Math 307 (Section 201) Applied Linear Algebra

JAN 3    You may register to piazza using the class sign up link.
JAN 4    See below for Wednesday's notes.
JAN 5    See below for Homework 1 (due on Mon, Jan 15).
JAN 12  Quiz 1 will cover everything until the end of our coverege of condition number (all of I.1 in the typed lecture notes). 
JAN 12   I posted some old midterm exams for additional practice. The following problems in these old midterms are on material covered in Quiz 1: 
               Midterm (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
JAN 12  Homework 2 (due on Wed, Jan 24) is posted below.
JAN 12 
The following files are for section 1.2.6 (which we will cover in class next week). 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)
JAN 17  The solutions of homework 1 and quiz 1 are posted below.
JAN 26 
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 2: 
             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
JAN 28   Homework 3 (not due) is posted below together with its solutions. You may use these problems for practice for Quiz 2. 
FEB 5   
Homework 4 (due on Mon, Feb 12) is posted below.
FEB 9    Correction: Homework 4 is due on Wed, Feb 14 (UBC is closed on Monday)
FEB 9   
Midterm will cover:
  • Chapter 1: everything except for I.2.4 and I.2.5
  • Chapter 2: all subsections of II.1 and all subsections of II.2

The following problems in these old midterms are on material covered in Midterm 1:
                Midterm from 2016 WT2: Everything,
                Midterm from 2016 WT1: Everything,
                Midterm from 2015: Everything,
                Midterm from 2014 : Everything except 4

MAR1   Homework 5 (due on Fri, Mar 9) is posted below. 

MAR 1  Here is the MATLAB file you need for Problem 3 in Problems for Section 2.3: hmkgraph.m
MAR 2  The solutions of the midterm exam are posted below.
MAR 5  Quiz 3 will cover Sections II.3 (Graphs and resistor networks) and III.1 (except for III.1.5) (Projections).

The following problems in the old midterms and finals are on material covered in Quiz 3
Midterm from 2014 : Problem 4
Final exam from 2013: Problems 3, 4
                Another final from 2013: Problems 4, 5
                Final exam from 2011: Problems 4, 5
MAR 9  The solutions of Homework 5 are posted below.


Week 1
    Jan 1
    No class        
Jan 3              
class notes
Jan 5            
class notes
matlab script
Week 2
    Jan 8
    class notes
Jan 10
class notes
matlab script
Jan 12
class notes

Week 3
    Jan 15
    class notes
    matlab script
Jan 17
class notes
Quiz 1 solutions
Jan 19
class notes
matlab script
Week 4
    Jan 22
    class notes
    matlab script
Jan 24
class notes
Jan 26
class notes
matlab script 1, script 2
Week 5
    Jan 29
    class notes
Jan 31
class notes
Quiz 2 solutions
Feb 2
class notes
Week 6
    Feb 5
    class notes
Feb 7
class notes
Feb 9
class notes
Week 7
   Feb 12
   No class
Feb 14
class notes
Feb 16
Midterm with solutions
Week 8
   Feb 26
   class notes
Feb 28
class notes
Mar 2
class notes
Week 9
   Mar 5
   class notes
   matlab script
Mar 7
class notes
Mar 9
class notes
Week 10
   Mar 12
   class notes
Mar 14
class notes
Mar 16
class notes
Week 11
   Mar 19
   class notes


Instructor: Ozgur Yilmaz
Email :
Office: Math Annex 1113
Office Hours: Tue 11am-12pm, Fri 2-3pm, or by appointment.
Phone: (604) 822-5963
Section: 201
Class times and location: 
Day Start Time End Time Building Room
MWF 12:00 PM
1:00 PM

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. These assignments will be posted below.  

Quizzes: There will be 4 quizzes over the term: Jan 17, Jan 31, Mar 12, and Mar 28. 

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 you are expected to hand in your own work.

There will one midterm exam on Friday, February 16 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.

Homework Assignments

The homework assignments are posted below.

Homework 1 (due Mon, Jan 15) 1a, 2, 5, 7, 13, 14 in problems_1.1.pdf
  Solutions of 1-15 in problems_1.1        
Homework 2 (due Wed, Jan 24)
  16, 18 in problems_1.1.pdf, 
  1, 2, 3, 4 in problems_1.2.pdf
    Solutions of all problems 1.1
    Solutions of problems 1.2
Homework 3 (not due)
  1, 2, 3, 4, 5, 6 in problems_1.3.pdf     Solutions of problems_1.3
Homework 4 (due Mon, Feb 12)
1, 3, 4, 5, 6, 7 in problems_2.1.pdf
1 in problems_2.2.pdf
    Solutions of problems 2.1
    Solutions of problems 2.2
Homework 5 (due on Fri, Mar 9)
1, 2, 3, 4 in problems_2.3.pdf
4, 5, 7, 9 in problems_3.1.pdf
    Solutions of problems_2.3
    Solutions of problems_3.1


Wednesday, Jan 3
First lecture                                             
Wednesday, Jan 17
Quiz 1 
Wednesday, Jan 31
Quiz 2
Monday, Feb 12 
Family Day -- university closed.
Friday, Feb 16
Week of Feb 19
Mid-term break. No lectures.
Monday, Mar 12
Quiz 3
Wednesday, Mar 28
Quiz 4
Friday, Mar 30
Good Friday -- university closed.
Monday, Apr 1
Easter Monday -- university closed.
Friday, Apr 6
Last day of classes
Tuesday, Apr 10
Examinations begin...
Final exam