Math 545

Analysis I (Real Analysis)

Instructor: Dr. Stefan Richter, 302B Aconda Court, Tower 3, Tel.: 974-4286
e-mail: Richter at math dot utk dot edu
Class: MWF 9:05-9:55, room HBB 132
Office hours: MWF 11-11:30, Th 1-2:30 & by appointment

Lecture Notes

HW # 11, due Wednesday Nov. 25 (new due date!)

HW # 10, due Nov. 13

Midterm exam: Friday, October 30 Solutions

HW # 9, due Oct. 30 Solutions
Rudin, page 71 #4a,b, d, e, # 7

HW# 8, due Oct. 23 Solutions

HW# 7, due Oct. 9, Solutions

HW# 6, due Oct. 2, Solutions

HW# 5, due Sept. 25 Solutions

HW# 4, due Sept. 18 Solutions

HW# 3, due Sept. 11 Solutions

HW# 2, due Sept. 4 Solutions

HW# 1, due August 28

Background Check Solutions
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Text: Real & Complex Analysis, 3rd edition, by Walter Rudin, McGraw-Hill series in higher mathematics.

Course content: Chapters 1, 3 and parts of 4, 6, and 8.
Abstract measure spaces, Borel and Lebesgue measures, measurable functions, convergence theorems (Fatou's Lemma, monotone and dominated convergence theorems), Hoelder, Jensen, and Minkowski inequalities, L^p-spaces, L^p-convergence, and completeness, Egoroff's theorem, elementary Hilbert space theory, Radon Nikodym theorem, product measures, Fubini's and Tonelli's theorems.
Differentiation and the Fundamental Theorem of Calculus, if time permits.

Class, test, and grading policies:

1. Attendance is mandatory.
2. Read the text along with what we are doing in class.
3. There will be weekly assignments.
4. There will be one in class exam and a two hour comprehensive final exam.
Final exam: Monday 12/7, 8-10
4. Your final grade will be determined by use of the following key:
Homework 50%, Exams 50% (hour exam 16.6%, final exam 33.4%)