### 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.