Math 442: Differential Geometry of Curves and Surfaces

David Dumas

University of Illinois at Chicago
Spring 2009

Cornu spiral
The Cornu spiral, a plane curve whose curvature is a linear function of arc length.

Final exam information

The final exam will be held in SEO 636 on Friday, May 8, 10:30am-12:30pm.

The exam consists of two problem lists (A and B) with four problems each. For full credit, you must complete two problems from each list during the two-hour exam period.

List A is available below. You will receive list B on the day of the exam.

You may not discuss the problems on list A with anyone else until after the exam.

General information

Lectures MWF 10:00 - 10:50am in SEO 636
Text Differential Geometry of Curves and Surfaces by Manfredo do Carmo (see also: list of errata)
ISBN-13: 978-0-13-212589-5
Instructor David Dumas (ddumas | atsymbol | math | dot | uic | dot | edu)
Office hours Mondays 2-3pm, Wednesdays 11am-12pm in SEO 503
Homework Policies Homework will be assigned after most lectures and collected weekly on Monday (or in the first lecture of the week, if Monday is a holiday). The list of challenge problems will also be updated on a regular basis; you must complete two (undergraduates) or four (graduates) of these problems and submit your written solutions before the end of the semester.
Late homework will not be accepted.
You can discuss the homework with other students, but you must write (and understand!) your own solutions.
The homework problems depend on material from both the assigned reading and the lectures. Do not leave the problem sets or reading to the last minute!

Handouts

These documents are available for download in PDF format.

Important Dates

There will be one midterm exam and a cumulative final exam.
Midterm Exam Wed, Mar 4 In class
Final Exam Fri, May 8, 10:30am-12:30pm SEO 636

Grading

Your course grade will be determined on the following basis:
Homework 30%
Midterm Exam 30%
Final Exam 40%

When computing your homework grade, the lowest weekly homework score will be dropped, and the remaining scores will be averaged with your challenge problem scores. (That is, each challenge problem is worth as much as a weekly homework assignment!)

Assignments

Try out 3d-XplorMath.

Reading

Unless otherwise noted, all reading assignments refer to the textbook, Differential Geometry of Curves and Surfaces by Manfredo do Carmo.
Date Reading
Apr 22 Sections 4.6-4.7
Mar 30 Secion 4.5
Mar 20 Section 4.4
Mar 11 Sections 4.1-4.3
Feb 27 Sections 3.4-3.5
Feb 16 Section 3.1, 3.2
Feb 13 Sections 2.6-2.8
Feb 6 Sections 2.4-2.5
Jan 21 Sections 2.1-2.3
Jan 12 Chapter 1

Weekly Problems

The list of homework problems was last updated on Friday, April 24. The most recently assigned problems are shown in green.

Hwk # Due Problems
13 Mon, Apr 27 From problem list: P11
Section 4.6: 1, 2, 4
12 Mon, Apr 20 Section 4.5: 1, 2, 3, 4
11 Mon, Apr 13 From problem list: P10
Section 4.4: 13, 17, 18, 20
10 Mon, Apr 6 Section 4.4: 1, 4, 5, 12
9 Mon, Mar 30 Section 3.4: 8, 13
Section 4.3: 1, 2, 4, 6, 8
8 Mon, Mar 16 From problem list: P9
Section 3.5: 11, 12
Section 4.2: 6, 7
7 Mon, Mar 2 Section 3.2: 2, 4, 8
Section 3.3: 5(a)-(d), 1, 13, 16
6 Mon, Feb 23 From problem list: P8
Section 2.5: 1, 7, 8, 9
Section 4.2: 19
5 Mon, Feb 16 Section 2.3: 1, 2, 5
Section 2.4: 4, 12, 17
4 Mon, Feb 9 From problem list: P6, P7
Section 2.2: 1, 2, 3, 13, 19
Section 2.3: 12
3 Mon, Feb 2 From problem list: P3, P4, P5
Section 1.7: 12
2 Mon, Jan 26 From problem list: P2
Section 1.6: 3
Section 1.7: 4, 5
1 Wed, Jan 21 From problem list: P1
Section 1.3: 4
Section 1.4: 8
Section 1.5: 2, 4, 7, 9, 11, 12

Lists

Online Resources

These online tools (java applets, etc.) complement the material from the textbook and lectures.
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