**Class Policy**

The class policy is posted here.

It contains all the information about
homework, exams, grades, add/drop,

class rules, calculators, office hours etc.

Please read and understand the Class Policy.

If you have questions, let me know.

**Lecture**

MWF 9:00 -- 9:50, Chemistry, Rm 134

**Instructor **

Matthias Morzfeld

Email: mmo [at] math [dot] arizona [dot] edu

Office hours:
Tu 12-1, W 1-2 in S331 ENR2; F 2-3 in Math 220

**UTA**

Hannah Knight

Office hours: Tu 2-3, Th 12:30-1:30, in Math 220

Discussion hour: Th 3:30-4:30 (Math 102)

**Textbook**

Applied Linear Algebra

by Peter J. Olver and Chehrzad Shakiban. Pearson.

**Course Description**

Applications and methods of linear algebra emphasizing matrices and systems of equations,

determinants, eigenvectors and eigenvalues. This course is an excellent introduction

to linear algebra for students who are interested in a math minor.

It does not satisfy requirements for the math major.

**Announcements**

I willpost what material was covered in class here after each lecture.

- Lecture 1: Intro to matrices and vectors and their arithmetic (Section 1.2)
- Lecture 2: Gaussian elimination (Section 1.3)
- Lecture 3: Gaussian elimination and LU factorization (Section 1.3)
- Lecture 4: Gaussian elimination and LU factorization (Section 1.3)
- Lecture 5: Gaussian elimiation with pivoting, PA = LU (Section 1.4)
- Lecture 6: Inverse of a matrix (Section 1.5)
- Lecture 7: Transpose and symmetric matrices (Section 1.6)
- Lecture 8: Determinants (Section 1.9)
- Lecture 9: Review
- Lecture 10: Exam 1
- Lecture 11: General linear systems (Section 1.8)
- Lecture 12: General linear systems (Section 1.8)
- Lecture 13: Homogeneous problems and vectors spaces (Sections 1.8 and 2.1)
- Lecture 14: Subspaces (Section 2.2)
- Lecture 15: Span and linear combinations (Section 2.3)
- Lecture 16: Liner independence (Section 2.3)
- Lecture 17: Bases and dimension(Section 2.4)
- Lecture 18: Bases, dimension and fundamental matrix subspaces (Sections 2.4 and 2.5)
- Lecture 19: Fundamental theorem of linear algebra (Section 2.5)
- Lecture 20: Inner products and norms (Section 3.1)
- Lecture 21: Review
- Lecture 22: Exam
- Lecture 23: Post-Exam disucssion
- Lecture 24: Inner products and inequalities (Sections 3.1 and 3.2)
- Lecture 25: Positive definite Matrices (Section 3.4 and 3.5)
- Lecture 26: Orthogonal bases (Section 5.1)
- Lecture 27: Gram-Schmidt (Section 5.2)
- Lecture 28: More of Gram-Schmidt and orthogonal matrices (Section 5.2)
- Lecture 29: QR factorization (Section 5.3)
- Lecture 30: QR factorization (Section 5.3)
- Lecture 31: Orthogonal projection (Section 5.5)
- Lecture 32: Least squares (Section 5.5)
- Lecture 33: Least squares and data fitting (Section 4.4)
- Lecture 34: Least squares and data fitting (Section 4.4)
- Lecture 35: Eigenvalues and eigenvectors (Section 8.2)
- Lecture 36: Review
- Lecture 37: Exam
- Lecture 38: Exam Discussion
- Lecture 39: Eigenvector bases and diagonalization (Section 8.3)
- Lecture 40: Eigenvalues of symmetric matrices (Section 8.4)
- Lecture 41: Optimization principles for eigenvalues (Section 8.4)
- Lecture 42: Power method (Section 10.6)
- Lecture 43: Jacobi method (Section 10.5)
- Lecture 44: Singular value decomposition (Section 8.5)
- Lecture 45: Review

It is your responsibility to check for the additional handwritten homework.

The due date is written on each homework set.

The handwritten homework is due in class, before class starts.

I recommend that you do more handwritten problems from the textbook.

HW Set 1, posted 1/11, due 1/20 -- 1.2.32, 1.3.10, 1.3.11

HW Set 2, posted 1/19, due 1/27 -- 1.3.22, 1.4.5

HW Set 3, posted 1/26, due 2/3 -- 1.4.20(a), 1.5.7, 1.6.28

HW Set 4, posted 2/3, due 2/10 -- 1.6.22, 1.9.19(a), 1.9.10

HW Set 5 posted 2/10, due 2/17 -- 1.8.2(d), 1.8.25

HW Set 6 posted 2/17, due 2/24 -- 2.1.7, 2.2.14, 2.3.4(b)

HW Set 7 posted 2/24, due 3/3 -- 2.4.16, 2.5.1(c)

HW Set 8 posted 3/7, due 3/10 -- 3.1.1, 3.1.7

HW Set 9 posted 3/19, due 3/24 -- 3.2.22, 3.4.20

HW Set 10 posted 3/24, due 3/31 -- 5.1.4, 5.2.4(a)

HW Set 11 posted 3/31, due 4/7 -- 5.3,16(a), 5.3.27(a), 5.5.3

HW Set 12 posted 4/7, due 4/14 -- 5.5.2(c), 4.3.15(c) (use matlab to solve normal equations)

HW Set 13 posted 4/14, due 4/21 -- 8.2.19, 8.2.26

HW Set 14 posted 4/21, due 4/28 -- 8.3.10(a), 8.4.19

HW Set 15 (bonus) posted 5/1, due 5/3 -- 10.6.1(b) (use Matlab), 10.6.5(a)

For the tutorials, you do not need to give me a typed document,

handwritten explanations and some print outs from Matlab are fine.

TUTORIAL 1: complete Tutorial 1 of the Matlab tutorials whenever you can, no need to hand this in.

TUTORIAL 2: posted 1/27, due 2/17 -- complete Tutorial 2 of the Matlab tutorials

TUTORIAL 3: posted 2/24, due 3/10 -- complete Tutorial 3 of the Matlab tutorials

Matlab project 1: posted 4/6, due 4/21 -- Code the qr factorization for a 3x3 matrix. Hand in your code and results for one example.

Discussion 1.

Discussion 2.

Discussion 3.

Discussion 4.

Discussion 5.

Discussion 6.

Discussion 7.

Discussion 8.

Discussion 9.

Discussion 10.

Suggested review problems.

Matlab code for solving least squares problems.

Matlab code for the power method to find eigenvalues.

Matlab code for the Jacobi method to solve Ax=b.