Math 307 (Section 101) Applied Linear Algebra

SEP 6     You may register to piazza using the class sign up link
SEP 6     Notes from today's lecture are posted below.
SEP 8     Homework 1 (due on Fri, Sep 15) is posted below.
SEP 13   In Homework 1, you may skip parts (f) and (g) of problem 12.
SEP 18   Quiz 1 will cover everything until the end of our coverege of condition number (all of I.1 in the typed lecture notes).
SEP 18   I posted some old midterm exams for additional practice. The following problems in these old midterms are on material covered in Quiz 1:
               Midterm from 2016 WT2: Problem 1c and all parts of 2.
               Midterm from 2016 WT1: Problem 1a,c and all parts of 2.
               Midterm from 2015: All parts of 1 and 2a
               Midterm from 2014 : All parts of 1 except 1d
SEP 22  Homework 2 (due on Fri, Sep 29) is posted below.
SEP 22  Solutions of Quiz 1 are posted below.
SEP 23 
  • The following files are for section 1.2.6 (which is covered in class). You will need plotspline2.m for Problems 3 and 4 in Homework 2, problems_1.2.pdf.
  • Note that plotspline2.m needs the other two files below (splinemat2.m and plotcubic2.m) to be in the same folder as plotspline2.m. So, save these three files in the same folder and make sure your MATLAB command window is working in that folder.
             splinemat2.m splinemat2(X) returns the spline matrix for the points X=[x1,,xn].
             plotcubic2.m  plotcubic2(x_l,x_u,y_l,y_u,z_l,z_u) plots the cubic polynomial p(x)on the interval [xl,xu] with values p(xl)=yl, p(xu)=yu, p′′(xl)=zl, p′′(xu)=zu.
             plotspline2.m plots the cubic spline through points X,Y when you type plotspline2(X,Y)

SEP 29 Quiz 2 will cover everything we did on interpolation (I.2.1, I.2.2, I.2.6, I.2.7) and finite difference approximations (I.3.1, I.3.2). The following problems in the old midterms are on material covered in Quiz 1:
             Midterm from 2016 WT2: Problem 3
             Midterm from 2016 WT1: Problem 1d and all parts of 4.
             Midterm from 2015: All parts of 3, 4
             Midterm from 2014 : All parts of 2
SEP 29 Homework 3 (due on Wed, Oct 4) is posted below.
OCT 2  Here is the file heat.m that you need in Homework 3.
OCT 2  The due date of Homework 3 is postponed to Friday, Oct 6.
OCT 2   Solutions of Homework 2 are posted below.
OCT 5   Solutions of Quiz 2 are posted below.
OCT 13 Midterm 1 will cover:
  • Chapter 1: everything except for I.2.4 and I.2.5
  • Chapter 2: all subsections of II.1, II.2.1, and II.2.2
The following problems in these old midterms are on material covered in Midterm 1:
                Midterm from 2016 WT2: Everything except 1d,e,f,g; 4c,d,e,f
                Midterm from 2016 WT1: Everything except 1g, 3b,
                Midterm from 2015: Everything except 2b,c
                Midterm from 2014 : Everything except 3,4
OCT 16  Solutions of Homework 3 are posted below.
OCT 18  I will have extra office hours tomorrow (Thursday, Oct 19) 11am-12 noon in my office (Math Annex 1113).
OCT 27 Homework 4 (due on Fri, Nov 3) is posted below.
NOV 3   Quiz 3 will cover Section II.2 (all subsections) and Sections III.1, III.2, and III.3. The following problems in the old midterms and finals are on material covered in Quiz 3:
             Midterm from 2016 WT2: Problem 1defg, all parts of 4
             Midterm from 2016 WT1: Problem 1fg, all parts of 3 
             Midterm from 2015: All parts of 2
             Midterm from 2014 : All parts of 3
             Final exam from 2013: Problem 3
             Another final from 2013: Problem 4
             Final exam from 2011: Problem 3,
NOV 3 Homework 5 is posted below along with its solutions and it is NOT due. You may use problems 1, 3, 4, and 9 as practice problems for Quiz 3. The remaining two assigned problems are on polynomial interpolation and is NOT included in the Quiz (but will be included in the final exam).

NOV 10 Homework 5 (due on Mon, Feb 20) is posted below.


Week 1
    Sep 4
    No class           
Sep 6                  
class notes
Sep 8
class notes         
matlab script       
Week 2
    Sep 11
class notes
Sep 13
class notes         
matlab script   
Sep 15
class notes
Week 3
    Sep 18
    class notes
Sep 20
class notes         
matlab script
Quiz 1 solution
Sep 22
class notes
Week 4
    Sep 25
    class notes         
    matlab script
Sep 27
class notes         
matlab script
Sep 29
class notes  
Week 5
    Oct 2
    class notes        
    matlab script 1
    matlab script 2
    matlab script 3
Oct 4
class notes
Quiz 2 solution
Oct 6
class notes
Week 6
    Oct 9
    No class
Oct 11
class notes
Oct 13
class notes
Week 7
    Oct 16
    class notes
Oct 18
class notes
Oct 20
Week 8
    Oct 23
    class notes
Oct 25
class notes
Oct 27
class notes
Week 9
    Oct 30
    class notes
Nov 1
class notes
Nov 3
class notes
matlab script
Week 10
   Nov 6
   class notes
Nov 8
class notes
Quiz3 solution
Nov 10
class notes
Week 11
  No class
Nov 15
class notes

Past midterms: Midterm from 2016 WT2, Midterm from 2016 WT1, Midterm from 2015, Midterm from 2014

Past finals (with solutions): 2013 (disregard 5), another 2013 (disregard 5), 2011 (disregard 4,6)


The weekly (written) homework assignments are posted below.

Homework 1 (due Fri, Sep 15) 1a, 2,  4, 5, 7, 12, 13, 15 in problems_1.1.pdf
Solutions of 1-15 in problems_1.1 
Homework 2 (due Fri, Sep 29) 16, 18 in problems_1.1.pdf,
1, 2, 3, 4 in problems_1.2.pdf
Solutions of problems_1.1
Solutions of problems_1.2
Homework 3 (due Wed, Oct 4) 1, 2, 3, 4, 5, 6 in problems_1.3.pdf
Solutions of problems_1.3
Homework 4 (due Fri, Nov 3)
1, 3, 4, 5, 6, 7 in problems_2.1.pdf Solutions of problems_2.1
Homework 5 (NOT due)
1, 3, 4, 5, 7, 9 in problems_3.1.pdf Solutions of problems_3.1
Homework 6 (due Mon, Nov 20)
1, 2ab, 3 in problems_3.2.pdf
1, 3, 8, 9 in problems_3.3.pdf
1, 2, 3, 4, 5 in problems_4.1.pdf

Instructor: Ozgur Yilmaz
Email :
Office: Math Annex 1113
Office Hours: MF 2-3pm or by appointment
Phone: (604) 822-5963
Section: 101
Class times and location: 
Day Start Time End Time Building Room
MWF 1:00 PM
2:00 PM
HENN 201

Course web page: will be updated throughout the term.

Pre-requisite: One of MATH 152, MATH 221, MATH 223 and one of MATH 200, MATH 217, MATH 226, MATH 253, MATH 263.


This course is organized around a collection of interesting applications. Examples from past years are:
Finite difference approximations
Formula matrix of a chemical system
Least Squares
Fourier series
Graphs and Networks
JPEG compression
Power method
Recursion relations
The Anderson tight binding model
Markov chains
Google PageRank
We will study a selection of these in this class. Each application will be preceded by discussion of the relevant concepts from Linear Algebra. These will be partly review from your previous linear algebra course and partly new material. You will also learn how to do Linear Algebra on a computer using MATLAB or Octave.

Learning Goals: See here for a detailed list of prerequisites and learning goals of Math 307.
Text: There is no required textbook for this course. Instead there is a set of typed notes designed for this course, which is available here:
Chapter 1   :  Linear Equations
Chapter 2   :  Subspaces, bases, and dimension
Chapter 3   :  Orthogonality
Chapter 4   :  Eigenvalues and Eigenvectors
Computational aspects: To complete the work for this course, you will need access to MATLAB software. MATLAB is a widely used program for numerical computations with matrices. Since September 2016, MATLAB is available to all active UBC students at no cost. For instructions on how to download and activate MATLAB, see:

You can also access MATLAB in the math department computer labs. These are located in LSK 121 and 310. The labs 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 class. Please contact me if you have difficulty logging in. If you prefer, you may also use GNU Octave instead of MATLAB, which is an open source MATLAB clone that is available for free. It is included in most Linux distributions. Windows and Mac versions are available for free download.  However, the professor will only be able to answer questions regarding MATLAB.


Homework: There will be weekly written homework assignments, due at the beginning of class each Wednesday. These assignments will be posted below.  

Quizzes: There will be 4 quizzes over the term: Sep 20, Oct 4, Nov 8, and Nov 24. 

Late homework will not be accepted.  However, your lowest (written) homework score will be dropped (so you can miss one homework if necessary).  Nevertheless, even if you miss a deadline, its a good idea to do the problems, since this is the best way to prepare for the tests and exam. You are welcome to discuss the homework problems with your friends, but are expected to hand in your own work.

There will one midterm exam on Friday, October 20 in class. Note that the final exam date is currently unavailable, but will be released during the term. Do not make end-of-term travel plans until this date has been fixed.

You will not be permitted to bring calculators to the test and exam.

Missing a homework, quiz, or midterm normally results in a mark of 0. Exceptions may be granted in two
cases: prior consent of the instructor or a medical emergency. In the latter case, the instructor must
be notified within 48 hours of the missed test, and presented with a doctor's note immediately upon
the student's return to UBC. Failure to comply results in a 0 mark. If a midterm was missed for legitimate reasons, the weight of the missed midterm will be transferred to the final. Make-up midterms will, in general, not be provided.

Your grade for the course will be computed roughly as follows:

Homework:  10%
Quizzes:       10%
Midterm:      30%
Final exam:  50%


  • Piazza: You may find Piazza a useful resource for all class-related questions and discussion. Piazza is a question-and-answer platform specifically designed to expedite answers to your questions, using the collective knowledge of your classmates and instructor. It has several features that facilitate discussion of mathematics, most notably support of mathematical typesetting (LaTeX). You are encouraged to answer your classmates' questions, or to brainstorm towards answers, every bit as much as you are encouraged to ask questions. Here are the links:

            You will need a UBC email address to sign up for Piazza.

  • Math Learning Center: The Math Learning Centre (MLC) is a space for undergraduate students to study math together, with support from math tutors, who are graduate students in the math department. Please note that while students are encouraged to seek help with homework, the MLC is not a place to check answers or receive solutions, rather, its aim is aid students in becoming expert learners; to develop critical thinking and skills in a mathematical setting.

If you need help, or would like to discuss any aspect of this course, please make an appointment to see me in my office.


Wednesday, Sep 6
First lecture                                             
Wednesday, Sep 20
Quiz 1
Wednesday, Oct 4
Quiz 2
Monday, Oct 9                    
Thanksgiving Day -- university closed.
Friday, Oct 20
Wednesday, Nov 8
Quiz 3
Monday, Nov 13
Statutory holiday in lieu of Remembrance Day. University closed.
Friday, Nov 24
Quiz 4
Friday, Dec 1 Last day of classes
Tuesday, Dec 5
Examinations begin...
Final exam