Course: Analysis II
Instructor: Robert Chang
Email:
Office Hours: 24/7 (just drop by Nightingale 534 or email)
Lectures: TR 3:25–4:55 p.m. at 102 Kariotis Hall
Textbook: Real Analysis by Stein and Shakarchi
Syllabus: 2020s5102_syllabus
Homework should be typset with LaTeX and submitted electronically to my inbox.
This .tex template should get you started.
Class Notes: This set of memoirs (updated on 4/11) outline the topics covered in each lecture. Refer to any of the recommended texts for more detailed discussions.
Calendar: Red = Exams; Blue = Holidays; § refers to section from textbook
| Week | Dates | Topics | Exercises |
| 1 | 1/7 1/9 |
Real numbers, Riemann integral Riemann integral and the FTC |
HW0 (Remarks) HW1 (Soln) |
| 2 | 1/14 1/16 |
Lebesgue outer measure Lebesgue outer measure |
HW2 (Soln) |
| 3 | 1/21 1/23 |
Lebesgue measure Lebesgue measure |
|
| 4 | 1/28 1/30 |
Measurable functions Littlewood’s three principles |
HW3 (Soln) |
| 5 | 2/4 2/6 |
Lebesgue integration Convergence theorems |
HW4 (Soln) |
| 6 | 2/11 2/13 |
L¹, completeness, modes of convergence Fubini–Tonelli |
HW5 (Soln) |
| 7 | 2/18 2/20 |
Fubini–Tonelli Change-of-variables and polar coordinates |
|
| 8 | 2/25 2/27 |
Lebesgue differentiation theorem Lebesgue differentiation theorem |
HW6 (Soln) |
| 3/3 3/5 |
Spring Break Spring Break |
||
| 10 | 3/10 3/12 |
Integrating derivatives Integrating derivatives |
|
| 11 | 3/17 3/19 |
Midterm Lp inequalities |
|
| 12 | 3/24 3/26 |
Lp, completeness, modes of convergence Lp duality |
HW7 (Soln) |
| 13 | 3/31 4/2 |
Abstract measure theory Abstract measure theory |
|
| 14 | 4/7 4/9 |
Abstract measure theory | |
| 15 | 4/14 |