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Math 2605 N1 and N2, Fall 2007 -- Calc III for CS

Please open the following document to get schedule of tests, coverage, and general course information such as grading policy:
CourseScheduleM2605Fall2007.pdf

HELP SESSION for final exam is Sunday, Dec.9 at 5 PM.

FINAL EXAM is on Monday, December 10, 2:50 PM, in our usual classroom.
It will cover the material that was covered (with the same omissions)up through test 3(that is, Chapter 5, section 3), and chapter 6 on multiple integrals (sections 1 through 3). We have done sections 1 and 2 from chapter 6, and will do section 3 on Friday, the last day of class.
Be sure to learn that stuff from chapter 6, there will be a question on if for sure. The rest of the exam will be somewhat randomly chosen from the stuff that we covered; of course not every single thing can get asked, because of time.
You may bring 20 CHEAT SHEETS to the final, and a calculator as usual.

LAST-MINUTE HELP SESSION: I will do this on Sunday Dec. 9 late afternoon or early evening, if some express an interest. I will post the exact time on Friday or Saturday.

BELOW are the tests and quizzes we had this semester, along with the answer keys. I'm sorry to say I do not have last semester's final exam, that file was lost, but the material was very similar to the tests and quizzes, with the exception of a problem from chapter 6.

Test3 fall07.pdf
Solutions to third test 07
Quiz3 fall07.pdf
Solutions to third quiz 07
Test2 fall07.pdf
Solutions to second test 07
Quiz2 fall07.pdf
Solutions to second quiz 07
Test1 fall07.pdf
Solutions to first test 07
Quiz1 fall07.pdf
Solutions to first quiz 07




TEST 3 IS ON THURSDAY, Nov. 29. It will cover through section 3 of chapter 5 (that is, two more sections than the quiz), and also you need to know how to compute exp(tA) for a 2x2 matrix A (see the supplement below called matrixetA.pdf). The rules for the test are the same as they were for test 2 (see below), with 8 cheat-sheets.
REVIEW SESSION for test 3 is on Wed, Nov 28, at 7PM in our classroom.

After test 3, we will do no more of chapter 5. We will do chapter 6 on multiple integrals in the remaining four lectures; the material that we cover from chapter 6 will included on the final exam.

NOTE!! QUIZ 3 postponed until Thursday Nov 15 !!!

QUIZ 3 will cover sections 2-3 from chapter 4 (and being aware of just the basics of complex numbers), and section 1 from chapter 5 (we started section 2 already, but will not be on this quiz). As usual, you may have three cheat sheets.

AS OF OCT 29, we have now completed chapter 4 section 2 on vectors and matrices in C(n), and had a quick review of complex numbers. There will probably be some skipping of details at least from sections 3-5, so we can get to section 6 quickly enough. I will let you know.
Here are some notes on complex numbers that I had made for some other class (calc 2, I think) that gives a brief introduction to them for those who haven't done them before. Everyone has gotten as far as knowing about i^2 = -1 I'm sure, but the notes give you at least a description of the geometrical representation of complex numbers, and geometrical picture of the operations, especially multiplication and exponents and roots. Maybe this will be helpful. You can't escape complex numbers, they are in all kinds of applied math.
Complex1.pdf
complex2.pdf
Complex3.pdf

Here's something on the exponential matrix.
matrixetA.pdf


TEST 2 is Thursday, Oct 25. The material you are responsible for is the same as what is written below for quiz 2, WITH the addition of sections 4 and 5 of chapter 3, on the SVD.
You will be allowed 8 cheat sheets, just because that was what someone suggested in class, and who cares? And calculators, as before

NOTE:!! QUIZ 2 has been POSTPONED until Tuesday, Oct 16.
THE QUIZ will cover the supplement on quadratic surfaces, chapter 1 section 9 on optimization, chapter 2 which is more on optimization with more variables (and there is some further discussion of Lagrange multipliers in a supplement), chapter 3 sections 1 and 2 on Jacobi method of finding eigenvalues of symmetric matrices, and chapter 3 section 3 on Gershgorin's theorems for estimating eigenvalues of almost diagonal matrices (which will be discussed on Friday).


Our online text is Calculus++ by Eric Carlen, which has 7 chapters numbered 0 through 6. Here are chapters 0 through 5:
chap0 JE.pdf
chap1.pdf
chap2.pdf
chap3.pdf
chap4.pdf
chap5.pdf
chap6.pdf


Here are some solutions. I have not proof-read them; let me know if you find errors, and we will try to get them corrected.
chap0sol.pdf
chap1s1-2sol.pdf
ch2s1sol.PDF
ch2s2sol.PDF
c3SOLNS.pdf
chap4sec1-3sol.pdf
chap4sec5-6sol.pdf
chap6sol.pdf

PROJECTS: PLEASE NOTE THIS. Here is the link to the projects:
http://www.math.gatech.edu/~loss/07falltea/2605/PROJECTS/projectpage.html
We will be doing the same projects as Dr. Loss's class. So far there are two projects there, from chapter 1 material on the gradient, and from chapter 0 material on reflections and parametric lines. Recall you must do two projects throughout the semester, but you can do more. More projects will be added during the semester.


Here are a few short supplementary discussions of some of the material . The material on level surfaces is not in the text, so you must read it here. The material on quadric surfaces was put here so that for example spheres would indeed be quadric surfaces.
DistanceBetweenLines.pdf
Curves supplement to chapter1 section3.pdf
LevelSurfaces supplement to chapter1 section4.pdf
QuadricSurfaces supplement to chapter1 section7.pdf
ConstrainedOptimization supplement.pdf (for chs 1 and 2).



NOTE: TEST 1 is Tuesday, Sept 25. It will be on material from chapter 0 and from chapter 1 through section 8. Because we did not have time to do it in class, I will not have any questions on this test about quadratic surfaces as level surfaces in R3 (the material in that supplement I put up), perhaps later. The only eigenvalue /eigenvector problems will be for 2x2 matrices, just like the text.
YOU WILL BE ALLOWED 3 CHEAT SHEETS, front and back, standard 8.5 by 11 paper. That will be enough, and the process of making them will be good review.



NOTE: QUIZ 1 is Thursday, Sept 6. It will be on material from chapter 0 and from chapter 1 through section 2. Calculators are allowed, but no books or notes for this quiz. You may view quiz 1 from spring 2006 semester (see link one page back). That quiz was given at a different point, so only problems 1 and 3 (a through c) apply. (prob 2 is about a level surface, and prob 3(d) is about a level curve.