# Math 268: Multidimensional Calculus Fall 2015

Instructor Gautam Iyer.   WEH 6121.   gi1242+268@cmu.edu. MWF 3:30--4:20 in WEH 5312. Mon 11:30--12:20, Fri 10:30--11:20 Son Van.  WEH 8205.   vansp@cmu.edu. Tue 10:00--11:15 and 2:30--3:20 Tu 3:30-4:20 in WEH 5320. Wednesdays, at the beginning of class. Late homework will not be accepted Wed, Sep 30 (in class) Wed, Nov 4 (in class) Sun, Dec 20, 1:00PM-4:00PM (WEH 5415) 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

### 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.