### Dr. Sarah's Math 2240 Class Highlights Summer 2007 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 June 25 Discuss linear transformations and prove that a rotation matrix rotates vectors. Discuss other 2-D transformations. Computer graphics demo on WebCT.

• Tues June 26
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 matrix A that is close to the identity matrix, but scales in the x and y spot 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.
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. Read over study guide on the main page. If time remains, take questions on the test or test revisions.

• Wed June 27 Test 3

• Thur June 28 Discuss the importance of orthogonal matrices. Motivate Yoda via the data at the bottom of Tim's Page. Yoda in Maple. Discuss final project abstracts. Evaluations. Hand back test 3 and discuss revisions.

• Fri June 29 Final Project presentations.
• Mon June 18 Finish 4.5 and go over WebCT comments on span and linear independence. Do group work and prepare to present your responses.

• Tues June 19 Finish going over group problems. 4.6. In groups do 4.6   22, 31 Go over practice problems. Go over spacecurve command on columns and implicitplot3d command on the rows.

• Wed Jun 20 Begin 7.1 and the geometry of eigenvectors via WebCT demo, including zero valued eigenvalues. Continue 7.1 with the Fox problem via WebCT demo and the eigenvector decomposition.

• Thur June 21 Continue the eigenvector decomposition and discuss the necessity for diagonalizability and then do 7.2. Time to review problem set and test material.

• Fri June 22 Test 2. After test, review 7.1 and 7.2 and then show WebCT dynamical demo.
• Monday June 11 Finish chapter 3. 4.1. Geometry of linear combinations and determinants.

• Tuesday June 12 Review Monday's work and finish. Coffee mixing problem and numerical methods issue related to decimals versus fractions. Go over practice problems. Begin 4.2.

• Wednesday June 13 4.2 continued. Begin 4.3.

• Thur June 14 4.3 and 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);

Fri June 15 Test 1. Continue with 4.5.
• Monday June 4 Fill out information sheet. 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. History of matrices and elimination via the Chinese and Gauss.

• Tuesday June 5 Meet in 205. Open Maple 11 (Local Apps/Maple 11/Maple 11 icon). Hand out PS 1 Hints. Used ReducedRowEchelon on last 2 examples from Monday that we plotted and solved by-hand. Go over text comments in Maple and web pages and bulletin board and solutions. Go over 59 b and 73 in Maple using Gaussian. Go back to the classroom. 1.2 by-hand and 1.3.

• Wed June 6 Begin 2.1 via Image 1   Image 2   Image 3   Image 4   Image 5   Image 6   Image 7. Continue 2.1. Powerpoint file Go over 43 and 49 on the practice problems, including the geometry of 43. Continue with 2.2. html file

• Thur June 7 2.3. Begin 2.5 on coding, regression line and Markov/stochastic matrices and stability. If time remains, go to the computer lab and work on Markov

• Fri Jun 8 Markov/stochastic matrices and stability continued. Finish Markov. Begin 3.1