Math 311 Fall 1999 materials

First day handout.
Answers to first quiz . This also contains a take-home credit opportunity.
The inversion algorithm, and the problems we discussed in class sept. 7
A Maple sheet about the geometry of multiplying by a matrix.
Solutions to quiz 2 .
A Maple sheet related to determinants.
Bonus point offer: One point to anyone who states Hadamard's inequality on the next quiz. (You might want to look at the Maple sheet).
Solutions to the third quiz here .
Sept 23 Maple sheet. .
Solutions to exam 1 here.
New schedule for the next several weeks: Oct 5-7 pp. 150-169. Hwk p 154 # 3, 5, 7, 14. p 167 # 1, 2, 3, 6, 9, 12, 20.
Oct 12-14: p 170-195. Oct 19-21 p 196-223. Oct 26-28 p 224-245.
Exam 2, Thursday Nov 5 in class, same day as previously scheduled.
Nov 3 p 246-259.
Solutions and discussion of the in-class problems for last Oct 7.
Hwk for week of Oct 12: p 180 # 2,4,8,11. P 192 # 1, 2, 4, 8, 10, 11, 19-23.
Some Maple sheets. One about rotation in space and one about the perpendicular subspace to a given space, and subspaces and kernel for the case of an operator from R^n to R^p.
Maple sheet about homework 6, and about the lecture Tuesday Oct 19 on heat distribution in a bar (New and improved incorporating Oct 21 lecture ideas)
Maple sheet incorporating the homework assignment for this week .
Quiz 7 solutions .
Remarks on recent homework and a related Maple sheet .
Further discussion of the implicit function theorem. This sheet contains a homework assignment.
Additional homework for Oct 26-28: p 222 # 4, 7. p 233 # 1, 2, 5, 8 p. 243 # 1, 3, 4, 5, 6. Double checked.
Maple sheet with example of implicit function theorem and Newton's method.
Solutions to the Maple sheet homework. Another Maple sheet .
Some more links. They'll fill in by and by. link1 , link2
Solutions (rough and ready) to exam 2, here
Gram-Schmidt algorithm sheet.
Homework due Tues Nov 16: p 257 #1, 3, 5, 6, 16. p 271 #1, 2, 4, 8, 9, 12.
Quiz solution here Maple says here
Simpson's rule and Vandermonde matrices Maple sheet here .
Notes for Nov 18, part one . And, part 2.
Solution to the quiz of Nov 23: What we are trying to accomplish with our numerical integration method is that at least it shall give the exact answer for any quadratic polynomial. In particular, it must work for 1, x, and x^2. But that says that c_1+c_2+c_3=1, 0+2/3*c_1+1*c_3=1/2, and 0+(2/3)^2*c_2+1*c_3=1/3 because the integrals of 1, x and x^2 from 0 to 1 are 1, 1/2 and 1/3.
The double integral of e^(-(x-y)^2) over the square x from 0 to 1, y from 0 to 1 is equal to half [Jacobian effect] the double integral over the diamond with corners at (0,0), (1,+-1) and (2,0) of e^(-t^2) ds dt with the change of variable s=x+y,t=x-y. By symmetry this integral is twice the integral over the left triangle s from 0 to 1 , t from -s to s. That, though, and cancelling the factors 2 and 1/2, is int_0^1(int_(-s)^s e^-t^2 ds dt=int_0^1 2*t*e^-t^2=1-1/e.
Take a look at this Maple file
Homework: p 359 # 1,2,6,8,9,16 p370 #1,2,4.