Math 313 - Section 001 - Fall 2016

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 10:00 -- 10:50, Engineering 314

Instructor
Matthias Morzfeld
Email: mmo [at] math [dot] arizona [dot] edu
Office hours: M 11-12, W 1-2 in S331 ENR2; F 11-12 in Math 220

UTA
Hannah Knight
Office hours: Th 2-4, Math 220
Discussion hour: T 3-4, Math 102

Textbook
Linear Algebra and Its Applications,
Custom Edition for University of Arizona, Pearson

Course Description
An algorithmic approach to solving systems of linear equations
transitions into the study of vectors, vector spaces and dimension.
Matrices are used to represent linear transformations and
this leads to eigenvectors and eigenvalues.
The precise use of definitions plays an important role.
Examinations are proctored.
This course is required in the math major and prepares students to take Math 323.
It is a prerequisite to the majority of the higher level courses in mathematics.
Enrollment Requirements:
MATH 129, MATH 223, MATH 243, MATH 254, or CSC 245.

UA Linear Algebra Website
http://math.arizona.edu/~math313/

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

Lecture 1: Systems of linear equations (Section 1.1)
Lecture 2: Row reduction and echolon forms (Section 1.2)
Lecture 3: Row reduction and and vectors (Sections 1.2 and 1.3)
Lecture 4: Vector equations and Ax = b (Sections 1.3 and 1.4)
Lecture 5: Sets of linear systems (Section 1.5)
Lecture 6: Linear independence (Section 1.7)
Lecture 7: Transformations and matrices (Section 1.8)
Lecture 8: More transformations and matrices (Section 1.9)
Lecture 9: Review
Lecture 10: Exam 1
Lecture 11: Matrix operations (Section 2.1)
Lecture 12: The inverse of a matrix (Section 2.2)
Lecture 13: The inverse of a matrix (Section 2.2)
Lecture 14: The inverse of a matrix and the ``giant theorem'' (Section 2.2 and 2.3)
Lecture 15: LU factorization (Section 2.5)
Lecture 16: Determinants (Section 3.1, 3.2)
Lecture 17: Determinants again (Section 3.2)
Lecture 18: Review
Lecture 19: Exam 2
Lecture 20: Vector spaces and subspaces (Section 4.1)
Lecture 21: Vector spaces and subspaces (Section 4.1)
Lecture 22: Nullspace and columnspace (Section 4.2)
Lecture 23: Nullspace and columnspace, linearly independent sets (Sections 4.2 and 4.3)
Lecture 24: Coordinate systems (Section 4.4)
Lecture 25: Coordinate systems (Section 4.4)
Lecture 26: Dimension of a vector space (Section 4.5)
Lecture 27: Row space and rank (Section 4.6)
Lecture 28: Eigenvalues and eigenvectors (Section 5.1)
Lecture 29: Characteristic polynomial and characteristic equation (Section 5.2)
Lecture 30: Diagonalization (Section 5.3)
Lecture 31: Summary: eigenvalues and eigenvectors (Section 5.1-5.3)
Lecture 32: Inner product, length, orthogonality (Section 6.1)
Lecture 33: Inner product, length, orthogonality (Section 6.1)
Lecture 34: Orthogonal sets (Section 6.2)
Lecture 35: Review
Lecture 36: Exam 3
Lecture 37: Orthogonal projections (Section 6.3)
Lecture 38: Orthogonal projections (Section 6.3)
Lecture 39: Orthogonal projections and the Gram Schmidt process (Sections 6.3 and 6.4)
Lecture 40: The Gram Schmidt process (Section 6.4)
Lecture 41: Least squares (Section 6.5)
Lecture 42: Least squares (Section 6.5)
Lecture 43: Review

Homework
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.

Handwritten homework
HW Set 1, posted 8/22, due 8/31 -- 1.1 - 28; 1.2 - 8,18; 1.3 - 13,32
HW Set 2, posted 8/30, due 9/9 -- 1.4 - 26, 32; 1.5 - 10, 20; 1.7 - 2
HW Set 3, posted 9/9, due 9/16 -- 1.8 - 10,32; 1.9 - 20,26
HW Set 4: see Matlab tutorial below
HW Set 5, posted 9/26, due 9/30 -- Handwritten HW: 2.1 - 24; 2.2 - 24; 2.3 - 27
HW Set 6, posted 9/30, due 10/7 -- Handwritten HW: 2.5 - 7; 3.1 - 38; 3.2 - 42
HW Set 7, posted 10/14, due 10/21 -- Handwritten HW: 4.1 - 22; 4.2 - 24
HW Set 8, posted 10/21, due 10/28 -- Handwritten HW: 4.3 - 26, 33; 4.4 - 32
HW Set 9, posted 10/29, due 11/4 -- Handwritten HW: 4.5 - 21; 4.6 - 20; 5.1 - 26
HW Set 10, posted 11/5, due 11/14 -- Handwritten HW: 5.1 - 29; 5.2 - 23; 5.3 - 27, 31
HW Set 11, posted 11/11, due 11/21 -- Handwritten HW: 6.1 - 24, 31
HW Set 12, posted 11/28, due 12/2 -- Handwritten HW: 6.2 - 34; 6.3 - 23
HW Set 13, posted 11/28, due 12/7 -- Handwritten HW: 6.4 - 20; 6.5 - 19

Matlab tutorials
For any of the tutorials, you do not need to give me typed document, handwritten explanations and some print outs from Matlab are fine.
TUTORIAL 2: posted 9/16, due 9/23 -- complete Tutorial 2 of the Matlab tutorials
You do not need to do chapter 2.3, An application to Economics: Leontief Models. Do not worry about the Matlab quizzes.
TUTORIAL 3: posted 9/28, due 10/14 -- complete Tutorial 3 of the Matlab tutorials
TUTORIAL 4: posted 11/11, due 11/21 -- complete Tutorial 4 of the Matlab tutorials
TUTORIAL 5: posted 11/21, due 12/7 -- complete Tutorial 5 of the Matlab tutorials

Matlab project
The Matlab project is due on November 28.
The task is: code up row-reduction to bring an arbitrary 3x3 matrix into row-echolon form.
Try to use for-loops.
You should hand in: an example that your code is working as well as the source code.

Additional practice problems
Download a list of practice problems here

Solutions and additional materials
To see what a HW solution should look like, download these solutions, prepared by Hannah (our UTA).
Here are solutions to the first Matlab tutorial, prepared by Hannah.
Here is a link to my review for exam 1.