Office: LCB 104

Phone: (801)581-5272

E-mail: milicic@math.utah.edu

We plan to cover chapters 7 to 11 of the textbook.

We will assume that students are familiar with routine calculations done in regular calculus courses, so these will be deemphasized in the course.

First we shall study the topology of spaces of continuous real functions on compact spaces including Stone-Weierstrass theorem.

Then we shall study local theory of differentialbe functions of several variables, including the inverse function theorem. This will be applied to develop the theory of differential forms and their integration. Finally we are going to prove the general Stokes' theorem.

At the end, we are going to sketch the theory of Lebegue integral.

Homeworks will be assigned on regular basis, but not collected or graded. Some interesting homework problems will be discussed in class after students worked on them.

There will be three take-home midterm tests. They will be posted here on regular intervals.

The problems on these tests will be of different degree of difficulty. They will require from students to write up detailed proofs of various statements related to the material covered in class. The students will have about two weeks to work on each take-home exam.

The final grade will be based on the score on these three exams.

Last edit by dm, January 2, 2018.