Homework, Fall 2008

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Homework, Fall 2008

Fall 2008 Computer Projects, Due Tuesday Dec 2 at 12 noon.

HW14: Due Thursday 4 Dec
Solve dx/dt = A x ; x(0) = b where

A =
-32 60
-18 34
and b = (3,4)

HW 13: Due Thurs Nov 20th

C&C, page 218: 5.4,5.5
C&C page 231: 6.5,6.9,6.12
Let A be the matrix

1 1 2
-1 2 -1
0 1 1
1 0 1
1 2 3

And let b = (1 2 3 4 5). Find a x in ker(A^T) that shows that
Ax = b has no solution. (That is, such a w with w . b not equal to zero. Here A^T is the transpose of A)

Find the eigenvalues and eigenvectors of the matrix

3 -1
-1 2

HW12: Due Thursday Nov 13:

C&C: page 151: 5.1,5.2,5.4
C&C: page 230: 6.4,6.5

HW 11: Due Tuesday Nov 4th NOT COLLECTED

C&C page 206: 4.4., 4.5, 4.10,4.19
C&C page 230: 1,2,9a

HW 10: Due Thirsday Oct 30:

page 184: 2.1,2.2, 2.4, 2.5

HW9: Due Thursday October 23

C&C page 167: 1.1, 1.2, 1.8
C&C, page 196: 3.1, 3.2,3.7,3.11, 3.12,

HW8: Due Thursday October 16

C&C PaGE 116: 3.3, 3.5, 3.6, 3.8,3.9

HW7: Due Thursday October 2 NOT COLLECTED

C&C: page 29: 2.3, 2.5, 2.7, 2.10,1,19, 2.22
C&C page 45: 3.5, 3.6, 3.7, 3.16
C&C page 70: 5.4, 5.13, 5.14
C&C: page 83: 6.1,6.4

HW6: Due Tuesday 30

13.4, page 670: 15,16,17,36,37,38
13.5 page 677: 2,315,16,35,36
13.6 page 686: 5,6,23,24,38,39

HW 5: Due Thursday 25th (?)

Find all solutions to

2 x + 3 y -z + w + r + s =2
z + 2w -3r + s = 4
2 r -4 x = 5

For what values of c does

2 x - y - z = 3
-x + 2 y -z = 2
-x - y + 2 z = c

Have: a) No solutions, b) exactly one solution and c) infinitely many solutions

13.2 page 652: 25,27,31,40.42
13.3 page 661: 6,7,11,39,40, 44,45

HW 4: Due Tuesday 15th
For Simson's Rule (Composite) see http://en.wikipedia.org/wiki/Simpson%27s_Rule
also http://mathworld.wolfram.com/Newton-CotesFormulas.html
Use error bounds to calculate the following integrals to within 10^-3 by Simpson's Rule and Trapazoid rule. Don't actually compute the trapazoid, just say find what n to use:

Integral from 0 to Pi/4 or tan(x)
Integral from -pi/2 to pi/2 of cos(x)
Integral from 0 to 2 of e^-(x^2)

Trap: Error = (b-a)^3 M /(12 n^2)
Simp: Error = M (b-a)^5/ (180 n^4) n must be even

HW3 -- NOT COLLECTED, but is covered on quiz 1:

12.9: page 621, 4,6,24,26,28,30, 32,36

Due Tuesday 26 NOTE: Change of due date

Section 12.6: 2,4,12,14,1822,26,28,36,40

Due Thursday 4th

Section 12.2: 2,3,4,10,16,18,20
Estimate 1 + 2^2 + 3^2 + ... + n^2 from above and below by integrals

Does anyone know of a good podiatrist in town? EMAIL me: mailto:morley@math.gatech.edu

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