Vector Calculus 375, Fall 2010
Time: Lectures - Tuesday and Thursday, 9:10 - 10:25; Problem sessions -- Tuesday and Thursday, 5:00 - 6:00
Place: Fulmer 150 (Both Lectures and Problem Sessions)
Text(s): I am using several texts for this course. All are free or inexpensive.
The main one is a text by Michael Corral. The secondary text is Griffel's, Applied Functional Analysis, see description below
Here is how the course is organized. I am following the text by Corral and supplementing that with extra notes in class and extra work and reading out of Griffel. Given the fact that the students in the class are very capable and motivated, I will be adding quite a bit of other material that falls under the areas of differential geometry/geometric analysis and functional analysis. I will refer to the references listed below throughout the frequent, sometimes impromptu detours in the neighborhood of those subjects.
Reading: you are all responsible for reading the reading assignments before the lectures. This is an advanced mathematics course, in comparison with calculus and the first courses in linear algebra and differential equations. But the material is also highly geometric, and fact will help many of you master it more easily.
Homework: it will be assigned, collected and lightly graded. To compensate, we will have problem sessions in which we go over problems together.
Tests: We will have three based on homework, though not identical to the homework -- their purpose is strictly to inspire you to do all the homework since if you do you will learn the material well. The tests should be non-events for anybody doing the homework.
Other References
Loomis and Sternberg, Advanced Calculus: Phenomenal book on advanced calculus; You can download it here (http://www.math.harvard.edu/~shlomo/docs/Advanced_Calculus.pdf)
Griffel's, Applied Functional Analysis: available from Dover books, new price is 22.95 but you can get it for less than 10$ from used book sellers (the older editions are the same as the Dover reprint.
Ted Shifrin's book, DIFFERENTIAL GEOMETRY: A First Course in Curves and Surfaces which is free and can be downloaded from here (http://www.math.uga.edu/~shifrin/ShifrinDiffGeo.pdf); Note: if you are not taking my class, you are still welcome to download this, but Ted would appreciate an email (shifrin@math.uga.edu) letting him know that you are using it and how/why etc. An email is a small price to pay for this book!
Another is a text by David Santos.
Assignments
Chapter 1 of Corral: Due date and reading
- Aug 31 Corral 1-19
- Sept 2 Corral 20-30
- Sept 7 Corral 31-39
- Sept 9 Corral 40-50
- Sept 14 Corral 51-64
- Sept 16 Corral 51-64, again
- Sept 21 Corral 65-74, Griffel chap. 4
- Sept 23 Corral 75-82, Griffel chap. 4
- Sept 28 Corral (no lecture, in class problem session)
- Sept 30 Corral 83-88, 96-100 Griffel chap. 4 problems
Oct 5 Quiz, open book, open notes, in class, covering reading and problems from Corral, with extra credit from Griffel and notes. This is mostly to give you a feel for the final takehome. If you are slacking off in the class, it will wake you up ;~). In fact, while I want to see what you can do in class. I will bring two copies for each of you, letting you take the second copy home to study and think about.
- Oct 7 read Corral 101-109, Griffel chap. 4 problems
- Oct 12 read Corral 110-116, do all problems on pages 104 and 109 of Corral, read through problems in Griffel chap. 4
- Oct 14 read Corral 117-127, attempt some problems from Griffel chap. 4
- Oct 19 hand in problems on page 112 and 123 Corral, read chapter 5 of Griffel
- Oct 21 read Corral 135-142, read chapter 5 of Griffel
- Oct 26 hand in problems on page 142 of Corral, read chapter 5 of Griffel
- Oct 28 read Corral 143-155, read problems in chapter 5 of Griffel
- Nov 2 hand in problems on page 149 and 155 of Corral, attempt problems in chapter 5 of Griffel
Nov 4 read Corral 156-164, quiz over everything up to page 156 of Corral and chapters 4-5 of Griffel
- Nov 9 hand in problems on pages 163-164 of Corral, read Griffel chap. 6
- Nov 11 Veteran's Day Holiday
- Nov 16 read Corral 165-176, read Griffel chap. 6
Nov 18 hand in problems on pages 175-176 of Corral, read Griffel chap. 6, take-home final given out
- Nov 23 Thanksgiving Holiday
- Nov 25 Thanksgiving Holiday
- Nov 30 read Corral 177-186, problems from Griffel chap. 6
- Dec 2 hand in problems on page 186 of Corral, problems from Griffel chap. 6
- Dec 7 Lectures on how to start the extra credit problems on final
- Dec 9 Review and Synopsis
Specific Problems: Go here
Notes: Go here
Tests and Quizzes: Go here