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Math 2605 C1 and C2,Spring 2007 -- Calc III for CS

Questions and some answers, M2605 C1 and C2, Spring 2007
CourseScheduleM2605Spring2007.pdf

Project 1
Project 2
Project 3
Project 4
Project 5
Project 6

PROJECTS: Turn in to your TA one project by Tuesday, April 3
LAST DAY TO TURN IN 2nd project (or any others): Tuesday, Apr 24. After that, we could not have time to grade them.

ON the project on the power method for eigenvalues, if you want you may restrict your matrices to only symmetric matrices. The non-symmetric ones will not always converge because the largest-magnitude eigenvalue may be complex, and therefore it's conjugate (of the same magnitude) will also be an eigenvalue. There is a way to handle this, but we did not discuss it, so it is ok if you want to just generate symmetric matrices for your experiments.

FINAL EXAM is on Monday, 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)which we will do in the remaining classes. You may bring 15 CHEAT SHEETS (that is the number for all the cheat sheets you made for the first three tests, plus 4 more for new material).


Text for Math 2605: Calculus++ by Eric Carlen, Spring 2004 version, may be found at:
http://www.math.gatech.edu/%7Ecarlen/2605S04/bookS04/index.html
Solutions to selected exercises in text

Standing homework assignment is all the exercises in the text (there are not that many), keeping up with where we are in class (additional exercises may be suggested for certain sections).

Here is a short description of how to compute the matrix exp(tA) needed in chapter 5, for 2x2 matrices.
matrixetA.pdf

THIRD TEST is on Thursday, Apr 19. It will cover chapter 3, sections 4 and 5, and chapter 5, sections 1 through 3. You may bring 4 CHEAT SHEETS that you make, using both front and back. You may also bring a calculator. The test is not open book.
Test3 M2605 spring07.pdf
Solutions to third test

THIRD QUIZ is on Tuesday, Apr. 17. It will cover chapter 3, sections 4 and 5, and chapter 5, sections 1 and 2. The rules are the same as for quiz 2.
Quiz3 spring07.pdf
Solutions to third quiz

SECOND TEST is on Thursday, March 15. It will cover chapter 1, section 6, through chapter 3, section 3. You may bring 4 CHEAT SHEETS (I added one) that you make, using both front and back. You may also bring a calculator. The test is not open book.
Test2 M2605 spring07.pdf
Solutions to second test


SECOND QUIZ is on March 8 (Thursday). It will cover chapter 1, section 6, through chapter 3, section 2. You may bring 3 CHEAT SHEETS that you make, using both front and back. You may also bring a calculator. The quiz is not open book.
Quiz2 spring07.pdf
Solutions to second quiz

FIRST TEST is on Feb. 8 (Thursday) and will cover material up through section 5 of chapter 1.
ON THE FIRST TEST, you may bring 3 CHEAT SHEETS that you make, using both front and back. You may also bring a calculator, though it is not that helpful for current material. The test is not open book; I think the cheat sheets will be better, you will learn from making them. The section 5 question(s) will be like the exercises, except in addition you will need to be able to compute eigenvectors to find directions of max and min curvature, as we said in class.
Test1 spring07.pdf
Solutions to first test

FIRST QUIZ will be on Jan. 30 (Tuesday) and will cover material up through chapter 1, section 4 (we may be past that section by the time of the quiz, but the quiz stops at section 4).
Quiz1 springl07.pdf
Solutions to first quiz

Here is an alternate method for finding the distance between two lines(I described this very briefly in class but this should be clearer and gives an example, the same example as in the text, which has a numerical error by the way):
DistanceBetweenLines.pdf

Here is a supplement to the material in chapter 1 section three, which states a very important chain rule and gives some more understanding of what the gradient means.
PLEASE GET THIS AGAIN, IT WAS CHANGED ON JAN. 25 (about 8PM):
Curves supplement to chapter1 section3.pdf

Here is a supplement to the material of chapter 1 section four, which treats the important idea of a surface as a level set of a function of three variables (for example x^2 + y^2 + z^2 = 1 is a sphere), and how to find a normal vector to a surface given this way (it is just the gradient!)
LevelSurfaces supplement to chapter1 section4.pdf

(UPDATED Mar. 4) TO FIX a small misprint in example 1, and to add some partial solutions to the exercises.) Here is a supplement to the material of chapter a section 6, on quadratic functions and quadric surfaces, including level surfaces of functions of three variables such as spheres. There are also a couple of exercises, sorry there are not more.
QuadricSurfaces supplement to chapter1 section6.pdf

Here is a supplment to chapter 1, section 8. So far it is just one example of a contracting map problem, I will soon add a chain rule problem.
Chapter2 section8 supplement.pdf

(UPDATED Mar. 4 to finish solution to example). Here is some information about constrained optimization (Lagrange multipliers), supplementing chapter 2 section 2. I go over the solution of problem 7 in the exercises of that section, after changing it slightly. This is not final, I will add more exercises; I just wanted to get something up to get you started. SEE section 15.7 of Salas et. al calculus book for more exercises on constrained optimization.
ConstrainedOptimization supplement chapter2 section2a.pdf