ESC103: Engineering Mathematics and Computation

Q: What happens when an arrow and a mountain climber cross paths?
A: Nothing — you can’t cross a vector and a scalar!


Welcome, engineering mathematician! ESC103 is the second math course you’ll be taking in the Fall semester. Get ready to learn about linear algebra and computational methods.

The first half of the course covers linear algebra concepts. Some—like vectors, dot products, cross products, and matrices—may be familiar to you. Others will be more advanced. These topics include projections, eigenvalues, eigenvectors, and Gaussian elimination. 

In the second half of the course, you will use linear algebra to perform advanced computations. You will learn about different computational techniques, including Euler’s Method. These allow you to approximate solutions to systems of equations. It would take all day to do the approximation calculations by hand; that’s where MATLAB comes in handy.

This course is less content-heavy than CIV102 or ESC194. This makes it easier for some students, especially if they covered vectors and matrices in high school. For others, the content of ESC103 is entirely new. However, if this is the case for you, do not worry! Professor Cluett teaches the course as if you’ve never seen any of the material before.


Professor William Cluett 

Professor William Cluett [Source]

Professor William Cluett has taught ESC103 for over 10 years now! He is originally from the Department of Chemical Engineering & Applied Chemistry. He was the Chair of Engineering Science from 2005 to 2011. He is currently the Director of EngSci. From all this experience, he has a deep understanding of EngSci courses. He uses this to create connections between ESC103 and other courses you are taking (CIV102, ESC180). Outside of lectures, he loves talking to students about ESC103, EngSci, and even non-EngSci related things like the Cleveland Browns!

Fun Fact: Professor Cluett created this course in 2009 (with the help of many others involved with the EngSci curriculum).



  • You will learn a new programming language, MATLAB.  This language is better adapted to engineering calculations than Python, which you’ll be learning in ESC180. 

  • Linear algebra proofs are arguably more fun and intuitive than Calculus proofs.

  • Professor Cluett likes to provide you with a visual representation of the concepts taught. So, you’ll often find him bringing in props for demonstrations. 

  • There is typically a great team of TAs for this course, most of whom are upper-year EngScis or program alum.

  • Although you will all come into ESC103 with different levels of experience, everyone will leave on the same page.

  • The group format of tutorials fosters a collaborative environment in class – you will soon learn that collaboration is key in engineering. You’d be surprised at what you can learn from a discussion with your peers!

Week in the Life of an ESC103 Student 


There are typically two hours of lecture per week for ESC103. Professor Cluett is very clear with his notes and presentation, so make sure you go to these! 

How lectures ran online: Prof. Cluett held synchronous (live) lectures on BbCollaborate. His lectures were easy to follow. He would write on a virtual whiteboard as he spoke, meaning that students could take notes at a comfortable pace. Lectures were recorded and available for viewing throughout the semester.


First Half of the Course

There is a two-hour tutorial each week. Your TA will summarize the material learned in lecture that week before giving you a set of questions. They might work through some of these, but it is mostly up to you to solve the problems. You will do this in small groups during the tutorial session. You may not complete all problems during the tutorial. However, you are encouraged to finish them on your own time. 

Make sure you are comfortable completing these tutorial questions: the midterm and final will include very similar problems.

Second Half of the Course

Starting in early November, your tutorial time will be spent working through a weekly MATLAB lab with the help of your TAs. Unlike ESC180 labs, these ESC103 labs are very doable within a two-hour tutorial. Through the labs, you will apply computational techniques learned in lecture to real-world situations.

How tutorials ran online: No difference.


There are no practicals for ESC103. 


There is only one formal assignment (worth 5%). Last year, it was what you might call a “ESC103 x CIV102” group assignment. We had to analyze a truss bridge using linear algebra concepts and MATLAB.


There is typically a midterm, a MATLAB test, and a final exam. 

The midterm and final exam should be straightforward, as long as you keep up with the coursework and weekly tutorial problems. Past midterms/exams are also good practice.

The MATLAB test questions are very similar to the weekly labs. To prepare, make sure that you complete the labs. It is important that you both understand the reasoning behind each solution and can write the code on your own. Professor Cluett may also give you access to past MATLAB tests: these are a good source of additional practice problems. 

How to Succeed

Quick Tips & Equations

  • det(A – λI) = 0 — The characteristic equation, useful in both ESC103 and MAT185 (Linear Algebra).

  • Indexing for MATLAB starts at 1, not 0. 
    This is good to remember because you will be learning Python at the same time, where indexing DOES start at 0.

  • yn+1 = yn + hF(tn+1, yn+1) — Euler’s method! You’ll see more of this soon.

Graph depicting the use of Euler’s approximation. [Source]

  • Row reduction using Gaussian elimination! — Learn this well in ESC103. It will continue to be used in other courses, including MAT185.
Linear algebra meme: Hand drawing of a stick person next to a floating canoe. Next to it, the caption: 'Why does Neo keep destroying canoes? He's big on row reduction.' And the stick person, Neo, says, 'Stupid oars.'

[Edited – Source]

More Details

Copy Everything on the Board

As mentioned earlier, Professor Cluett’s lectures are well structured, and his notes are thorough. Copy these down and treat them as the course textbook. 

Stay on Top of the Course

You may find the first few weeks of the course relatively easy, but don’t let that fool you! This course starts moving fast when you least expect it. Be on guard to avoid getting lulled into a false sense of security. It will be very difficult if you save all your studying for the day before the exam.

Attend Tutorials

Attend all tutorials throughout the semester. Not only will they help you understand concepts and practice applying them, it’s also free marks. No, seriously: you get participation marks for simply attending tutorials! This counts for 10% of your final grade.

Solutions to Tutorial Problems: Use Them Wisely

As stated earlier, tutorial problems are your best resource when it comes to learning course content and preparing for the midterm/exam. Full solutions are posted at the end of each week: use these to check your answers and solution methods. Please don’t get into the habit of just checking the solutions and tricking yourself into thinking you can solve the problems without any practice! This can backfire on the midterm and final exam.

Ask Questions During Lectures and Tutorials

Studying for a pure math course for the first time can be challenging. Nevertheless, there are plenty of supports available. Professor Cluett’s experience with this course has allowed him to make the lectures very compact, giving students time for questions. The TAs for ESC103 are also very helpful. Almost all of them are EngSci graduates who have taken the course, so they are familiar with its challenges. Feel free to reach out to them if you get stuck on a problem. 

What Will You Take Out of It?

  • You will be introduced to problem-solving in pure math, something you likely haven’t seen before. This includes solving problems using both geometric and algebraic perspectives.

  • Your exposure to MATLAB will help you in other EngSci courses and beyond.

  • The linear algebra portion of the course will prime you for MAT185 in the Winter semester. Second-year MAT292 (Ordinary Differential Equations) will combine these courses to solve a new kind of problem: differential equations!