theorem and Stokes’s theorem.

Textbook and References

  • Textbook: Advanced Calculus (5th Edition) by Wilfred Kaplan. (Homework problems will be assigned from this book. I will cover roughly chapters 2 through 5.)
  • Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach by Hubbard and Hubbard.
  • Multivariable Mathematics: Linear Algebra, Multivariable Calculus, and Manifolds by Shifrin.

Class Policies


  • If you must sleep, don’t snore!
  • Be courteous when you use mobile devices.


  • Homework must be turned in at the beginning of class on the due date.
  • Late homework will NEVER be accepted. Really!
  • To account for unusual circumstances, the bottom 20% of your homework will not count towards your grade.
  • Working in groups is encouraged, but solutions must be written up on your own.
  • Nearly perfect student solutions may be scanned and hosted here, with your identifying information removed. If you don’t want any part of your solutions used, please make a note of it in the margin of your assignment.


  • All exams are closed book, in class.
  • No calculators, computational aids, or internet enabled devices are allowed.
  • The final time will be announced by the registrar here. Be aware of their schedule before making your travel plans.


  • Homework will count as 20% of your grade.
  • Between 25% and 50% of your exams will consist of homework questions.
  • Your better midterm will count as 30% of your grade. (Your worse midterm will not count at all.)
  • Your final will count as 50% of your grade.