THE UNIVERSITY OF BRITISH COLUMBIA - 2025-2026 WINTER TERM 2
MATH 152:202 - Linear Systems
Instructor :  Pablo S. Ocal
Office hours :  W 14:00-15:30 (LSK 301)
Table of Contents
1. Description
2. Class Notes
3. Schedule
4. Homework
5. Computer Laboratory
6. Exams
7. Resources
Description

The course on Linear Systems will treat, among others, geometry in two and three dimensions, vectors and matrices, linear systems of equations, eigenvalues and eigenvectors, relations between these concepts, and applications to engineering. The prerequisites required for this course are covered in Math 100.

The course will have weekly classes on

  • Mondays, Wednesdays, and Fridays in HENN, room 201, from 13:00 to 13:50.

The most updated version of the book we will be following is maintained on a GitHub repository by Colin B. Macdonald. We will be covering material in Chapters 1, 2, 3, 4, 5, and 6. You may find all the information you will need on Canvas and you may ask any questions you have on Piazza.

Class Notes

The following notes written by Richard Froese and Brian Wetton are the version of the book we will be covering. If you find mistakes (typographical or other) in these notes, or have comments, please let me know.

The following are additional materials closely related to the class notes.

Tentative Schedule
Jan 5-9 Sections 2.1, 2.2, 2.3.
Vectors, coordinates, length, dot product, projection. Notes.
Jan 12-16 Sections 2.4, 2.5.
Determinant, crossed product, lines, planes. Notes.
Jan 19-23 Sections 2.6, 3.1.
Solutions of linear systems, geometry of linear systems, linear dependence, linear independence.
Jan 26-30 Sections 3.2, 3.3.
Echelon form, reduced row echelon form, rank, homogeneous equations.
Feb 2-6 Sections 3.4, 3.5.
Geometric applications, resistor networks.
Feb 9-13 Sections 4.1, 4.2.
Matrix multiplication, linear transformations. Midterm 1
Feb 16-20 No material.
Break.
Feb 23-27 Sections 4.2, 4.3.
Rotations, projections, reflections, composition of linear transformations.
Mar 2-6 Sections 4.3, 4.4, 4.5, 4.6.
Random walks, transpose of a matrix, inverse of a matrix, determinant (revisited).
Mar 9-13 Sections 5.1, 5.2, 5.3, 5.4.
Complex numbers.
Mar 16-20 Section 6.1.
Eigenvalues, eigenvectors. Midterm 2.
Mar 23-27 Sections 6.2, 6.5.1, 6.5.2.
Diagonalization of a matrix, powers of a matrix, random walks (revisited).
Mar 30-Apr 3 Sections 6.3, 6.5.4.
Systems of linear differential equations, matrix exponential.
Apr 6-10 TBD.
TBD.
Apr TBD Sections 2.1-2.6, 3.1-3.5, 4.1-4.6, 5.1-5.4, 6.1-6.3, 6.5.1-6.5.4.
Final exam.
Homework

There will be typically weekly homework on WebWork, please check it frequently. The assignments will be due on Sunday at 23:59. You are encouraged to work in groups.

Computer Laboratory

There will be six MATLAB sessions and six MATLAB assignments, in alternating weeks. Assignments are due the week after the session on the Assignments tab of Canvas. The assignments will be due on Monday at 22:00. You are encouraged to work in groups.

The MATLAB programming language is proprietary software owned by MathWorks. The Octave programming language is a free and open source software part of the GNU project. Octave is mostly compatible with MATLAB.

Exams

Here the exams and their solutions will be posted. You can find information on the UBC schedule for the final exams here.

Feb TBD Midterm 1,
HENN 201 from 13:00 to 13:50.
Mar TBD Midterm 2,
HENN 201 from 13:00 to 13:50.
Jun 8 Final exam,
TBD.

The past exams for Math 152 are archived below.

  • The Department of Mathematics archive can be found here.
  • The Math Exam Resources Wiki archive can be found here.
Resources

There are many resources available for a student at UBC, I encourage you to use them and make the most out of them. Here are some materials specific to this course:

  • The open office hours at the Math Learning Center can be found here.
  • The MATLAB documentation you will need can be found on the MATLAB for UBC Mathematics website.
  • The Octave documentation can be found here.
  • The online calculator Wolfram|Alpha can be found here.

Here are some general materials about the Department of Mathematics, the Faculty of Science, and UBC:

  • The Frequently Asked Questions of the Department of Mathematics can be found here.
  • The Frequently Asked Questions of the Faculty of Science can be found here.
  • The Science Peer Academic Coaches can be found here.
  • The UBC Academic Calendar can be found here.
  • The UBC Wiki can be found here.
  • The UBC support page with resources for students affected by unanticipated circumstances can be found here.

I also encourage you to form study groups with your classmates. However, please keep in mind that you will only learn how to do the exercises if you try them on your own: without trying, looking up the solutions or copying others' work is absolutely useless.