18.101: Analysis II

Fall 2008

Class Information

MWF 1-2 in room 2-139
Professor Guillemin
- Email: vwg AT math DOT mit DOT edu
- Office hours: MWF 2-3 in office 2-170
Ana Rita Pires (grader)
- Email: arita AT math DOT mit DOT edu
- Office Hours: M 4-5 in office 2-251

Announcements

November 5: Here is the material for the rest of the semester. Four lectures on manifolds: 1, 2, 3, 4; two lectures on vector fields: 1, 2; and six lectures on integration: 1, 2, 3, 4, 5, 6.
October 27: The material for the next few weeks is BR: Birkhoff-Rota, chapter 6.
October 27: Midterm was today.
October 22: On Friday (Oct 24), there will be a review session for the midterm on Monday (Oct 27). The midterm will cover Munkres sections 1-16.
September 29: The class website is up and with information up to date. Sorry for the one month delay!

Homework

Homework 1, due September 26
Homework 2, due October 3
Homework 3, due October 17
Homework 4, due October 31 (actually, due the Monday after that, November 3)
Homework 5, due November 21
Homework 6, due December 5

Material covered and recommended work

Lecture 1	(September 3):	Munkres, section 3.	Recommended problems:	Munkres, section 3, exercises 4,7,9
Lecture 2	(September 5):	Munkres, section 4.	Recommended problems:	Munkres, section 4, exercises 1,2,3
Lecture 3	(September 8):	Munkres, section 5.	Recommended problems:	Munkres, section 5, exercises 2,3,4,6
Lecture 4	(September 10):	Munkres, section 6.	Recommended problems:	Munkres, section 6, exercises 1,2,5,6,7
Lecture 5	(September 12):	Munkres, section 7.	Recommended problems:	Munkres, section 7, exercises 1,2,3
Lecture 6	(September 15):	Munkres, section 8.	Recommended problems:	Munkres, section 8, exercises 1,2,3,4
Lecture 7	(September 17):	Munkres, section 9.	Recommended problems:	Munkres, section 9, exercises 5 and Spivak, exercise 2-37
Lecture 8	(September 19):	Munkres, section 10.	Recommended problems:	Munkres, section 10, exercises 1,2,3,4,5
Lecture 9	(September 24):	Munkres, section 11.	Recommended problems:	Munkres, section 11, exercises 1,2,3,4,6,8
Lecture 10	(September 26):	Munkres, section 11.
Lecture 11	(September 29):	Munkres, section 12.	Recommended problems:	Munkres, section 12, exercises 1,2
Lecture 12	(October 1):	Munkres, section 13.	Recommended problems:	Munkres, section 13, exercises 1,2,4,5
Lecture 13	(October 3):	Munkres, section 14.	Recommended problems:	Munkres, section 14, exercises 1,2,5,6,7,8
Lecture 14	(October 6):	Munkres, section 15.	Recommended problems:	Munkres, section 15, exercises 1,2,4,5
Lecture 15	(October 8):	Munkres, section 16.	Recommended problems:	Munkres, section 15, exercise 8
Lecture 16	(October 10):	Munkres, section 16.	Recommended problems:	Munkres, section 16, exercises 1,2,3,4
Lecture 17	(October 15):	Munkres, section 17.	Recommended problems:	Munkres, section 17, exercises 1,3,4,5,6
Lecture 18	(October 17):	Munkres, section 18.	Recommended problems:	Munkres, section 18, exercise 1
Lecture 19	(October 20):	Munkres, section 19.	Recommended problems:	Munkres, section 19, exercises 1,2,5ab
Lecture 20	(October 22):	Munkres, section 20.
Review Session	(October 24):	Review Session.
Midterm	(October 26):	Midterm.
Lecture 21	(October 29):	BR, section 6.3.	Recommended problems:	BR, section 6.3, exercises 1,4,7,12
Lecture 22	(October 31):	BR, sections 6.4 and 6.5.	Recommended problems:	BR, section 6.5, exercise 4 (see example 2 on p. 158)
Lecture 23	(November 3):	BR, sections 6.6 and 6.7.	Recommended problems:	BR, section 6.7, exercises 1,3,6,7
Lecture 24	(November 5):	BR, section 6.7.	Recommended problems:	BR, section 6.7, exercises 11,13,14
Lecture 25	(November 7):	BR, section 6.7.	Recommended problems:	BR, page 180 exercise 8
Lecture 26	(November 12):	Material posted online	Recommended problems:	Vector fields lecture 2, exercise 3 a),b),c)
Lecture 27	(November 14):	Material posted online	Recommended problems:	Vector fields lecture 1, exercises 1,2,3
Lecture 28	(November 17):	Material posted online	Recommended problems:	Vector fields lecture 2, exercise 1 and Manifolds lecture 1, exercises 1,2
Lecture 29	(November 19):	Material posted online	Recommended problems:	Manifolds lecture 1, exercises 3,4,5,6
Lecture 30	(November 21):	Material posted online	Recommended problems:	Manifolds lecture 3, exercises 2,3,4,5,
Lecture 31	(November 24):	Material posted online	Recommended problems:	Manifolds lecture 4, exercises 2,3,6,8
Lecture 32	(November 26):	Material posted online	Recommended problems:	Integration lecture 1, exercises 1,2,3,9,10
Lecture 33	(December 1):	Material posted online	Recommended problems:	Integration lecture 2, exercises 1,2,3,5,7*
Lecture 34	(December 3):	Material posted online	Recommended problems:	Munkres, section 22, exercise 2 (read section 22!), Integration lecture 2, exercise 7*
Lecture 35	(December 5):	Material posted online	Recommended problems:	Integration lecture 1, exercise 3, Integration lecture 2, exercise 8, Integration lecture 4, exercise 2
Lecture 35	(December 8):	Material posted online	Recommended problems:	Integration lecture 4, exercises 9,10,11 (see also #3 from Friday's homework assignment), Integration lecture 5, exercise 1

Class Textbooks

Analysis on Manifolds by James R. Munkres
Calculus on Manifolds by Michael Spivak