# 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 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).

Homework 2 is now posted, due Fri Sep 29.

Quiz 2(Wed, Oct4) will be based on all the matrials we learned on the interpolation and finite difference approximation which I will finish on Monday.
Here is the suggested practice problem set for Quiz 2.
2016 WT2 Midterm : All parts of problem 3.
2016 WT1 Midterm : Problem 1 d) and all parts of 4.
2015 Midterm : All parts of problems 3 and 4.
2014 Midterm : All parts of problem 2.

Homework 3 is now posted, Due Fri, Oct 6. Notice that the due date is changed.
heat.m file is also uploaded here. heat.m

The solutions for homework 2 is now up.

No class on Monday, Oct 9. Have a good thanksgiving!

MIDTERM INFORMATION
The midterm (Fri, Oct 20) is based on the follwoing material in the text book:
Chapter 1: All sections except I.2.4. and I.2.5.
Chapter 1: Section II.1, II.2.1, and II.2.2.

Here is the suggested practice problems from the past midterms for midterm.
2016 WT2 Midterm : All problems except 1d,e,f,g and 4c,d,e,f.
2016 WT1 Midterm : All except 1g, 3b.
2015 Midterm : All problems except 2b,c.
2014 Midterm : Everything except problem 3, 4.

Homework 4 is now posted, Due Fri, Nov 3.

Quiz 3 (Wed, Nov 8) will he based on the materials on Section II.2, Section III.1.1, III.1.2, and III.1.3. Here is the practice problems for the quiz.
2016 WT2 Midterm : Problem 1d,e,f,g and all parts of problem 4
2016 WT1 Midterm : Problem 1fg, all parts of problem 3.
2015 Midterm : Problem 2.
2014 Midterm : Problem 3.
2013 Final : Problem 3.
Another 2013 Final : Problem 4.
2011 Final : Problem 3.
There is also a suggested problem set from the homework 5 with no submission: problems 1, 3, 4, and 9. I posted its solution as well for your prepartion for the quiz.

Homework 6 is posted, Due Mon, Nov 20.

The solutions for Quiz 3 is now posted.

Quiz 4 will be based on Section III.1.4, and all subsections of III.2, III.3, IV.1. The suggested practice problems for Quiz 4 are as follows:
2013 Final : Problem 1(Ignore the answers involving Hermitian matrices), Problem 4
Another 2013 Final : Problem 2bc.
2011 Final : Problem 5c, 8a.

The solutions for Quiz 4 is now posted.

Homework 7(No submission, No due date) with the solution is also posted.

The corrected lecture note for final lecture is posted.

I put all the homework and quizzes (including Quiz 4) in front of my office PIMS 4134.

Extra office hours on Thursday, Dec 14, 2-4pm in LSK 300C.

## FINAL EXAM INFORMATION AND RESOURCES

The final exam will be held on DEC 18 2017 8:30 AM in CIRS 1250.

The material for final exam is as follows:
Chapter 1: everything except section I.2.4 and I.2.5.
Chapter 2: all of II.1 and II.2.
Chapter 3: all of III.1 except for III.1.5 and all of III.2, all of III.3.
Chapter 4: all of IV.1, IV.2.1-3,5, all of IV.3, IV.4, IV.6.1-3. Here is an article for Google PageRank (except 4,6). IV.7.1.3 and the nullspace, range, rank of a matrix in the SVD form in the lecture note.

Past final exams with solutions 2013 Final (except problem 5) , Another 2013 Final (except 5) , 2011 Final (except 4,6).
For more practice exam resources, check out this link to UBC wiki (except 4,6).

Extra office hours will be helo on Thursday, Dec 14, 2-4pm in LSK 300C.

## 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

Office : PIMS 4134 in ESB

## 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.

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.

## 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.

Lecture 7 (20/09/2017) : Lagrange interpolation and Splines.

Lecture 8 (22/09/2017) : Splines and Cubic splines.

Lecture 9 (25/09/2017) : Cubic spline example. Matlab script

Lecture 10 (27/09/2017) : Cubic spline. Lagrange interpolation Matlab script

Lecture 11 (29/09/2017) : Finite difference approximation.

Lecture 12 (02/10/2017) : Finite difference approximation.

Lecture 13 (04/10/2017) : Finite difference approximation MATLAB code. Vector spaces. Matlab script 1 , Matlab script 2

Lecture 14 (06/10/2017) : Vector spaces and vector subspaces.

Lecture 15 (11/10/2017) : Linear independence.

Lecture 16 (13/10/2017) : Linear independence, Span, Basis

Lecture 17 (16/10/2017) : Basis, Null spaces and Range of a matrix

Lecture 18 (18/10/2017) : Null spaces and bases for the range of A and A^T.

Lecture 19 (23/10/2017) : Four fundamental subspaces of a matrix. Orthogonality of vectors and subspaces.

Lecture 20 (25/10/2017) : Orthogonality of subspaces and its consequence on the four subspaces. The formular matrix of a chemical system.

Lecture 21 (27/10/2017) : The formular matrix of a chemical system and its reaction. Orthogonal projections on a line.

Lecture 22 (29/10/2017) : Orthogonal projections on a line.

Lecture 23 (1/11/2017) : Orthogonal projection matrices and their properties.

Lecture 24 (3/11/2017) : The least squre and corresponding orthogonal projection.

Lecture 25 (6/11/2017) : Polynomial fits and Complex numbers.

Lecture 26 (9/11/2017) : Complex numbers.

Lecture 27 (11/11/2017) : Complex numbers, Complex vector spaces and inner product

Lecture 28 (15/11/2017) : Orthonormal basis, Orthogonal and unitary matrices, Eigenvalues and eigenvectors.

Lecture 29 (17/11/2017) : Orthonormal basis, Orthogonal and unitary matrices, Eigenvalues and eigenvectors.

Lecture 30 (20/11/2017) : Diagonalization, Hermition matrices.

Lecture 31 (22/11/2017) : Power method and Recursion relations.

Lecture 32 (24/11/2017) : Recursion relations and Markov chains.

Lecture 33 (27/11/2017) : Markov chains and Google Page Rank.

Lecture 34 (29/11/2017) : Google Page Rank and SVD.

Lecture 35 (1/12/2017) : SVD. There was a mistake in finding the null space of A* in the example in this lecture note.
You need to read off the third row of V* since that is the third column of V associated the zero siggular value. I have corrected it and am sorry for the confusion.

## Homework

Homework 2 (16, 18 in problem_1.1.pdf and 1, 2, 3, 4 in problem_1.2.pdf) (Due Fri , Sep 29)
Matlab files for problem set 1.2 splinemat2.m , plotcubic2.m , plotspline2.m
Solutions for problems 16, 18 in problem set 1.1   Solutions for problem set 1.2

Homework 3 (1, 2, 3, 4, 5, 6 in problem_1.3.pdf ) (Due Fri, Oct 6 ) heat.m file for problem 3, 4, 5, 6 heat.m     Solutions for problem set 1.3

Homework 4 (1, 2, 3, 4, 6, 7 in problem_2.1.pdf ) (Due Fri, Nov 3 ) Solutions for problem set 2.1

Homework 5 (1, 3, 4, 5, 7, 9 in problem_3.1.pdf ) (No due date) Solutions for problem set 3.1

Homework 6 (1, 2ab, 3 in problem_3.2.pdf   1, 3, 8, 9 in problem_3.3.pdf   1, 2, 3, 4, 5 in in problem_4.1.pdf ) (Due Mon, Nov 20)
Solutions for problem set 3.2   Solutions for problem set 3.3   Solutions for problem set 4.1

Homework 7 (No submission, NOT due ) (1, 2 in problem_4.2.pdf   1, 2 in problem_4.3.pdf   1, 2 in in problem_4.4.pdf   1, 2,3 in problem_4.6.pdf   1, 2 in problem_4.7.pdf
Solutions for problem set 4.2   Solutions for problem set 4.3   Solutions for problem set 4.4 Solutions for problem set 4.6 Solutions for problem set 4.7