Math 307: Applied Linear Algebra, W17 Term 1, Section 102

Announcement

The first lecture will be on Wednesday, September 6.

The first lecture note is posted! I will use different pens next time to make the characters in the note more stand out.

The second lecture note is now posted. The MATLAB examples we saw in the class will be uploaded shortly with comments.

The first homework posted. Notice the unusual due date.
You may skip the part f) and g) of problem 12.

The next homework due is at least next Friday and most likely there will be no homework submission next week.
The first quiz on Wednesday will be based on the material we learned in the first two weeks. Here are the practice problems for the quiz:
2016 WT2 Midterm : Problem 1c and all parts of problem 2 except part e).
2016 WT1 Midterm : Problem 1 a), c) and all parts of problem 2.
2015 Midterm : All parts of problem 1 except the condition number part of b) and problem 2 a).
2014 Midterm : All parts of problem 1 except part d).

Course Information

Lectures: Mon, Wed, Fri 1pm-2pm at Mathematics building, room 102
Course webpage: http://www.math.ubc.ca/~hajeong/Math307Winter.html

Text book: We will use the following online book as the main text.
Chapter 1 : Linear Equations
Chapter 2 : Subspaces, Bases, and Dimension
Chapter 3 : Orthogonality
Chapter 4 : Eigenvalues and Eigenvectors

Instructor Information

Instructor: Halyun Jeong
Office hour: Tuesday 3:30-5:30 pm in LSK 300C
Email: hajeong@math.ubc.ca

Course Outline

Our goal is to cover most of the following topics in the course lecture notes: Interpolation, Finite difference approximations, Formula matrix of a chemical system, Graphs and Networks, Least squres, Fourier series, Fast Fourier Transform, JPEC compression, Power method, Recursion relations, The Anderson tight binding model, Markov chains, Google PageRank.

Grading Policies

The course mark will be deteremined based on homeworks(10%), quizzes(10%), a midterm(30%), and a final(50%).

The homework is due each Wednesday. Please hand in our homework when the class starts. The late homework will not be accepted but the lowest marked homework will be dropped in the final grade calculation. Students are encouraged to discuss homework, but should write up their homeworks individually.

Under any circumtances, there will be no make-up midterm. If a student misses the midterm with a valid reason, his or her final exam will be re-weighted to incorporate the midterm weight. The valid excuses for missing homework or exams include a prior approval of the instructor or medical emergency which must be supported by a physician's note within 72 hours. Missed homework, quizzes, exams without these reasons will be marked as 0.

Exam Information

All exams are closed books and no calculators are allowed.

There will be four 10 mininutes in-class quizzes on Sep 20, Oct 4, Nov 8, and Nov 24.

The in-class midterm will be held on Friday, Octorber 20.

The final exam date is fixed by UBC (the date/time will be announced soon). Please plan your end-of-term travel carefully according to this date.

Computational software support

You will need access to MATLAB software to complete the work for this course. MATLAB is a widely used program for numerical computations with matrices. As of now, MATLAB is available to all UBC students at no cost. For the information including download and activation, follow this link: https://it.ubc.ca/services/desktop-print-services/software-licensing/matlab#getMATLAB

You can also access MATLAB in the math department computer lab which is located in LSK 310. The lab hours are posted here. You may use any free terminal in the labs during these times. Your username and password will be given out in the class. Let me know if you have difficulty in login. You may also use GNU Octave and they are also free. However, the instructor will only be able to answer questions regarding MATLAB.

Piazza link for this course

You can ask questions regaring homework, course note, MATLAB,etc. and your instructor, TA, fellow stduents can answer them.

UBC's academic misconduct policies

Lecture notes and MATLAB scripts

Lecture 1 (06/09/2017) : Linear systems with one or two unknowns, The inverse of a matrix (There was a page mixed up (page 3 and 4) but now it is fixed. I apologize for this.)

Lecture 2 (08/09/2017) : Solving general form of systems of linear equations by Gaussian Elimination. The definition of a norm, Matlab script

Lecture 3 (11/09/2017) : Vector norm examples: l1, l2, lp, l norms. Their geometric properties and relations. As for notation, for real number a, |a| = a if a is nonnegative and |a| = -a otherwise. For complex numbers, say a = s + it where s and t are real numbers, |a| =  s^2 + t^2  . So, |i| = |0+1i| =  1^2  = 1 whereas i^2 = -1 by the definition of the complex number i.

Lecture 4 (13/09/2017) : Vector norms and Matrix norms. The operator norm for matrix A is defined in terms of the vector norm of x and Ax, so we need to specify the vector norm when we work with an operator norm. For example, if the vector norm is l1 norm, then it is denoted by ||A||1 → 1 . If the vector norm is the l 2 norm, sometimes we don't need to specify what the vector norm is, i.e., we just denote the operator norm as ||A||. Matlab script

Lecture 5 (15/09/2017) : Operator norms and Condition number.

Lecture 6 (18/09/2017) : Condition number and Lagrange interpolation.

Homework

Homework 1 (Submit the following problems in the problem set: 1a, 2, 4, 5, 7, 12 a) - e), 13, 15) (Due Fri , Sep 15) Solution for problem set 1.1