MACM 316 — Numerical Analysis I

Mon, 11 May 2026 00:00:00 +0000

Summer 2026

Course Information

Instructor:	Tareq Uz Zaman — tarequzz@sfu.ca
Lectures:	Mon / Wed / Fri, 10:30–11:20 AM (Room SSCB9201)
Term:	May 11 – August 10, 2026
Midterm:	Friday, July 3, 2026 (in class)
Prerequisites:	MATH 152 or 155 or 158; and MATH 232 or 240; and computing experience.

Class Components

Canvas

Assignments, due dates, announcements, and other course-related information will be posted on Canvas. It is your responsibility to check Canvas regularly.

Lectures

Lectures are held in person three times a week. I will primarily present the material by writing on my iPad, which will be connected to and projected onto a large screen during class.

Tutorials

Tutorials begin in Week 2 and are led by the teaching assistants. They are an important supplement to lectures, focusing on homework-style problems and material from recent lectures. Please try to attend the section you are registered for.

If you need to communicate with your TAs, use the appropriate Canvas discussion groups or speak to them in person during tutorials. Please do not send email.

Tutorial schedule and TA assignments:

Day	Time	Section	Room	TA
Wednesday	14:30–15:20	D101	WMC 2830	TA A
Wednesday	14:30–15:20	D108	WMC 3253	TA B
Wednesday	15:30–16:20	D102	WMC 2830	TA A
Wednesday	16:30–17:20	D103	WMC 2830	TA A
Wednesday	16:30–17:20	D107	WMC 3253	TA B
Thursday	9:30–10:20	D104	WMC 2830	TA C
Thursday	10:30–11:20	D105	WMC 2830	TA C
Thursday	11:30–12:20	D106	WMC 2830	TA C

Computational Workshops

In addition to tutorials, optional drop-in computational workshops are scheduled weekly, starting in Week 2. These sessions are dedicated to helping you with the current computing assignment and with MATLAB programming. All workshops are held in person.

Workshop schedule:

Day	Time	Room	TA
Monday	14:30–17:20	WMC 2820	TA A and TA B
Friday	14:30–17:20	WMC 2820	TA C

Office Hours

The easiest way to reach me is in person right after lecture. I think this is the best time to answer your questions, and I am happy to stay on for as long as needed to make sure your question is fully addressed. You are also welcome to post questions on the Canvas discussion board.

Email Policy

Questions about computing assignments, textbook problems, or course material will not be answered by email. Please attend office hours, tutorials, or computational workshops, or post on the Canvas discussion board.

Email is appropriate for private matters such as reporting a missed assessment or a personal circumstance. When writing to me, please use Canvas mail, include a brief subject line describing the issue, and include your full name and SFU ID.

Assessment

Component	Weight	Notes
Computing assignments (best 4 of 5)	25%	Due at 11:59 PM on assigned dates
Midterm exam (in person)	25%	Friday, July 3, 2026 (in class)
Final exam (in person)	50%	Scheduled during the August exam period

Passing requirement. Implementing and understanding numerical algorithms is an essential part of MACM 316. To pass the course, you must earn at least 40% on the computing assignment component, in addition to achieving an overall passing grade.

Homework problems

Five sets of homework problems will be assigned over the term. These are not graded and not handed in, but they give you regular practice with the course material and are good preparation for the exams. Selected solutions will be provided.

Computing assignments

Five computing assignments will be posted over the term. For each one, you will submit a written report as a PDF on Crowdmark. Please read the Guidelines for Computing Assignments on Canvas before submitting the first one.

You may use ChatGPT or other AI tools only to help polish the English writing of your report. They are not permitted for coding, mathematics, algorithm design, or any analytical part of the work.

Midterm and final exams

Both exams are held in person and are closed-book. The midterm covers the material taught up to the lecture before the midterm. The final exam is cumulative and covers all material from the course.

Late and Missed Assessment Policy

Computing assignments. Late submissions receive an automatic 25% penalty per day. Since only the best four out of five assignments count toward your grade, one missed assignment will not affect your final mark. If you miss more than one assignment for a documented reason, contact me as soon as possible.
Missed midterm. There is no makeup midterm. If you miss it for a valid, documented reason, your final exam grade will be used in place of the midterm grade. If your final exam grade is higher than your midterm grade, it will also be used in place of the midterm.
Missed final exam. A medical note or equivalent documentation is required in all cases. Please see the SFU Academic Concessions page and the Self-Declaration Form for the correct procedure.

Course Topics

The following topics will be covered as time permits. Section numbers refer to the 10th edition of the textbook.

Number systems and errors — Ch. 1 (about 1.5 weeks)
- Floating-point representation of real numbers
- Round-off error, error propagation, error estimation
- Review of key concepts from calculus
Nonlinear equations — Ch. 2 (about 2 weeks)
- Bisection, secant, and Newton's methods
- Fixed-point iteration
- Rate of convergence
Systems of linear equations — Chs. 6 and 7 (about 3 weeks)
- Gaussian elimination: factorization, pivoting, matrix inverses
- Norms, determinants, condition numbers
- Iterative methods
- Eigenvalue problems
Interpolation and approximation — Ch. 3 plus Secs. 8.1 and 8.5 (about 2 weeks)
- Interpolating polynomials: Lagrange and Newton forms, error formula
- Spline interpolation
- Trigonometric interpolation and Fourier series
- Least-squares fitting
Numerical differentiation and integration — Ch. 4 (4.1–4.4, 4.7) (about 1.5 weeks)
- Numerical differentiation, finite difference approximations, Richardson extrapolation
- Numerical integration: quadrature rules, extrapolation
Initial value problems for ODEs — Ch. 5 (about 2 weeks)
- Euler's method
- Taylor and Runge–Kutta methods
- Convergence, stability, stiffness
- Systems of differential equations

Textbook

Numerical Analysis, 10th edition, by R. L. Burden, J. D. Faires, and A. M. Burden (Cengage Learning, 2016). ISBN: 978-1-305-25366-7.

A one-year electronic rental is available from the SFU VitalSource store: sfu-store.vitalsource.com. Your personalized textbook list is also available through the SFU Bookstore.

Older editions (9th or earlier) contain mostly the same material, but question and page numbers differ.

Computing with MATLAB

Computing is an integral part of MACM 316. MATLAB will be used for in-class demos, tutorials, and computing assignments. You are expected to write short MATLAB scripts from scratch, although some assignments might involve modifying code that I provide.

MATLAB is free for SFU students through your computing ID. Install it from the SFU MATLAB page.

If you are new to MATLAB, the following resources are useful:

Kermit Sigmon's MATLAB Primer
David Griffiths' Introduction to MATLAB
MIT OpenCourseWare: Introduction to MATLAB Programming
Coursera: Introduction to Programming in MATLAB (free to audit)

Technology Requirements

For any workshop or meeting held online, you will need a webcam, a reliable internet connection, and SFU Zoom. Using SFU Zoom involves the disclosure of personal information to Zoom Video Communications; see the consent information here.

Classroom Conduct

A respectful and focused classroom benefits everyone. In this class you are expected to:

Treat classmates, teaching assistants, and the instructor with courtesy and respect.
Keep cell phones silent. If you need to use a laptop, please sit in the back rows so screens do not distract others.
Participate thoughtfully and be considerate of perspectives different from your own.

As a student, you are also expected to follow the SFU Student Conduct Policy (S 10.05).

Equity, Diversity, and Inclusion

I aim to create a classroom where students of every background — gender, race, religion, age, national origin, sexual orientation, neurodiversity, and ability — feel welcome and supported. If there is anything I can do to better support your learning, please let me know, ideally during the first week of term.

The Department of Mathematics has an Equity, Diversity and Inclusion Advisory Group that works to keep our department a safe and inclusive space. Please feel free to contact them with any concerns or suggestions.

Academic Integrity

Honest work is the foundation of a university education. Dishonesty harms your own learning and is unfair to classmates who are doing the work properly. I take academic integrity very seriously in this course.

The following will be treated as academic misconduct:

Submitting work (in whole or in part) that was written or generated by someone else, including AI tools, solution manuals, online sources, or other students.
Discussing exam or quiz questions with anyone during an assessment.
Using unauthorized notes, devices, or reference materials during a test.
Sharing or distributing course test materials.

You are welcome to discuss ideas with classmates when working on computing assignments, but everything you submit must be your own work, written in your own words and code. A confirmed instance of dishonesty will result in a grade of zero on the work in question, a record in your academic file, and notification of the Chair of the Department of Mathematics. Depending on severity, further action may follow under the SFU Policies and Procedures for Student Discipline (S 10.02).

For further information, see:

Accommodations

Academic concessions (illness or emergency)

If you are unable to meet a course requirement due to illness, injury, or another circumstance beyond your control, contact me as soon as possible. For short-term illness the Academic Concession Self-Declaration Form is usually sufficient. A medical note is required for any missed final exam. The final decision about accommodation rests with the instructor.

Religious accommodation

If you anticipate needing an accommodation for religious observance during the term, please let me know in writing by the end of the first week of classes (or as soon as possible if you add the course later). Details are available on the SFU Multifaith Religious Accommodations page.

Disability-related accommodations

Students requiring accommodations due to a disability should register with the Centre for Accessible Learning and inform me as early in the term as possible.

Approximate Schedule

May 11: Number systems and errors — theory
May 13: Number systems and errors — theory (continued)
May 15: Number systems and errors — exercises; Homework Assignment 1; Homework Assignment 1 solutions; Computing Assignment 1; Textbook reference exercises
May 18: Victoria Day — no class
May 20: Number systems and errors — theory (continued); Number systems and errors — exercises (continued); Review of calculus
May 22: Review of calculus (continued)
May 25: Review of calculus (continued); Calculus review sheet
May 27: Review of calculus (continued); Stability, Conditioning, and Big-O
May 29: Nonlinear equations; Textbook reference exercises; Homework Assignment 2; Homework Assignment 2 solutions
Jun 01: Nonlinear equations (continued); Computing Assignment 2
Jun 03: Nonlinear equations (continued)
Jun 05: Nonlinear equations (continued)
Jun 08: Nonlinear equations (continued)
Jun 10: Newton's method for nonlinear systems; Review of linear algebra; Systems of linear equations; Past midterm exams uploaded; Cheat sheet guidelines
Jun 12: Systems of linear equations (continued); Computing Assignment 3; Homework Assignment 3; Homework Assignment 3 solutions; Textbook reference exercises
Jun 15: Systems of linear equations (continued)
Jun 17: Systems of linear equations (continued)
Jun 19: Systems of linear equations (continued)
Jun 22: Iterative methods for linear systems; Sample midterm question
Jun 24: Iterative methods for linear systems (continued); Textbook reference exercises; Computing Assignment 4
Jun 26: Polynomial interpolation

Copyright

All material presented or distributed in MACM 316 — including lecture slides, notes, problem sets, solutions, computing assignments, and any audio or video recordings — is protected by copyright. Some of this material is the work of the instructor, Tareq Uz Zaman; other items are used with permission from their respective authors or publishers. In either case, you may not record, reproduce, distribute, or share any part of the course materials, in any form or by any means, public or private, without the instructor's prior written permission.

This outline may be updated during the term. Any changes will be announced in lecture and posted on Canvas.

Numerical Analysis | Tareq Zaman