Math-UA.326.001: Analysis II (Courant Institute, NYU, Fall 2012)

Announcements:

Tues Dec 11: ----1. Here is a sheet of practice questions to help you prepare for the final: Final practice.
----2. Format of the final: it will consist of a Part I and a Part II. Part I will be multiple choice, and worth about 30% of the total; do all of it. Part II will consist of a few long, multi-part questions requiring proofs; CHOOSE TWO OF THEM (you don't need to do them all).
----3. There will be an additional additional office hour on Friday 14th at 12.30

Mon Dec 10: I expanded the list of definitions and statements given you before the midterm so that it is a suitable guide for the final: Final cheatsheet

Tues Nov 20: Question 7(a) on Homework 9 is actually quite tricky, so I have expanded the hint.

Thurs Nov 8: Since I have presented the Inverse Function Theorem rather differently from Wade -- in particular, using the Contraction Mapping Principle -- I have written my own notes for this topic: Inverse Function Theorem notes.

Thurs Nov 1: With NYU still closed in the aftermath of Hurricane Sandy, I have prepared some special topical reading for you: Hurricane-related reading. It is not for credit, but is interesting and also excellent practice in the ideas of the course; I strongly encourage you to give it some time.

Thurs Oct 18: Sample answers for the midterm

Tue Oct 9: With the midterm approaching next Thursday, I have prepared a list of the main definitions and statements that you may need to remember during the exam: Cheatsheet

Mon Sep 10: ---- I will be traveling from the evening of Thurs Sep 13 to Mon Sep 17. For that reason, the first homework should be returned to the grader instead of to me. It is due by the start of his recitation on Fri Sep 14, and should either be handed in at the recitation or placed into my or his pigeonhole in the lobby of Warren Weaver Hall. Later homeworks will usually be handed to me on Thursdays, as announced previously.
My travels also mean that I may be sluggish replying to emails during that weekend -- apologies in advance.

Thurs Sep 6: ----1. Slight change to homework policy: work will now generally be due by the end of the Thursday class after the problems are posted, NOT at midnight. This is because I need to meet with the grader later on Thursdays.
----2. The Main Book Store has informed me that more copies of the textbook are now available for anyone who still needs one.


Lectures: Tuesdays and Thursdays 2.00 -- 3.15, in Warren Weaver 1302

The recitation leader is Naftali Cohen. His recitation (Math-UA.326.002) is on Fridays 9.30 -- 10.45, in Warren Weaver 312

Office Hours: Provisionally, Tuesdays 3.30 -- 4.30 and Wednesdays 11.00 -- 12.00, or by appointment (email or ask in person)

Grading: 20% homeworks, 30% midterm and quizzes, 50% final

Provisionally, midterm will be on Oct 11 (TBC). The final will be on Tuesday, Dec 18th, at 2pm. If you have a final exam conflict then you must email me by September 14th.

Textbook: Chapters 8 -- 13 of `An Introduction to Analysis', William R. Wade, Prentice Hall 2010, ISBN 978-0-13-229638-0.

A more detailed syllabus can be found here.

Homeworks will be posted below in advance of the classes on most Thursdays: provisionally, on Sept 6, 13, 20, 27, Oct 4, 11, 25, Nov 1, 8, 15, 29, and Dec 6. (Oct 18 is omitted owing to the Midterm, and Nov 22 is Thanksgiving.) Usually I will ask to have them returned to me by the end of class the following Thursday, either in person, to my mailbox, under my office door, or by email.

Homework 1 (background and preliminaries).

Homework 2 (open and closed sets, limits of sequences and functions).

Homework 3 (continuous functions). [Corrected version of Thurs Sep 20, 6.00pm]

Homework 4 (compactness and connectedness).

Homework 5 (linear functions and differentiation).

Homework 6 (review of pre-midterm material).

Homework 7 (more about differentiation).

Homework 8 (contraction mappings and the Inverse Function Theorem).

Homework 9 (The Implicit Function Theorem, and some review of one-dimensional integration).

Homework 10 (Lengths, curves, and the beginnings of higher-dimensional integration).

Homework 11 (More about higher-dimensional integration).


Tim Austin,
Warren Weaver Hall, office 803,
Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, U.S.A.
tim AT cims DOT nyu DOT edu