I am on sabbatical for Fall 2009.
In Spring 2010 I will teach Math 198 (Complex Geometry) in the Campus Honors Program (MWF at 1:00). The course will be somewhat similar to the course given in Fall 2008 described below, but the lecture notes are now available:
To see these lecture notes go to http://www.math.uiuc.edu/~jpda/jpd-complex-geometry-book.pdf Complex Analysis and Geometry
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For Fall 2008 I will be teaching two classes:
Math 198 section F1H MWF at 2:00 in 141 Altgeld Hall
Math 241 section CL1 MWF at 12:00 in 134 Temple-Hoyne-Buell
Web pages for these courses: http://www.math.uiuc.edu/~jpda/teaching.html
Office Hours will be MWF 10 and W 3, or by appointment.
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Information on Math 198: Complex Geometry
POSSIBLE GOAL. Together we write up and publish beautiful notes on this material!!!!
Here are the topics and approximately how much time we will spend on them:
Complex numbers (2 hours lecture, 1 hour student presentations and problem solving)
Geometry of the circle (3 hrs. lecture, 3 hrs. student presentations and problem solving)
Pythagorean triples (1 hr. lecture, 2 hrs. student presentations and problem solving)
Diagnostic midterm (1 hr., 2 hrs. student presentations and problem solving) Will be held Oct. 6. If useful we could have a second one in November.
Fibonaccci numbers and difference equations (2 hrs. lecture, 4 hrs. student presentations and problem solving)
Line integrals, geometry, and physics (9 hrs. lecture, 10 hrs. student presentations and problem solving)
Riemann surfaces (2 hrs. lecture)
Grading:
One quarter of the grade will be based on class participation and presentations of solutions, one half of the grade will be based on written work handed in (both the mathematics and the exposition will matter), and one quarter will be based on a final exam during the usual exam period (the exam will be shorter than typical finals, but full time will be allowed, in order to encourage careful writing).
The final will be held Tues. Dec. 16 1:30 -> 4:30 in 141 Altgeld.
There will be a diagnostic mid-term which will not count in the grade, but will give students appropriate practice.
There is no required text. On occasion students will need to augment what is done in class by outside reading from easily accessible sources.
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Recent Information on Math 241
The final exam on Dec. 17 will include considerable material on chapters 6 and 7. Please contact me by Wed. Dec. 3 if you have a conflict. The final be will be worth 300 points; earlier I had said 250 points, but 300 seems to be beneficial to the class as a whole.
The final will include a question on Green's theorem, a question on Stokes's theorem, and a question on Gauss's (divergence) theorem. Please learn the statements of these results and how to apply them.
To see accumulated scores so far go to http://www.math.uiuc.edu/~jpda/jpd-241-12-1.results.pdf course-results-so-far
The test (shorter than usual) on Dec. 1 will cover Chapter 6 and 7.1 and 7.2. You need to know how to do line integrals, how to state and use Green's theorem, what it means for a vector field to be conservative, how to use surface integrals to find surface area, and how to do surface integrals involving F dot n dS.
The test on Nov, 7 covers Chapter 5. The following applications might be asked: areas, volumes, centroids, moments of inertia. I will not ask about probability, nor about radius of gyration.
To see data about the test and accumulated scores up to Nov. 11 go to http://www.math.uiuc.edu/~jpda/jpd-241-11-7.results.pdf course-results-so-far
Remember that the accumulated scores are much more accurate than trying to average individual test scores.
To see grade data (for both the course and the test) after the test on Oct. 10 go to http://www.math.uiuc.edu/~jpda/jpd-241-10-10-results.pdf test results
The test on October 10 will include at least one problem from 4.3 and one from 4.2. Thus you need to understand max-min in several variables. It will also include at least two problems from Chapter 3. You need to be able to find grad, div, curl. You need to be able to find the basic information about parametrized curves, including speed, arc-length, curvature. I will not ask you about torsion. (Torsion is intriguing but not crucial at this stage.) I will not ask you about Kepler's laws. Please also note that we will cover in lecture many aspects of chapter 3 a bit more efficiently than is done in the book. Skip the information on higher order Taylor polynomials and formulas for the remainder term that appear on pages 241-245.
Comment on Lagrange multipliers. You must be able to do these computations, and you must also be able to understand the method geometrically. Draw pictures of the level sets of the objective function in every possible example.
CALCULATOR POLICY. I will allow calculators on the quiz given Sept. 12. You will see that they are not very useful, and in fact are a distraction. After that calculators will not be allowed to be used during exams.
Omit "Standard Bases" stuff from p. 69-70.
QUIZ ON SEPT. 12 will cover Chapter 1 and a small amount of the material on quadric surfaces in Chapter 2.
To see data about the quiz, go to http://www.math.uiuc.edu/~jpda/jpd-241-9-12-results quiz results
To see data about the test, go to http://www.math.uiuc.edu/~jpda/jpd-241-9-19-results.pdf test results
TEST ON SEPT. 19 will cover Chapter 1 and sections 1-3 of Chapter 2. It will also cover elementary uses of the gradient, as discussed in lecture and on the "gradient skills" page below. It will not cover higher order derivatives or the chain rule. They will be tested later.
Omit p. 130-137 from Chapter 2.
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General Information on Math 241
Text: Vector Calculus: third edition, by Susan Jane Colley, Prentice-Hall 2006.
We will cover the first seven chapters; at the end of the semester we will mention Chapter 8, but the final will not include it.
Important Dates: (Note: Additional quizzes can be given in discussion sections.)
All of the following tests will be held in the regular classroom:
QUIZ (50 points) Fri. Sept. 12
EXAM (100 points) Fri. Sept. 19
DROP DATE
EXAM (100 points) Fri.Oct. 10
EXAM (100 points) Fri. Nov. 7
QUIZ (50 points) Mon. Dec. 1
LAST DAY OF CLASS Wed. Dec. 10
FINAL (250-300 points) Wed. Dec. 17, 1:30 -> 4:30
Lectures will be in 134 Temple Hoyne Buell MWF at 12:00. There are many different discussion (recitation) sections. Students should do as many problems as possible, and students should insist that the TA solve problems during discussion sections.
Routine HOMEWORK. You must keep current with these problems. Routine homework need not be handed in. * problems are often less routine.
REMARK. Roughly speaking we will spend two weeks on each of the first seven chapters.
August 26; section 1.1: 5,9,11,17,23, 24. section 1.2: 11
August 28; section 1.2: 14, 16, 22, 23, 27, 30, 32, 33, 35, 37. section 1.3: 5, 7, 10, 14, 16, 24*, 25*, 26*.
Sept. 2; section 1.4 5,6,9, 12, 14,16, 18, 20, 21. section 1.5: 1,3,4, 7, 10, 11, 16,18, 21, 27, 29, 32*, 35*. section 1.6: 6, 10,
Sept. 4; section 1.7 1-10, 15. (later on we will return to these ideas at which time you should do more problems)
Sept. 9; section 1.9. 8, 9, 10, 13, 14, 15, 16, 17. section 2.1. 1, 10,11,14, 15, 16, 19,
Sept. 11; section 2.1. 8, 29, 31, 32, 34, 35, 44, 47. section 2.2. 8,10,11,12,16,17, 28-33
Sept. 16; section 2.3. 1-3, 6, 7, 9, 11, 15,19,
Sept. 18; section 2.3. 25, 30, 32, 34. section 2.4, 9, 14, 15, 16, 20,
Sept. 23; section 2.5. 1,2, 9, 11, 15, 18, 27, 29. Section 2.6, 3,5,16,17, 23, 24,
Sept. 25; section 2.8. 6, 7, 18, 22, 37, 43. section 3.1 7, 17, 32
Sept. 30; section 3.2. 1,3,7,8, 13, 17, 23, 26, 27, section 3.3 1,2,3,7,23
Oct. 2. section 3.4, 1,2,5, 7,8,11, 17,18, 3.5, 14-19 3.6, 1, 5, 39 section 4.1, 8,9,10, 14,16, 22,23,25,30,
Oct. 7. 4.2 1-19 (do at least ten of them), 23. section 4.3. 1,2,3,4,5
Oct. 9. section 4.3 16,17,18, 19,24,set up 30, 32. Section 4.5. 7, 9,10, 16, 17, 18, 19,
Oct. 16 section 5.1 1,5,6,9,11, 13, 16.
Oct. 21 section 5.2 1,2,3,4,8,9.11, 13,21, 20, 22, 23, 25, 26a, 27,
Oct. 23 section 5.3 1,3,4,10,11,13,14,16, 17
Oct. 28 section 5.4 5,6,9,11, 19, 20, 22,
Oct. 30 section 5.5 1,2, 3, 8, 11,12, 18, 20, 21, 25, 27
Nov. 4 section 5.6 3, 5, 8, 11, 12, 21. Find moments of inertia about the axis of symmetry of the following (assume uniform mass density, total mass M) cylinder of radius R and height H, sphere of radius R, circular cone of height H and radius R
Nov. 6 section 5.8 1, 2, 7, 11, 14, 15, 17, 26, 27, 43.
Nov. 11 section 6.1. 1,2,3,4,7,11, 13, 18, 19, 23, 31
Nov. 13 section 6.2 1-4, 7, 8, 10, 15,16, 19, 20. section 6.3 1,3, 11, 19, 21
Nov. 18 section 6.4. 1, 19, 24, section 6.5 2, 19, 23,
Nov. 20 section 7.1. 3, 8, 11, 19, 22, 23,
Dec. 2 section 7.2, 1, 5, 7, 9,
Dec. 4 section 7.2. 19,21. section 7.3 1,3 7, 9,
Dec. 9 section 7.3. 11, 14, 16. section 7.6 3ab, 4, 5, 7. Read section 7.4
Dec. 8, Dec. 10 Last two lectures will unify the course.
IMPORTANT INFO. ******************** On August 29, I passed out a prerequiste form to fill out during lecture. If you didn't come that day, please ask about it. If you didn't take 220 or 231 at UIUC you might need to see someone at the Math Undergrad Office (313 Altgeld Hall) by SEPTEMBER 3 to ensure that you get credit for them.
To read the basic course handout, go to http://www.math.uiuc.edu/~jpda/jpd-241-handout-08.pdf.1 course information
To read the handout about vectors, go to http://www.math.uiuc.edu/~jpda/jpd-241-dot-cross.pdf.2 vectors
To read the handout about lines and planes, go to http://www.math.uiuc.edu/~jpda/jpd-241-lines-planes.pdf.1 lines-planes
To read the handout about basic skills, go to http://www.math.uiuc.edu/~jpda/jpd-241-skills-1.pdf skills
To read about the Cauchy-Schwarz inequality, go to http://www.math.uiuc.edu/~jpda/jpd-241-Cauchy.pdf Cauchy-Schwarz inequality
To read about the gradient, go to http://www.math.uiuc.edu/~jpda/jpd-241-skills-gradient-2.pdf gradient-skills
To read about basic skills needed fr curves in space, go to http://www.math.uiuc.edu/~jpda/jpd-241-skills-curves.pdf skills-curves
To read a handout about Kepler's laws, go to http://www.math.uiuc.edu/~jpda/jpd-kepler.pdf.1 Kepler's Laws
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To read about LAS teaching awards, go to
http://www.las.uiuc.edu/news/2005spring/05april_teachingawards.html