Q: What do you call an old, reused calculus joke?
A: Derivative humour
ESC194: Calculus I is the first calculus course you will take in Engineering Science. It is arguably the most important courses in Fall semester — it will change the way you look at mathematics and lay the groundwork for your future Engineering Science courses. From rigorously logical proofs to challenging practice problems, you’ll be exposed to many different aspects of Calculus. The concepts that you learn will appear in many of the EngSci courses and will be used throughout your engineering career, so make sure you learn them well.
Professors
ESC194 is taught by Professors James (Jim) Davis (EngSci 8T2 aerospace grad) and Peter Stangeby. Both Prof. Davis and Prof. Stangeby are from the University of Toronto Institute for Aerospace Studies (UTIAS) and have taught the course for several decades. You’ll quickly learn that they are very fast writers, so try and adapt as soon as you can to keep up and take notes!
Professor James Davis
Professor James Davis
Professor Peter Stangeby
Professor Peter Stangeby [Source]
Interview
Highlights
- The fast pace of the course will teach you to learn more efficiently and effectively than you have before. It is a difficult adjustment at first, but this skill will be incredibly valuable in the future.
- You’ll learn about a side of calculus that you may not have been exposed to: integral calculus. Now you’ll be able to find both the slope of a curve and the area under it. Integrals show up all over engineering and science. Learning about them will give you new tools for solving a variety of problems.
- The first principles approach of ESC194 helps you understand high school concepts on a fundamental mathematical level. The logical thinking skills you develop here will help you in your other courses, including MAT185 in the Winter semester.
- This course also serves as a small introduction to differential equations, a field of math you’ll study in second year in MAT292. This part of the course is covered pretty quickly at the end of the semester, so it may be tempting to skip over it. However, solving differential equations will form a large part of most of the technical courses you take as an undergraduate engineering student, so make sure you pay attention!
Week in the Life of an ESC194 Student
Lectures
There are typically three lectures per week for ESC194. The lectures are fast-paced and cover lots of material. The professors aim to do about 1-2 textbook sections per lecture, so get ready for an hour of intense focus. Lectures cover theory and many worked examples.
Tutorials
ESC194 tutorials happen once a week and usually cover about 30-40 minutes of material from the lectures. This is the best time to ask questions about material you don’t understand or to simply follow along with the worked examples! The instruction is followed by a 10- to 15-minute quiz on the material you just went over. These quizzes seem small, but quiz marks can add up and the skills and concepts you learn and practice will help you succeed on the midterms and final. Completing the assigned problems each week – or as many as you can, will help you prepare for the weekly quizzes, midterms, and final.
Practicals
There are no practicals for ESC194.
Assignments
There are no formal assignments for the course. However, you are provided with recommended practice problems every week. DO THESE! It will build your calculus skills and help prepare you for assessments. Indeed, some questions on quizzes, midterms, and exams are similar to those assigned.
We cannot stress this enough: the only way to understand concepts and succeed in ESC194 is by practicing. Spending a few extra hours per week on calculus questions will make a huge difference for you!
The assigned problems are all from the course textbook, Stewart’s Calculus. A nice thing about the textbook is that it can be bought in a package with a student solution manual. This contains worked solutions to all odd-numbered problems. You can use it to check your work, discover alternate solution methods, and help yourself if you get stuck!
Note: Although it can be useful, the student solution manual is not required for this course. The Stewart textbook already contains the final answers to all odd-numbered questions.
Exams
ESC194 has historically had two midterms and a final exam. The best way to study for these is by doing any remaining homework questions in addition to as many past exams as possible. Past midterms and exams are an amazing resource for ESC194 (perhaps more than any other course). Similar topics appear on the assessments almost every year, so if you determine what those topics are, you will know what you need to focus on when studying.
Keep in mind that although the above strategy has worked for us, it is not universal. If it is not a good fit for you, that’s OK! Try different things and, if needed, consult with your Academic Advisor or the Engineering Learning Strategist.
Time is also an important factor on ESC194 assessments, so try to practice doing the questions quickly in addition to doing them well.
How to Succeed
Quick Tips & Equations
- Practice delta-epsilon proofs: \forall \varepsilon > 0 \exists \delta > 0 \text{ s.t. } 0 < |x-c| < \delta \Rightarrow |f(x) - L| < \varepsilon ;
Please don’t let this expression scare you! You are not expected to know this before coming into EngSci. You will get a step-by-step introduction at the beginning of the semester. - Evaluating limits: Always write “lim (variable->value)” until you have found the limit. You will lose points if you forget it!
- \frac{d}{dx} and \int dx . Pay attention to notation and don’t forget dx!
- Integration tip: Add “+ C” where necessary (for indefinite integrals).
- Practice curve sketching.
More Details
Treasure the Stewart textbook
The textbook for this course, Stewart’s Calculus, is quite comprehensive. It explains topics in a clear way and includes a plethora of practice problems. Additionally, the lectures are very well aligned with textbook content, so you can always get clarification from the text if you missed something in lecture.
Officially, this is your textbook for the next three semesters. However, you’ll probably be using it for a lot longer. The field of calculus is unlikely to change for a while, so this textbook might last you a lifetime! Take good care of it.
Make use of the assigned problems
You will be given an extensive list of textbook problems on the course syllabus. These are not marked or checked: they are just a selection of questions the instructors think is good practice. Use them to study and make sure you understand the material.
If constrained by time, do practice problems strategically
We recognize that there are a lot of questions in the assigned problems. If you don’t have time to work through every single one, do not despair. You are not the first EngSci student to be in that position, and it does not mean that you will fail the course. That being said, try your best to do as many problems as you can. Also, be strategic: if you are comfortable with a certain type of question and there are 15 such questions, you may be able to skip some of them (just don’t skip all of them!). Focus on problems that you find more difficult.
Leverage academic aid resources
If there are problems and topics that you really struggle with, don’t be afraid to ask for help! The TAs for this course are very enthusiastic and are there to support you.
GEARS (Guided Engineering Academic Review Sessions) is also a great resource. The hour-long sessions hosted by upper-year EngSci happen throughout the week. At each of these sessions, you can go through calculus questions/concepts.
More generally, any upper-year EngSci should be well-versed in calculus, so you can reach out to them as well.
Keep up with lectures
This course is fast-paced, and it is easy to fall behind. If this happens, you’ll miss out on important concepts and spend your time catching up on lecture content before midterms, rather than doing past exams. Most importantly, it is difficult to follow a lecture if you do not understand what happened in the previous one.
To avoid these challenges, we recommend being no more than 1-2 lectures behind in terms of content. Do not skip lectures for this course – even if you haven’t fully understood a lecture, go to the next one and take notes. You can parse through them and understand later.
Take advantage of tutorials
Since there is a quiz in each tutorial, attendance is basically mandatory. Additionally, TAs go over concepts and questions in a concise way that is ideal for note taking. They also leave time for student questions, so ask away!
Practice with past midterms and exams
Use past midterms and exams as much as possible when studying. As mentioned earlier, questions are very similar year-to-year and they generally follow the same format. Also, there are only a few proof questions assigned in the textbook – but at least one appears on the exam every year, so make sure to review these.
Do what works for you
Everyone coming into EngSci has a different background in math and calculus, so something you consider to be review might be challenging for your friend or vice versa. Therefore, it is essential that you find the study systems and strategies that work most effectively for you.
Write down your steps
In ESC194 and ESC195, part marks are your best friend. If you get a question wrong or don’t have time to finish a calculus assessment, you might still get some marks…if you write down your steps. Detailing your thought process in a legible way helps your marker follow your solution. From there, they can assess your understanding of the content.
What Will You Take Out of It?
- In this course, you’ll be introduced to an important feature of university test taking: time management and question selection. You’ll realize that time constraints may force you to choose between partially answering all questions on an exam or writing complete solutions for select questions.
- Calculus serves as a foundation for many engineering and science fields. Many of the concepts you cover in ESC194 reappear in other courses and will be useful throughout your engineering career!
Note: The course code for Calculus I used to be MAT194. You may still see it referred to as such on some websites (e.g. courses.skule.ca).