# Math 127C: Advanced Calculus Spring Quarter, 2006

## Announcement

Solutions to the final are posted below.

## Instructor

John Hunter
e-mail: jkhunter@ucdavis.edu
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

## TA

Yung-Ta Li
Office: 2123 Mathematical Sciences Building
Office hours: TR 2:00– 3:00 p.m.

There will be two in-class midterms and a final.

There will be no makeup exams.

### Modterm 1

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

Midterm 1
Midterm 1 solutions

### Midterm 2

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

### Final

The final exam will be comprehensive, and will cover material on differential forms in addition to the topics listed above.
• 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

### Homework

Homework will be assigned each week, and will be due in class on Wednesday.

Late homework will not be accepted.

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

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

## Text for Math 127C

Principles of Mathematical Analysis, Walter Rudin, Third edition, McGraw Hill, 1976.

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)
Here is a department syllabus (based on a different text).

## Homework Assignments

Set 1 (due Wednesday, April 5):

• Ch. 9, p. 239: 1, 2, 3, 4
Solutions

Set 2 (due Wednesday, April 12):

Solutions to supplementary problems
Solutions to Rudin problems

Set 3 (due Friday, April 21):

Set 4 (due Wednesday, May 3):

Set 5 (due Wednesday, May 10):

Set 6 (due Wednesday, May 17):

No homework due Wednesday, May 24

Set 7 (due Wednesday, June 7):