### Dr. Sarah's Math 2240 Class Highlights Fall 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.

• Tues Dec 5 Discuss final project abstracts. Evaluations. Hand back test 3 and discuss revisions.
• Tues Nov 28 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... Review Problem. Discuss the importance of orthogonal matrices. Motivate Yoda via the data at the bottom of Tim's Page. Yoda in Maple. Take questions on the test or test revisions. Collect final project proposal. Review in groups.

• Thur Nov 30 Test 3
Tues Nov 21 Meet in computer lab. Computer graphics continued. Work on problems.
Hints on Problem 1: Look at Section 1 example 1C, but use rotation by -Pi/6. We also need to shrink the triangle as it goes around, so, instead of letting M equal U.R.T, you need to add a dilation matrix A somewhere and M:=the product of the 4 matrices A, U, R, and T in some order that makes sense.
Hints on Problem 3: Try a rotation matrix composed with a translation matrix.
• Tues Nov 14 Discuss linear transformations and prove that a rotation matrix rotates vectors. Discuss other 2-D transformations.

• Thur Nov 16 Meet in computer lab. Computer graphics.
• Tues Nov 7 Continue the eigenvector decompotion and discuss the necessity for diagonalizability. 7.2.

• Thur Nov 9 Meet in the computer lab. Review 7.2. Continue with population dynamics.
• Tues Oct 31 Begin 7.1 and the geometry of eigenvectors, including zero valued eigenvalues and the relationship between the eigenvalues of a matrix and its inverse.

• Thur Nov 2 Contine 7.1 with the Fox problem and the eigenvector decomposition.
• Tues Oct 24 Have each person in the class make up a question related to test 2 material. Use this as a review. Take any remaining questions on test 2 material. If time remains, begin Chapter 7.

• Thur Oct 26 Test 2
• Tues Oct 17 Review thursday's group work. Collect and go over practice problems. 4.6. Group work on 4.6 number 22 and 31. Hand out study guide. If time remains, time to work on test 1 revisions and go over aspects of the study guide in groups.
• Tues Oct 10 4.4 and 4.5 definitions
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);

• Thur Oct 12 Go over pictures on ps 4 in order to review visualization of span and li. Finish 4.5 group work
• Tues Oct 3 Finish 4.2 and begin 4.3

• Thur Oct 5 Finish 4.3 and begin 4.4
• Tues Sep 26 4.2

• Thur Sep 28 Test 1
• Tues Sep 19 Finish Chapter 3. If time remains, begin chapter 4.

• Thur Sep 21 Meet in the computer lab. 4.1. Geometry of linear combinations and determinants. Coffee mixing problem and numerical methods issue related to decimals versus fractions.
• Tues Sep 12 Continue 2.5 including coding and regression line. Markov file.

• Thur Sep 14 Finish Markov file. Begin Chapter 3
• Tues Sep 5 Review 2.2. Do 2.3. If time remains, then begin 2.5 on coding and Markov/stochastic matrices and stability.

• Thur Sep 7 Convocation.
• Tues Aug 29 1.3 and 2.1 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 Aug 31 Finish 2.1 and 2.2 html file.
• Tue Aug 22 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

• Thur Aug 24 Meet in computer lab. Fill out information sheet. Introductions. Take questions on the syllabus. Go over web pages and text comments in Maple. Go over Gaussian Elimination Maple commands for 1.1 number 73. Elimination continued. History of matrices and elimination via the Chinese and Gauss. Section 1.2 by-hand and Maple commands. If time remains, begin 1.3.