Math 268: Multidimensional Calculus
Fall 2015

Instructor 
Gautam Iyer.
WEH 6121.
gi1242+268@cmu.edu.

Lectures 
MWF 3:304:20 in
WEH 5312.

Office Hours (instructor) 
Mon 11:3012:20, Fri 10:3011:20

TA 
Son Van.
WEH 8205.
vansp@cmu.edu. 
Office Hours (TA) 
Tue 10:0011:15 and 2:303:20

Recitation 
Tu 3:304:20 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, 1:00PM4:00PM (WEH 5415) 
Mailing list 
math268
(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
Lectures
 If you must sleep, don’t snore!
 Be courteous when you use mobile devices.
Homework
 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.
Exams
 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.
Grading
 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.