Course: MATH 131B, Analysis 2, Lecture 1, Winter 2015
Prerequisite: MATH 131A, Analysis 1; MATH 115A, Linear algebra.
Course Content: This course is a continuation of MATH 131A. We will treat the topics in real analysis from a more general perspective. Topics include: metric spaces, point-set topology, function spaces, convergence of sequences of functions, power series, analytic functions, and Fourier analysis. This course should develop your ability to write rigorous proofs.
Last update: 17 February 2015

Instructor: Steven Heilman, heilman(@-symbol)
Office Hours: Mondays, 10AM-12PM, Wednesdays, 11AM-12PM, MS 7370
Lecture Meeting Time/Location: Monday, Wednesday and Friday, 9AM-950AM, MS 5147
TA: Adam Azzam, adamazzam(@-symbol)
TA Office Hours: Tuesdays 12PM-150PM, MS 6139
TA Course Website: here
Discussion Session Meeting Time/Location: Thursday, 9AM-950AM, MS 5147
Required Textbook: Mathematical Analysis, 2nd Ed, T. Apostol
Other Textbooks (not required): T. Tao, Analysis II, Hindustan Book Agency, 2009.
First Midterm: January 30th, 9AM-950AM, MS 5147
Second Midterm: February 23rd, 9AM-950AM, MS 5147
Final Exam: March 18, 8AM-11AM, MS 5147
Other Resources: 131BH, Tao, Spring 2003: I would highly recommend reading these lecture notes. My own lecture notes below are meant to be a more condensed presentation of similar material. So, if you prefer a more thorough treatment, I recommend these notes (and the book). Note that we will probably not be covering the Lebesgue intergral.
An introduction to mathematical arguments, Michael Hutchings, An Introduction to Proofs, How to Write Mathematical Arguments
Exam Procedures: Students must bring their UCLA ID cards to the midterms and to the final exam. Phones must be turned off. Cheating on an exam results in a score of zero on that exam. Exams can be regraded at most 15 days after the date of the exam.
Exam Resources: Here is a page with past exams for the course. Here is another page with past exams for the course. Note that the content of these other courses may be slightly different than ours.

Homework Policy:

Grading Policy:

Tentative Schedule: (This schedule may change slightly during the course.)

Week Monday Tuesday Wednesday Thursday Friday
1Jan 5: 3.13, Metric Spaces Jan 7: 4.2, Convergence of sequencesJan 8: No homework due Jan 9: 3.14, Topology of metric spaces
2Jan 12: 3.15, Compact sets Jan 14: 4.8, 4.12, Continuous functions on metric spacesJan 15: Homework 1 due Jan 16: 4.13, 4.14, Continuity and compactness
3 Jan 19: No class Jan 21: 4.16, 4.17, 4.18 Connectedness Jan 22: Homework 2 due Jan 23: 9.1, 9.2, Sequences and Series of Functions
4 Jan 26: 9.3, 9.4, Uniform Convergence and continuity Jan 28: 9.8, Uniform convergence and integration Jan 29: Homework 3 due Jan 30: Midterm #1
5 Feb 2: 9.10, Uniform convergence and differentiation Feb 4: 11.15, 9.14, Approximation by polynomials, power series Feb 5: Homework 4 due Feb 6: 9.14, 9.15, 9.18, 9.19, More power series
6 Feb 9: Exponential and Logarithm Feb 11: 1.21-1.26, 1.32, Trigonometric FunctionsFeb 12: Homework 5 dueFeb 13: 11.1, Periodic Functions
7Feb 16: No class Feb 18: 11.2, Inner products on periodic functionsFeb 19: Homework 6 dueFeb 20: Trigonometric Polynomials
8Feb 23: Midterm #2 Feb 25: 11.3, 11.15, Approximation by trigonometric polynomialsFeb 26: No homework dueFeb 27: 11.3, Fourier inversion and Plancherel theorems
9Mar 2: 12.1, Differentiation in several variables Mar 4: 12.2, 12.9, Directional Derivatives, Chain RuleMar 5: Homework 7 dueMar 6: 12.13, Clairaut's Theorem
10Mar 9: Leeway/review Mar 11: Leeway/reviewMar 12: Homework 8 dueMar 13: Review of course

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Homework Supplementary Notes