### Dr. Sarah's Math 2240 Class Highlights 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 Apr 26**
Keeping a racecar on a track.
Discuss Yoda via the file yoda2.mw with
data from Lucasfilm LTD as on
Tim's Page which
has the data. Evaluations.

**Thur Apr 21** Test 3
**Tues Apr 19** Meet in the computer lab. Finish the last
part of the computer graphics demo. Finish
review work for chapter 7 [2 and 3].
If time remains
before we come back together, work on test 2
review until we return to the classroom. Take questions.

**Thur Apr 14** Latex Slides.
Show that a rotation matrix rotates algebraically as well as geometrically.
Discuss dilation, shear, and reflection. Discuss what transformation is
missing from our list.
Begin computer graphics demo via definition of
triangle := Matrix([[4,4,6,4],[3,9,3,3],[1,1,1,1]]); and then
ASULearn Computer Graphics Example D. Also look at Homogeneous 3D
coordinates and Example G.
Begin review work for chapter 7.
**Tues Apr 12**
Finish 7.2. Chapter 7 review.

**Thur Apr 7** Finish dynamical systems. Complete 7.2.
**Tues Apr 5** Review the algebraic by-hand eigenvectors of
Matrix([[1,2],[2,1]]) as well as the book presenting the coefficient matrix
instead of the augmented matrix fro the system Ax=lambdax.
Review Maple, geometry: staying on the same line through the origin, and
the general matrix multiplication turns to scalar multiplication.
Review and continue with eigenvectors clicker
questions. Foxes and Rabbits demo. Begin 7.2.
Dynamical systems demo.
Review the Healthy Sick worker problem from Problem Set 3.

**Thur Mar 31** Test 2
**Tues Mar 29** Finish the last example on
Geometry of Eigenvectors.
Compute the Eigenvectors of Matrix([[1,2],[2,1]) by-hand and on Maple.
Eigenvectors clicker questions.
Take questions on Test 2 and go over the
clicker review questions for Chapter 4

**Thur Mar 24**
Review the Healthy Sick worker problem from Problem Set 3. Begin 7.1
Define eigenvalues and eigenvectors [Ax=lambdax, vectors that are scaled
on the same line through the origin, matrix multiplication is turned into
scalar multiplication]. Examine
Geometry of Eigenvectors
and compare with Maple's responses.
**Tues Mar 22** Go over the group problems. 4.6 and revisit
problem set 1 questions in this context. Clicker question on the
definition of l.i.

**Thur Mar 17**
Collect homework. Review Definitions
Finish 4.5.
Go to 205. Look at Span and Linear
Independence comments.
If time remains then
group work on span, l.i. and basis

**Tues Mar 15**
Begin 4.4 and 4.5
Definitions. Maple work

Maple Code:

with(LinearAlgebra): with(plots):

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 Mar 3** Finish 4.2 and 4.3.
**Tues Mar 1**
Begin 4.2. Then 4.2 and 4.3 via group problems.

**Thur Feb 24**
Continue 4.1. Coffee mixing problem and numerical methods issue
related to decimals versus fractions. Algebra and geometry of linear
combinations of vectors.
**Tues Feb 22** Test 1 in 205.

**Thur Feb 17**
Clicker review. go over questions.
Continue 4.1. Geometry of vector combinations
Return to the proof that there were 0, 1, or infinitely many solutions to
any linear system. Examine the geometry in 2-D.
Coffee mixing problem and numerical methods issue related to decimals versus
fractions.
**Tues Feb 15** Discuss regression line.
Finish last chapter 3 clicker problem
Begin chapter 4.
Geometry of determinants and row operations via demo on ASULearn.

**Thur Feb 10**
3.3. Coding using matrices,
**This is the end of material for test 1**.
**Tues Feb 8**
3.1-3.2. Finish the Chapter 3 clicker
questions.

**Thur Feb 3**
Markov/stochastic/regular matrices.
Begin Chapter 3 via
Chapter 3 clicker questions
Chapter 3 in Maple via MatrixInverse command and then determinant work.
**Tues Feb 1**
Finish last two
clicker questions from 2.1 and 2.2..
Review the algebra of matrices. Review 2.1 #32 and
that we will see these later as representing rotation matrices
where A(alpha) +A(beta) = A(alpha +beta).
Prove that in a linear system with n variables and n equations
there may be 0, 1 or infinite solutions. Begin 2.5:
Applications of the algebra of matrices in 2.5.
2.5 clicker question

**Thur Jan 27** Continue with 2.1 and
2.2 clicker questions and
the algebraic operations of matrices. Complete 2.3.
**Tues Jan 25** 2.1 and 2.2:

Have you heard of Reginald Denny or Rodney King?

(a) yes

(b) no

(c) unsure

Image 1
Image 2
Image 3
Image 4
Image 5
Image 6
Image 7.

First few clicker questions
2.1 and 2.2 clicker questions
including matrix addition.

Powerpoint file.
Continue with the matrix multiplication.

**Thur Jan 20**
Go over 43 on the practice problems, including the geometry. Go over
text comments in Maple and distinguishing work as your own. 1.3 via the
traffic problem and circuit.
Gaussian review.
**Tues Jan 18**
Collect homework. Go over #73 by hand.

Also do in Maple:

implicitplot3d({x-2*y+z-2, x+y-2*z-3, (-2)*x+y+z-1}, x = -4 .. 4, y = -4 .. 4, z = -4 .. 4)

implicitplot3d({x+y+z-3, x+y+z-2, x+y+z-1}, x = -4 .. 4, y = -4 .. 4, z = -4 .. 4)

In 2-D how may solutions to a linear system of equations are possible?

(a) 0

(b) 1

(c) 2

(d) infinitely many

(e) more than one of the above answers is possible.

In 3-D how many solutions to a linear system of equations are
possible? What is the geometry? What is the Gaussian reduction?

Continue 1.1 and 1.2.

**Thur Jan 13** Take questions on the syllabus and read advise from
past students. Register *i-clickers*.
Questions.
Algebraic and geometric perspectives in 3-D and
solving using by-hand
elimination,
and ReducedRowEchelon and GaussianElimination.
**Tues Jan 11**
Fill out the information sheet
and work on the introduction to linear algebra handout.
History of linear equations and the term "linear algebra"
images.
Begin 1.1 and 1.2 including geometric perspectives,
by-hand algebraic Gaussian Elimination solutions, and
plotting, ReducedRowEchelon and GaussianElimination in Maple.
Gauss quotation and the historical context of
Gaussian and Gauss-Jordan.