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)ucla.edu
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)gmail.com
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.
Tentative Schedule: (This schedule may change slightly during the course.)
|1||Jan 5: 3.13, Metric Spaces||Jan 7: 4.2, Convergence of sequences||Jan 8: No homework due||Jan 9: 3.14, Topology of metric spaces|
|2||Jan 12: 3.15, Compact sets||Jan 14: 4.8, 4.12, Continuous functions on metric spaces||Jan 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 Functions||Feb 12: Homework 5 due||Feb 13: 11.1, Periodic Functions|
|7||Feb 16: No class||Feb 18: 11.2, Inner products on periodic functions||Feb 19: Homework 6 due||Feb 20: Trigonometric Polynomials|
|8||Feb 23: Midterm #2||Feb 25: 11.3, 11.15, Approximation by trigonometric polynomials||Feb 26: No homework due||Feb 27: 11.3, Fourier inversion and Plancherel theorems|
|9||Mar 2: 12.1, Differentiation in several variables||Mar 4: 12.2, 12.9, Directional Derivatives, Chain Rule||Mar 5: Homework 7 due||Mar 6: 12.13, Clairaut's Theorem|
|10||Mar 9: Leeway/review||Mar 11: Leeway/review||Mar 12: Homework 8 due||Mar 13: Review of course|
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