Math 396, Winter 2011.
Honors Analysis II
My office is 4859 East Hall,
and my office hours are Tuesdays 2-3pm and Thursdays 1-3pm.
The class meets on Mondays, Tuesdays, Wednesdays and Fridays, 1pm-2pm.
The MWF classes meet in room 2866, and the
Tuesday
classes meet in room 4096, of East Hall.
The course assistant is David Montague, continuing from the previous
term.
His office hours are on Thursdays, 5-6pm, in 2866 East Hall.
His review sessions are on Tuesdays, 5-6pm, in 2866 East Hall.
Syllabus in PDF
Final grade policies in PDF
The take-home midterm is scheduled for March
11-14.
The final exam will be held on
April 18, 5pm-8pm, in room 1360 of East Hall.
Exams
Final exam in PDF
Final exam solutions in PDF
Midterm exam in PDF
Midterm exam solutions in PDF
Homeworks
Homework 1 (due Friday,
January 14, at the beginning of class)
in PDF
Hints for selected problems in PDF
Solutions to Homework 1 in PDF
Homework 2 (due Friday,
January 28, at the beginning of class)
in PDF
Hints for selected problems in PDF
Click here for solutions to
Homework 2
Homework 3 (due Friday, February 11, at the
beginning of class) in PDF
Hints for selected problems in PDF
Click here
for solutions to
Homework 3
Homework 4 (due Friday, February 18, at the beginning of class) in PDF
Solutions to Homework 4 in PDF
Homework 5 (due Friday, February 25, at the beginning of class) in PDF
Hints for selected problems in PDF
Click here for solutions to
Homework 5
Homework 6 (due Friday, March 25, at the
beginning of class) in PDF
Some additional explanations in PDF
Supplementary material: a problem set (from Math 395 in the fall of
2009)
on direct sums and quotients of vector spaces in PDF
Solutions to Homework 6 in PDF
Homework 7 (due Friday, April 8, at the
beginning of class) in PDF
Hints for selected problems in PDF
Click here for solutions to
Homework 7
Homework 8 (due Friday, April 15, at the beginning of class) in PDF
Course
notes
- Notes on smooth structures in PDF
(about 19.6MB) and in DJVU (about 6MB)
- Notes on charts in PDF
(about 21MB)
- Notes on Lie derivatives, part 1 (vector fields and
differential 1-forms) in PDF (about
13.2MB) and in DJVU (about 2.8MB)
- Notes on Lie derivatives, part 2 (pushforwards,
pullbacks and flows) in PDF (about
13.2MB) and in DJVU (about 2.8MB)
- Notes on Lie derivatives, part 3 (construction of the
Lie derivative) in PDF (about
12.9MB) and in DJVU (about 2.7MB)
- Notes on orientations in PDF
- Notes on differential forms in PDF
- Notes on de Rham cohomology (part 1) in PDF
- Notes on de Rham cohomology (part 2) in PDF
Lecture
topics by week
- Differentiability for functions of several variables
(week of January 5 and 7)
- The Inverse Function Theorem; definition
of a smooth manifold (week of January 10)
- Manifolds with boundary; first examples of manifolds
(week of January 17)
- Tangent spaces and submanifolds; more examples (week of
January 24)
- Vector bundles and tangent bundles; orientability (week
of January 31)
- Introduction to vector fields (week of February 7)
- Integral curves and flows of vector fields (week of
February 14)
- Infinitesimal automorphisms and Lie derivatives (week
of February 21)
- Spring break (week of February 28)
- Differential forms (week of March 7)
- Pullbacks, wedge products and the de Rham differential
(week of March 14)
- Proof of Stokes' theorem; introduction to de Rham
cohomology (week of March 21)