Math 131B, Analysis MWF 11-11:50 MS5138
Instructor: Dimitri Shlyakhtenko, shlyakht@math.ucla.edu, MS7901
Office hours: M 2-3, W 10-11, W 3-4.
TA: Julia Dobrosotskaya, juliadob@math.ucla.edu, MS3921
TA's office hours: Tue 12-1 and Wed 2-4.
Course web page: http://www.math.ucla.edu/~shlyakht/131b.1.04w

This course is a continuation of Math 131a,  introduction to mathematical analysis. The goal of the course is to give a rigorous treatement of several topics, some going beyond the subjects touched upon in the regular calculus sequence.  The major themes of the course are: function spaces and notions of convergence of sequences of function; power series; and basic Fourier analysis, including its applications to the theory of the heat equation. The emphasis of this course continues to be on learning how to formulate and prove rigorous mathematical statements. Homework is a very important part of the course, since this is the only way for you to learn to invent and write proofs. Homework will be due on Wednesdays [corrected 1/12/04].

The course grade will be based on the best of the following scores: (i) two midterms (25% each), the final (30%), quizzes and homework (10% each), or (ii) the best of the midterms (25%), the final (55%), quizzes and homework (10% each) [updated 3/16/04]. Two lowest homework scores and one lowest quiz score will be dropped before computing the grade.

Class Calendar

Week of

We cover

Homework due Wednesday of next week

Notes

01/09/04
Review of 131, 5.6

5.6: 1, 3, 4

We'll cover the second half of 5.6 later in the course.
01/12/04
4.6, 4.6, 5.1
4.6: 2, 3, 4, 7, 8; 5.1: 1, 2, 3, 6, 8

01/19/04
Holiday, 5.2, 5.2
5.2: 1, 2, 3, 4, 5, 6, 8, 11

01/26/04
5.3, 5.3, 5.6
5.3: 1, 2, 3, 4, 5, 10; 5.6: 7, 9, 11, 12

02/02/04
5.7, Review, M1
5.7: 1, 3, 5, 9
Midterm 1 includes material up to §5.6 and will be on Friday, Feb. 6th.

Practice Midterm

Practice Midterm Solutions.

Midterm Solutions
02/09/04
5.8, 5.8, 6.1
5.8: 1, 3, 4, 7, 9, 11, 12; 6.1: 1, 2, 3, 5, 6, 7, 9

02/16/04
Holiday, 6.2, 6.2
6.2: 1abc, 2, 3, 4, 9, 12, 13
Practice Midterm

Practice Midterm Solutions
02/23/04
M2, 6.3, 6.3
6.3: 1, 2, 3, 4, 6, 14
Midterm 2 includes material in §5.7-§6.2
and will be held on Monday, Feb. 23rd.

Midterm Solutions
03/01/04
6.4, 6.5, 9.1
6.4: 1abcde, 2, 3, 5, 8, 12; 6.5: 1, 2, 3, 4, 5, 6, 7; 9.1: 1, 7, 8

03/08/04
9.2, 9.3, 9.3
9.2: 1, 3, 4, 5, 6; 9.3: 1, 2, 3, 6

03/15/04
9.4, Review
9.4: 2, 3, 6, 7, 8, 9, 10
Last h/w is due on 3/17.
Practice Final Problems (last 1/3 of the course only).
Solutions to Practice Final Problems

Final exam (comprehensive): Friday, March 19, 11:30-2:30, room 5138.