### Dr. Sarah's Math 2240 Class Highlights Summer 2006 Page

The following is NOT HOMEWORK unless you miss part or all of the class.
See the main class web page
for ALL homework and due dates.

**Mon Jun 26** Review span, linear independence, and subspaces from
test 2, and discuss test 3. Begin chapter 6. Discuss final project.
Hand back test 2 and give
students a change to work on revisions or the final project.

**Tues Jun 27** Hand back problem set and take
questions on test 3. c4s6 demo on geometric transformations and
computer graphics, and work on problems 1 and 3. Highlight the fact that
going back to the origin, performing a transformation, and then moving back
to where you started is similar in methodology to writing a solution
as a homogeneous solution plus a particular one...

**Wed Jun 28** Test 3 and then time to work on the final
project abstract.

**Thur June 29** Finish c4s5 demo and problems.
Discuss why the eigenvector matrix for certain transformations was a rotation
matrix. Evaluations. Hand back test 3 and discuss revisions and final
project abstracts.

**Fri June 30** Poster presentations.

**Mon June 19** Continue with 4.5 and 4.6.

**Tues June 20** Finish Chapter 4 with
group work.

**Wed June 21** 7.1 and the geometry of eigenvectors.
Begin dynamical systems by Fox problem and population dynamics from earlier.
Zero valued eigenvalues and projection matrices, and the relationship between
the eigenvalues of a matrix and its inverse.

**Thur June 22**
7.2 and then dynamical systems,
and then continue eigenvector decompositions for dynamical systems.

**Fri June 23** Collect test 1 revisions. Test 2 and
eigenvector decompositions for dynamical systems continued.

**Mon Jun 12** Finish Markov stability. 3.1, 3.2, and 3.3.

**Tues Jun 13** 4.1. Geometry of linear combinations and
determinants. Coffee mixing problem and numerical methods issue related to
decimals versus fractions.

**Wed Jun 14** 4.2

**Thur Jun 15** 4.3 and begin 4.4 and 4.5.
definitions.

**Fri Jun 16** Test 1 on Chapters 1-3. Continue with 4.4 and 4.5.

Maple Code:

>M:=Matrix([[1,0,-2],[2,1,0],[3,2,1]]):

>
a1:=spacecurve({[1*t,2*t,3*t,t=0..1]},color=red, thickness=2):

a2:=textplot3d([1,2,3, ` vector [1,2,3]`],color=black):

b1:=spacecurve({[0*t,1*t,2*t,t=0..1]},color=green, thickness=2):

b2:=textplot3d([0,1,2, ` vector [0,1,2]`],color=black):

c1:=spacecurve({[-2*t,0*t,1*t,t=0..1]},color=magenta, thickness=2):

c2:=textplot3d([-2,0,1, ` vector [-2,0,1]`],color=black):

d1:=spacecurve({[0*t,0*t,0*t,t=0..1]},color=yellow, thickness=2):

d2:=textplot3d([0,0,0, ` vector [0,0,0]`],color=black):

display(a1,a2, b1,b2,c1,c2,d1,d2);

**Monday June 5**
Introductions.
History of linear equations and the term "linear algebra".
html of file.
Begin 1.1.
Intro to Maple via Maple worksheet
(html version)
Continue 1.1 including geometric perspectives in 2 and 3-D.
Elimination

**Tues June 6**
Elimination continued.
Go over 59 part b. Collect homework. Go over 73.
Go over web pages and text comments in Maple.
History of matrices and elimination via the Chinese and Gauss. Section 1.2
by-hand and 1.3.

**Wed Jun 7** Go over some of the practice problems.
Go over web pages, ps 1 hints...
Begin 2.1 via
Image 1
Image 2
Image 3
Image 4
Image 5
Image 6
Image 7.
Continue 2.1. Powerpoint file.

**Thur Jun 8**
Continue with 2.2. html file.
2.3.

**Fri Jun 9**
2.5, coding and Markov/stochastic matrices and stability.
html file
Begin 3.1.