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

## Announcement

The first lecture will be on Wednesday, September 5.

The due date for the first assignment (Problems 1a, 2, 5, 7, 13, 14) is actually Mon , Sep 17!

Theese are some suggested problems for Quiz 1:

Midterm (2016 W2) : Problem 1c and Problem 2.
Midfterm (2016 W1) : Problem 1a,c and Problem 2.
Midfterm (2015) : Problem 1 and Problem 2a.
Midfterm (2014) : Problem 1 except part d.

The solution for the first assignment is now available.

The solution for the first quiz is posted!

The homework 2 is out and due on Friday, Sep 28.

The homework 2 is postponed and now due on Monday, Oct 1!

There were some typos in the lecture note 8 and 10 which are now corrected.

Homework 1 and Quiz 1 marks are up on the Canvas.

Quiz 2 will cover all the material by Oct 1 (All the matieral on the interpolation I.2.1, I.2.2, I.2.6, I.2.7 and finite difference approximation (I.3.1, I.3.2) ) !!

Suggested problems for Quiz 2:
Midterm (2016 W2) : Problem 3.
Midfterm (2016 W1) : Problem 1d and Problem 4.
Midfterm (2015) : Problem 3 and Problem 4.
Midfterm (2014) : Problem 2.

Homework 3 (not due, actually not homework but additonal practice problem set) is posted below with solution.

You can get the assignments and quizzes at the MLC assessment return station. The MLC is located at LSK301 and LSK302 and is open 5 days a week 11am-5pm.

MIDTERM INFORMATION
The midterm (Fri, Oct 19) is based on the follwoing material in the text book:
Chapter 1: All sections except I.2.4. and I.2.5.
Chapter 2: Section II.1, II.2.1 - II.2.6

Here is the suggested practice problems from the past midterms for midterm.
2016 WT2 Midterm : All problems except 1g.
2016 WT1 Midterm : All problems
2015 Midterm : Everything.
2014 Midterm : All problems except problem 4.

Homework 4 ( due Wed, Oct 17 ) is posted now.

Extra office hour on Tuesday Oct 16 2pm-3pm in LSK 300.

Homework 5 (due Wed, Nov 5) is posted.

Homework 5 problem change! : The problems in Problem set 3.1 are changed to: Problem 2, 3.

Quiz 3 (Wed, Nov 7) will cover all the material: Section II.3 (Graphs and Networks), III.1.1, III.1.2.
Suggested problems for Quiz 3:
Midterm (2014) : Problem 4.
Final (2013) : Problem 3.
Another Final (2013) : Problem 5.
Final (2011) : Problem 4.

The solution for the midterm is posted.

The solution for the Homework 5 is now posted.

The scope of Quiz 4 (Fri, Nov 23) is as follows: Section III.1.3 , III.1.4, III.2, III.3, and IV.1.
Here are the suggested problems for Quiz 4:
Final (2013) : Problem 3, 4.
Another Final (2013) : Problem 2c, 4.
Final (2011) : Problem 5c, 8a.

Homework 6 (not due, actually not homework but additonal practice problem set) is posted below with solution.

Homework 7 (not due, actually not homework but additonal practice problem set) is uploaded below with solution.

Quiz 4 solution is posted.

I will anounce the extra office hours soon.

FINAL EXAM INFORMATION
The final exam will be held on Wednesday, December 12, 8:30AM in WOOD 2.

The final is based on the follwoing material in the text book:
Chapter 1: All sections except I.2.4. and I.2.5.
Chapter 2: Everyting in section II.1, All of II.2 except II.2.3, All of II.3
Chapter 3: Everyting in section III.1 except III.1.5, All of III.2, All of III.3
Chapter 4: All of IV.1, all we covered in the class in IV2.1-2.4, all of IV.3, IV.4, IV6.1-6.2 (including the two pages of lecture note I added after the Lcture 34 ), IV7.1-7.3 including the nullspace, range, rank of SVD (including two pages after the lecture).

Here are the some suggested problems for final:
Final (2013) ,   Another Final (2013) ,   Final (2011).
There are other past exams you can study (some of them have no solutions) on this UBC Wiki.

EXTRA OFFICE HOURS FOR THE FINAL
Thursday, December 6, 3-5 pm, LSK 300B
Monday, December 10, 3-5 pm, LSK 300B

## Course Information

Lectures: Mon, Wed, Fri 1pm-2pm at room 182, Irving K Barber Learning Centre.
Course webpage: http://www.math.ubc.ca/~hajeong/Math307_2018W1.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: Thursday 3-5 pm, LSK 300B
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.

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

There will be weekly homework assianments. Please hand in your homework when the class starts on due date. 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 in-class quizzes on Sep 19, Oct 3, Nov 7, and Nov 23.

The in-class midterm will be held on Friday, Octorber 19.

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 notes will be uploaded here after each lecture.

Lecture 1 (05/09/2018) : Linear systems with one or two unknowns.

Lecture 2 (07/09/2018) : General system of linear equations, rref, Gaussian elemination.

Lecture 3 (10/09/2018) : Vector norms and Matrix norms Matlab script (10/09/2018)

Lecture 4 (12/09/2018) : Operator norm and Condition number.

Lecture 5 (14/09/2018) : Condition number.

Lecture 6 (17/09/2018) : Lagrange interpolation. Matlab script (17/09/2018)

Lecture 7 (19/09/2018) : Lagrange interpolation and Splines Matlab script (19/09/2018)

Lecture 8 (21/09/2018) : First method for Cubic spline interpolation (There was a typo in the note on the 4th condition for a cubic spline. Thanks for pointing it out!)

Lecture 9 (24/09/2018) : First method for Cubic splines, Second method for Cubic splines Matlab script (24/09/2018)

Lecture 10 (26/09/2018) : Second method for Cubic splines (There was a typo in the note. Thank you for letting me know.)

Lecture 11 (28/09/2018) : Second method for cubic spline. Finite difference approximation.

Lecture 12 (01/10/2018) : Finite difference approximation.

Lecture 13 (03/10/2018) : Finite difference approximation. Vector spaces.

Lecture 14 (05/10/2018) : Vector spaces, Subspaces, Linear independence

Lecture 15 (10/10/2018) : Linear independence and Span

Lecture 16 (12/10/2018) : Span, Basis, and Four fundamental subspaces

Lecture 17 (15/10/2018) : Four fundamental subspaces

Lecture 18 (17/10/2018) : Inner product, Orthogonality, and Orthogonal subspaces.

Lecture 19 (22/10/2018) : Orthogonality relations for the fundamental subspaces of a matrix. The formular matrix for a chemical system

Lecture 20 (24/10/2018) : The formular matrix for a chemical system, Graphs and Networks.

Lecture 21 (26/10/2018) : Graphs and Register networks.

Lecture 22 (29/10/2018) : Register networks and Laplacian (I changed the current direction in Ohm's law.)

Lecture 23 (31/10/2018) : Register networks and Laplacian. Orthogonal projection on lines.

Lecture 24 (2/11/2018) : Orthogonal projectors on lines, Orthogonal projection matrices.

Lecture 25 (5/11/2018) : The least square equation and its solution.

Lecture 26 (7/11/2018) : Polynomial fitting.

Lecture 27 (9/11/2018) : Polynomial fitting, Complex numbers Matlab script for polynomial fitting (9/11/2018)

Lecture 28 (14/11/2018) : Complex numbers and vectors

Lecture 29 (16/11/2018) : The inner product for complex vectors, Orthonormal basis

Lecture 30 (19/11/2018) : Orthonormal bases, Orthogonal matrices, and Eigenvalues/Eigenvectors

Lecture 31 (21/11/2018) : Eigenvalues/Eigenvectors

Lecture 32 (23/11/2018) : Diagonalization, Determinant and Trace, Power of diagonalizable matrices

Lecture 33 (26/11/2018) : Hermitian matrices, Power method, Recurrence relation

Lecture 34 (28/11/2018) : Recursion relation, Markov chain

Lecture 35 (30/11/2018) : Markov chain, SVD
Please study the last two pages I added after the lecture. These are very important parts of SVD!!

## Homework

Homework 1 : Problems 1a, 2, 5, 7, 13, 14 (Due Mon , Sep 17)   Solution for Homework 1

homework 2 (due Mon, Oct 1 ) : problems 16, 18 in problems_1.1.pdf ,   problems 1, 2, 3, 4 in problems_1.2.pdf
Matlab files for problem 3,4 in problem set 1.2 splinemat2.m , plotcubic2.m , plotspline2.m
You need to save all these Matlab files in the same working directory or folder which is usually Documents/MATLAB.
Also beware that the function name and its file name should match (such as splinemat2.m, plotcubic2.m, plotspline2.m).

If this is still not working, type "path" command in Matlab command window and save matlab files in one of those working directories.
Solution for all problems in 1.1 ,   Solution for all problems in 1.2

homework 3 ( No submission. Consider this additional exercise. ) : problems 1, 2, 3, 4, 5, 6 in problems_1.3.pdf , Solution for Homework 3

homework 4 (due Wed, Oct 17) : problems 1, 3, 4, 5, 6, 7 in problems_2.1.pdf , Solution for Homework 4

homework 5 (due Mon, Nov 5 ) : problems 1 in problems_2.2.pdf , problems 1, 2, 3, 4 in problems_2.3.pdf , problems 2,3 in problems_3.1.pdf ,
Matlab files for the Problem 3 in problem set 2.3 hmkgraph.m ,
Solution for all problems in 2.2 ,   Solution for all problems in 2.3 ,   Solution for all problems in 3.1 (1-3)

homework 6 ( No submission. Consider this additional exercise. ) :
problems 4, 5, 7, 9 in problems_3.1.pdf ,
problems 1, 2ab, 3 in problems_3.2.pdf ,
problems 1, 3, 8, 9 in problems_3.3.pdf ,
problems 1, 2, 3, 4, 5 in problems_4.1.pdf ,
Solution for problem set 3.1 ,   Solution for problem set 3.2 ,   Solution for problem set 4.1

homework 7 ( No submission. ) :
problems 1, 2 in problems_4.2.pdf ,
problems 1, 2 in problems_4.3.pdf ,
problems 1, 2 in problems_4.4.pdf ,
problems 1, 2 in problems_4.7.pdf ,
Solution for problem set 4.2 ,   Solution for problem set 4.3 ,   Solution for problem set 4.4 ,   Solution for problem set 4.7