Spring Quarter, 2006

e-mail:

Phone: (530) 752-3189

Office: 3230 Mathematical Sciences Building

Office hours: MW 12:40– 1:30 p.m., F 1:30– 2:30 p.m.

Lectures: MWF 10:00–10:50 a.m., PhysGeo 140

Discussion Section: T 10:00–10:50 a.m., PhysGeo 140

Important dates:

- Last day to add: Friday, April 14
- Last day to drop: Wednesday, April 26
- Last day of instruction: Wednesday, June 7
- Academic Holidays: Friday, March 31; Monday, May 29

Office: 2123 Mathematical Sciences Building

Office hours: TR 2:00– 3:00 p.m.

**
There will be no makeup exams.
**

Midterm 1: Monday, April 24, 10:00–10:50 a.m., PhysGeo 140

The exam will cover pp. 16–17 and pp. 204–220 of Rudin.

Specific topics are:

- Linear algebra
- Vector spaces
- Bases
- Linear maps

- Norms
- Euclidean norm
- Cauchy-Schwartz and triangle inequalities
- Norm of a linear map

- Derivatives
- Definition and properties
- Concept of derivative as a linear map
- Chain rule

- Partial derivatives
- Directional and partial derivatives
- Relationships between derivatives and partial derivatives
- Jacobian matrices

Sample Midterm 1 questions

Solutions to sample midterm questions

Midterm 2: Wednesday, May 24, 10:00–10:50 a.m., PhysGeo 140

Sample Midterm 2 questions

Solutions to sample midterm questions

The exam will cover pp. 30–36,pp. 52–55, and pp. 220–234 of Rudin, and the material on integration covered in class.

Specific topics are:

- Metric spaces
- Contraction mapping theorem
- Inverse and Implicit Function theorems
- Riemann integration in several variables
- Fubini theorem
- Change of variables formula

- Cells and parametrized surfaces
- Integral of a differential form over a surface
- Invariance of the integral under reparametrizations
- Algebra of differential forms (wedge product)
- Calculus of differential forms (exterior derivative)
- Closed and exact forms
- Stokes theorem

Final (Exam Code R): Wednesday, June 14, 10:30 a.m. – 12:30 p.m., PhysGeo 140

**Late homework will not be accepted.
**

The course grade will be based on (weights in parentheses):

- Homework (10%)
- Midterms (25% each)
- Final (40%)

The course will cover:

- Differentiation of functions of several variables (Ch. 9)
- Integration of differential forms (Ch. 10)
- Lebesgue measure (Ch. 11 --- if time permits)

Set 1 (due Wednesday, April 5):

- Ch. 9, p. 239: 1, 2, 3, 4

Set 2 (due Wednesday, April 12):

- Supplementary problems
- Ch. 9, p. 239: 6, 8, 9

Solutions to Rudin problems

Set 3 (due Friday, April 21):

- Supplementary problems
- Ch. 9, p. 239– 240: 12, 13, 14, 15

Set 4 (due Wednesday, May 3):

- Supplementary problems
- Ch. 2, p. 44– 246: 11, 22
- Ch. 9, p. 239– 240: 16, 17, 18

Solutions to supplementary problems

Set 5 (due Wednesday, May 10):

Solutions to supplementary problems

Set 6 (due Wednesday, May 17):

Solutions to supplementary problems

No homework due Wednesday, May 24

Set 7 (due Wednesday, June 7):