Q: What happens when a mosquito and a mountain climber cross paths?
A: Nothing — you can’t cross a vector and a scalar!
Welcome, engineering mathematicians! ESC103 is one of two math courses you’ll be taking in the Fall semester, alongside ESC194. 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, row picture and column picture, matrix factorization, 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. While you can solve systems of two or three equations quickly by hand, approximating solutions for higher-order systems would take much longer. This is where MATLAB comes in handy, which is a programming language as well as a platform for performing numeric computation and used by scientists and engineers to analyze large amounts of data more easily.
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. Although you will all come into ESC103 with different levels of experience, the course is designed so that everyone should hopefully leave on the same page.
Professor
Professor William Cluett
Professor William Cluett has taught ESC103 for over 10 years and has won multiple teaching awards including the Medal for Distinction in Engineering Education in 2021. His home department is Chemical Engineering & Applied Chemistry. He was the Chair of Engineering Science from 2005 to 2011 and completed a second term as Chair/Director from 2019 to 2022. He has a deep understanding of EngSci courses and uses it to create connections between ESC103 and other courses you are taking (CIV102, ESC180, and ESC194). Outside of lectures, he loves talking to students about ESC103, EngSci, and 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).
Interview
“I [cover] material which some have seen, some haven’t seen, but make it interesting for everyone — and hopefully something that everyone has a chance to learn from.”
“[The Teaching Assistants] are the greatest support provided to students because they not only help the students with the material itself but also, they’re people that the students can talk to about the EngSci program, and experience, and what it was like for them”
“I really stress helping students see the geometry and eventually visualize things in [2D] and [3D] […] I enjoy teaching the course because I know how valuable this particular field of mathematics is to engineers.”
Course Highlights
- 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.
- 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.
- The group format of tutorials fosters a collaborative environment in class, and you’ll 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
Classes
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! While there are no practicals for ESC103 there is a two-hour tutorial each week led by great TAs (most of whom are upper-year EngScis or alumni of the program). 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.
Starting in early November, your tutorial time will be spent working through a weekly MATLAB lab with the help of your TAs, during which you will apply computational techniques learned in lecture to real-world situations. These labs are very doable within a two-hour tutorial.
Assessments
There are no assignments for ESC103.
There is typically a midterm, a MATLAB test, and a final exam.
The midterm and final exam should be straightforward if 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 share some past MATLAB tests: these are a good source of additional practice problems.
Find past ESC103 exams in the Skule exam repository.
How to Succeed
Quick Tips & Equations
- Row reduction using Gaussian elimination! — Learn this well in ESC103. It will continue to be used in other courses, including MAT185.
- 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.
- y_{n+1} = y_n + hf(t_n, y_n) — Euler’s method! You’ll see more of this soon.
More Details
As mentioned earlier, Professor Cluett’s lectures are well-structured, and his notes are thorough. Copy these down and review them regularly.
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 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!
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.
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.
Beyond First Year
- 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 MATLAB skills will help you in other courses such as CIV102 and will be a great addition to your resume.
- 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.
Overall, the materials covered here will serve as the basis for many upper-year courses throughout EngSci.
