final project slides, final project criteria, final project rubric, library sources: When Life Is Linear : From Computer Graphics to Bracketology, Pandora,

evaluations

Applications to mathematical physics, quantum chemistry..., Standing wave, Eigenfunction, Tacoma Narrows

Google Scholar: eigenvalue in mathematics education research

THE $25,000,000,000 EIGENVECTOR by Kurt Bryan and Tanya Leise

final research presentations

Hamburger earmuffs and the pickle matrix

full guidelines, topics and sample projects introduction to LaTex.

review activity

Test 2 review, topics to study

Clicker in Chapter 5 #12-

diagonalization, diagonalization and computer graphics and eigenfaces

definitions matching

Clicker in Chapter 5 #4-10 Highlight predator prey, predator predator or cooperative systems (where cooperation leads to sustainability)

Geometry of Eigenvectors

Ex1:=Matrix([[0,1],[1,0]]);

Eigenvalues(Ex1);

Eigenvectors(Ex1);

Ex2:=Matrix([[0,1],[-1,0]]);

Ex3:=Matrix([[-1,0],[0,-1]]);

Ex4:=Matrix([[1/2,1/2],[1/2,1/2]]);

Horizontal shear Matrix([[1,k],[0,1]])

Continue Dynamical Systems and Eigenvectors

comic http://brownsharpie.courtneygibbons.org/comic/guest-artist-little-pete-is-emo/

eigensheep comic

Clicker in Chapter 5 #11

Review algebra of eigenvalues and eigenvectors. worksheet on eigenvector decomposition

M := Matrix([[6/10,4/10],[-125/1000,12/10]]);

Eigenvectors(M);

Eigenvector decomposition

Application: Foxes and Rabbits

Clicker in Chapter 5 #1-3

Compare with Dynamical Systems and Eigenvectors first example. Never cross me!

nullspace null=me

clicker in 2.8 and real-life applications.

Write down an example of a 2x2 matrix representation of each of the following transformations: reflection, dilation, and shear

eigenvalues and eigenvectors. Apply the characteristic equation to your examples. Eigenvalues of triangular matrices are on the diagonal.

Matrix([[2,1],[1,2]])

M := Matrix([[2,1],[1,2]]); Eigenvectors(M);

Introduce foxes and rabbits: M := Matrix([[6/10,4/10],[-125/1000,12/10]]);

Eigenvectors(M);

Clicker questions in chapter 3 #10

If space is the final frontier, then what's a subspace [Paramount and CBS]?

basis, null space and column space, 2.8 worksheet

Review Laplace expansion

Clicker questions in chapter 3 #4-6

Mention google searches: application of determinants in various fields including eight queens in game theory and volumetric strain in geology

The relationship of row operations to the geometry of determinants

Clicker questions in chapter 3 #7-9

final project products, peer review and rubric

LaTex Beamer slides

determinator comic

matrix operations and determinants

worksheet on definitions

Clicker questions in 2.7 continued

begin Clicker questions in chapter 3 #1-3

2x2 and 3x3 diagonals methods and Laplace's expansion (1772 - expanding on Vandermonde's method) method in general. [general history dates to the Chinese and Leibniz]

M:=Matrix([[a,b,c],[d,e,f],[g,h,i]]);

Determinant(M); MatrixInverse(M);

M:=Matrix([[a,b,c,d],[e,f,g,h],[i,j,k,l],[m,n,o,p]]);

Determinant(M); MatrixInverse(M);

Review geometric transformations of the plane

Computer graphics demo [2.7] Examples 1 and 2

Clicker questions in 2.7 #1-2

rotation matrix and 6.1

Application of 2.7 and 6.1: Keeping a car on a racetrack

Computer graphics demo [2.7] Examples 3-5

Begin Yoda (via the file yoda2.mw) with data from Kecskemeti B. Zoltan (Lucasfilm LTD) as on Tim's page

exam corrections

Review and introduction to linear transformations

geometric transformations of the plane

We can also apply the product matrix M repeatedly to create a simple animation: Here is a movie created by 20 frames of applying URT(triangle). Careful of the order! Careful of the order - if I do T.R.U(triangle) instead.

Clicker question in 1.3, 1.4, 1.5, 1.7 #11-

Bring up solutions to Problem Set 3 on ASULearn and compare with your problem set

worksheet on definitions

review slides, sample partial exam, study guide for exam 1

Clicker in 2.1-2.3 #20-22

Not on exam 1: Glossary of terms: Review and introduction to linear transformations, Guess the transformation, worksheet VLA Package from

Sheared Sheap comic from our book, general geometric transformations on R

2.2 #21, review 2.3 and chapter 1 definitions, and theorem 8

Clicker in 2.1-2.3 #11-13

Review and continue condition number and Hill cipher

Continue Maple file on condition number and Hill cipher, PDF

Clicker in 2.1-2.3 #14-19

Review 2.1 #23 (multiplicative argument and then pivot argument). Example where A doesn't have to be square---3x2 matrix A.

Clicker in 2.1-2.3 #8-10

Comic: associativity superpowers

Assume that A (square) has an inverse. What else can you say?

Theorem 8 in 2.3 [without linear transformations], not invertible but still square, not square? List relevant examples and course overview

What makes a matrix invertible

Begin applications of 2.1-2.3 via course overview and condition number

Maple file on condition number and Hill cipher, PDF

Begin the Hill cipher history

2.2 Algebra: Inverse of a matrix

Finish Clicker in 2.1-2.3 #5

twobytwo := Matrix([[a, b], [c, d]]);

MatrixInverse(twobytwo);

MatrixInverse(twobytwo).twobytwo

simplify(%)

1.3 and 1.7 vector and matrix equations, ASULearn solutions and optional

Applications of multiplication and the inverse (if it exists). The first of these should look familiar!

success

Clicker in 2.1-2.3 #6-7

Review span and l.i. and mention video and solutions on ASULearn

glossary for 2.1-2.3, glossary for 1.3, 1.4, 1.5, 1.7, glossary for 1.1 and 1.2

Begin Chapter 2:

Then Clicker in 2.1-2.3 #1-4

matrix multiplication and matrix algebra. AB not BA...

Introduce transpose of a matrix via Wikipedia, including Arthur Cayley. Applications including least squares estimates, such as in linear regression, data given as rows (like Yoda

Begin Clicker in 2.1-2.3 #5

1.3 and 1.7 vector and matrix equations

Review theorem 4 in 1.4. theorem in 1.7

Clicker question in 1.3, 1.4, 1.5, 1.7 #8-10

dependence comic. Shin Takahashi and Iroha Inoue The Manga Guide to Linear Algebra

Roll, Yaw, Pitch by ZeroOne cc 3.0, and Gimbal lock on Apollo missions

Continue Maple file on span and l.i.

Review 1.1, 1.2, 1.3, 1.4, 1.5, 1.7

Continue span and l.i.

Clicker in 1.3-1.7 # 6, 20

#1 on span and l.i.

Clicker in 1.3-1.7 #7 to motivate 1.7 and redundancy

1.3 and 1.7 vector and matrix equations

Review theorem 4 in 1.4. theorem in 1.7

Continue with span and l.i. in R^2 #2-4 and discuss 5.

Begin Maple file on span and l.i.

Discuss REUs, majoring or minoring in mathematics and fall schedule. Review Clicker in 1.3-1.7 #4

Decimals (don't use in Maple) and fractions. Geometry of the columns as a plane in R^4, of the rows as 4 lines in R^2 intersecting in the point (40,60).

Second glossary. Review 1.3 and 1.4

What's your span? comic

Completion in Moodle, Grades in ASULearn, Solutions

Theorem 4 in 1.4

Clicker in 1.3-1.7 #5 and in Maple, including equation for the span, its geometry, and finding vectors inside and outside of it by using and modifying the diagonal of the parallelogram.

1.5: vector parametrization equations of homogeneous and non-homogeneous equations.

parallelvectorline movie. Introduce t*vector1 + vector2 is the collection of vectors that end on the line parallel to vector 1 and through the tip of vector 2.

spand3dmovie

Clicker in 1.3-1.7 #1-3

Peer review hw

Begin 1.4.

Clicker in 1.3-1.7 #4

with(LinearAlgebra): with(plots):

Coff:=Matrix([[.3,.4,36],[.2,.3,26],[.2,.2,20],[.3,.1,18]]);

ReducedRowEchelonForm(Coff);

Coffraction:=Matrix([[3/10,4/10,36],[2/10,3/10,26],[2/10,2/10,20],[3/10,1/10,18]]);

ReducedRowEchelonForm(Coffraction);

Decimals (don't use in Maple) and fractions.

Theorem 4 in 1.4

3 unknowns in R^3, advice from previous students.

1.3 and Glossary for rest of chapter 1

Maple for span

Foxtrot vector addition comic by Bill Amend. November 14, 1999.

Clicker in 1.1 and 1.2 #2 onwards

Problem set 1

Turn in the hw. Review EBG #5. Prove using geometry of lines that the number of solutions of a system with 2 equations and 2 unknowns is 0, 1 or infinite.

Engagement with the the i-clickers Hand out i-clicker questions and do Clicker in 1.1 and 1.2 #1.

Gaussian and Gauss-Jordan or reduced row echelon form in general.

Review Gaussian and Gauss-Jordan for 3 equations and 2 unknowns in R

Drawing the line comic.

Parametrize x+y+z=1. Maple

with(LinearAlgebra): with(plots): Ex1:=Matrix([[1,-2,1,2],[1,1,-2,3],[-2,1,1,1]]);

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);

Ex2:=Matrix([[1,2,3,3],[2,-1,-4,1],[1,1,-1,0]]);

implicitplot3d({x+2*y+3*z=3,2*x-y-4*z=1,x+y-z=0}, x=-4..4,y=-4..4,z=-4..4);

Ex3:=Matrix([[1,2,3,0],[1,2,4,4],[2,4,7,4]]);

implicitplot3d({x+2*y+3*z = 0, x+2*y+4*z = 4, 2*x+4*y+7*z = 4}, x = -13 .. -5, y = -1/4 .. 1/4, z = 3 .. 5, color = yellow);

Ex4:=Matrix([[1,3,4,k],[2,8,9,0],[10,10,10,5],[5,5,5,5]]);

GaussianElimination(Ex4);

Ex4a:=Matrix([[1,3,4,k],[2,8,9,0],[10,10,10,5]]);

GaussianElimination(Ex4a);

Highlight equations with 3 unknowns with infinite solutions, one solution and no solutions in R

Course intro slides # 1 and 2

Work on the introduction to linear algebra handout motivated from Evelyn Boyd Granville's favorite problem (#1-3). At the same time, begin 1.1 (and some of the words in 1.2) including geometric perspectives, by-hand algebraic EBG#3, Gaussian Elimination and EBG #5 and pivots, solutions, plotting and geometry, parametrization and GaussianElimination in Maple for systems with 2 unknowns in R

Evelyn Boyd Granville #3:

with(LinearAlgebra): with(plots):

implicitplot({x+y=17, 4*x+2*y=48},x=-10..10, y = 0..40);

EBG3:=Matrix([[1,1,17],[4,2,48]]);

GaussianElimination(EBG3);

ReducedRowEchelonForm(EBG3);

In addition, do #4

Evelyn Boyd Granville #4: using the slope of the lines, versus full pivots in Gaussian (r2'=-4 r1 + r2):

EBG4:=Matrix([[1,1,a],[4,2,b]]);

GaussianElimination(EBG4);

Course intro slides continued.

How to get to the main calendar page: google

Vocabulary/terms/ASULearn glossary

Evelyn Boyd Granville #5 with k as an unknown but constant coefficient.

EBG#3, Gaussian Elimination and EBG #5

EBG5:=Matrix([[1,k,0],[k,1,0]]);

GaussianElimination(EBG5);

ReducedRowEchelonForm(EBG5);