Author: orientation

ESC195: Calculus II

Posted on by orientation
Q: Are monsters good at math?

A: Not unless you Count Dracula.

ESC195: Calculus II builds on the skills you learned from ESC194: Calculus I.  You’ll start by studying methods of integration—essentially, ways to compute the “unsolvable” integrals you might have encountered in Fall semester. You’ll also be introduced to sequences and series before diving into the world of multivariable calculus and vector functions. All these concepts are fundamental to science and engineering collectively!

Like ESC194, this course is a theoretical course that covers a lot of material at a fast pace and great depth, so keeping up with the work and further developing your problem-solving skills is key.

[Source]

Professor

The instructor for ESC195 is Professor Davis, whom you will recognize from ESC194.

Interview

“All of physics really came down to one equation – F = ma with calculus […] Everything from things like the Bernoulli equation governing fluid flow, to the rocket equation governing how big rockets have to be – it’s all just F = ma with calculus.”

“A student will only learn by doing. You’re not gonna learn by reading the textbook, you’re not gonna learn by attending the lectures alone. You actually have to do the work, and that’s the only way you’ll be able to learn this material”

“Anything that gets in between a student and pencil and paper is detrimental to the learning of mathematics.”

Course Highlights

  • You will learn integration by parts, trig substitution, and partial fractions. These may sound complicated now, but you’ll get the hang of them!

  • Infinite sequences and series – you’ll learn about some of their properties and applications, including how Fourier series can represent any periodic function.

  • A lot of multivariable calculus! You can now solve problems in three dimensions. 😄 

  • Sketching polar graphs (all the complicated-sounding graphs like limaçons, lemniscates, and cardioids), and 3D surfaces (all the even more complicated-sounding graphs like paraboloids and hyperbolas). 

Week in the Life of an ESC195 Student

Classes

ESC195 has three hours of lecture each week. It may not seem like that much but the lectures move very quickly. They cover derivations of course concepts and many worked examples. Sometimes students find it hard to take notes in this course because the professor tends to write quickly on the chalkboard. If you can’t keep up with his notes, we recommend you at least copy down all the examples. Knowing how professors solve examples can help you solve similar problems on your own. The course textbook (Stewart’s Calculus, same as in ESC194) supplements your course notes well. 

While there are no practicals, ESC195 has an hour of tutorial every week. As in ESC194, you will be in smaller classes (25-30 students). TAs will work through problems similar to the assigned homework questions. At the end of each tutorial, you will also do a quiz. Each quiz is worth 2% and they are a great way to check that you are staying on top of the material. The questions for the quiz stem directly from the homework set for that week, so it incentivizes you to do the homework each week.  

Assessments

As in ESC194, there are no formal assignments for this course. However, you are provided with recommended practice problems every week. DO THESE! They will build your calculus skills and help prepare you for assessments. Indeed, some questions on quizzes, midterms, and exams are similar to those assigned.  

The assigned problems are all from the Stewart textbook (same textbook as in ESC194). A great thing about the textbook is that you can buy it 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 alternative 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.  

Our recommendation to you, as in ESC194, is practice, practice, practice. Spending a few extra hours per week on calculus questions will make a huge difference for you! 

Assessments in ESC195 are very similar to those in ESC194. Check out the ESC194 course overview for advice on how to prepare and manage exams. Key takeaway: practice with the Stewart textbook as well as past midterms/exams and be strategic when writing the assessments. These tend to go fast for students, so start with the questions you know how to solve before moving to the hard ones. ESC195 exams have fewer questions than those in ESC194, but the questions can be significantly harder. 

How to Succeed

Quick Tips & Equations

Note: You are not expected to know the following technical information. You will learn it all in the course. 

  • Taylor series is an infinite series of polynomial terms that can be used to approximate complicated functions involving exp, cos, sin, and ln. As the degree of the polynomial (and number of terms) increases, the Taylor series becomes a better approximation for the function. Make sure you know how to derive a Taylor series (and possibly memorize some common ones), and how to calculate its error. 
  • Do A LOT of integration problems involving many different methods. Some integration problems will need trial and error to solve efficiently, unlike derivatives. Regular practice will let you solve them faster during exams. 
  • Practice sketching polar curves. Polar coordinates are essential to solving problems involving circles, cardioids, limaçons, etc. And the more comfortable you are in solving problems in the polar coordinates, the easier it will be for you to work with cylindrical and spherical coordinates, introduced in 2nd year courses.  
  • Gain an intuition for gradients, which are like derivates in higher dimensions, and how they work. You should be able to derive them from first principles and from an algorithm, and practice many problems with gradients such as tangent planes and Lagrange multipliers; you will learn about these methods in the last week of class, but do not ignore them as they will come up on the final exam! 
XKCD webcomic. A satirical representation of integration: flow chart showing the messy steps and dead-ends of integration.
Integration sometimes feels like this…but you’ll figure it out eventually! [Edited – Source]

More Details

All the tips from ESC194 will be useful here too, so check them out in the Calculus I overview. However, we still have one piece of advice specific to ESC195. 

Working with sequences and series is an important tool for engineers, so make sure you practice and understand these topics. When analyzing series, there will be many techniques to remember. To make it easier, we suggest creating a cheat sheet: list all the techniques (formally called “series convergence tests”) and when to use them. Then, as you are doing practice problems, you can reference this cheat sheet.

Beyond First Year

  • After ESC195, you’ll be able to appreciate not only more advanced scientific fields, but also more advanced math jokes—you know, jokes about cows and bears and all that.  

  • On a more serious note: the advanced math that you will learn in this course will help you understand and work in more specialized fields. Integration techniques and polar coordinates are used extensively in ECE259 (Electromagnetism) next year. Partial derivatives become important in a variety of other physics fields and vector functions are extremely important in computer science. 

Note: The course code for Calculus II used to be MAT195. You may still see it referred to as such on some websites (e.g. courses.skule.ca).

Side-by-side comparison showing a realistic polar bear on the left labeled
[Source]

ESC102: Praxis II

Posted on by orientation

Praxis II is a continuation of Praxis I. In this course, you will apply the processes and concepts you learned last semester to improve the lived experience of a community in the Greater Toronto Area (GTA). Even more so than Praxis I, Praxis II is all about teamwork. You will be divided into teams in the third week, and the rest of Praxis II will be based on team activities. 

Your first team project is to construct a community profile where you meet with and analyze a specific community’s baseline conditions and trends. After that comes the true heart of Praxis II. After identifying an engineering opportunity based around a specific community, you will create a Request for Proposal (RFP), which is like the design brief from Praxis I, except far more detailed. The teaching team will then select around 8-10 RFPs to share with the entire class, and your team will choose one of these RFPs and develop a solution for it. 

People are attending the Praxis showcase event in a hall with wooden vaulted ceilings, viewing posters and engaging in conversations. Tables with displays and informational materials are set up around the room.
Previous years’ students present their designs to professors and public attendees during the Praxis II Showcase at Hart House

Next, you’ll prototype, test, and document your solution. The difference from Praxis I is that now, the possibilities are much more open-ended. Your concepts can range from physical products to software or something else altogether. Most importantly, you are expected to make much more informed design decisions and perform much more rigorous verification. You’ll also get to take your solution to stakeholders in your community and ask them for feedback. At the end of the course, you’ll present and defend your chosen solution to the teaching team at a public event called “Showcase”. You can view previous Praxis II design projects on the Praxis II Showcase website. 

Professors

Professor Roger Carrick

Professor Roger Carrick

Professor Jennifer Lofgreen

Professor Jennifer Lofgreen

The instructors for Praxis II are Professor Jennifer Lofgreen and Professor Roger Carrick, whom you will recognize from ESC101 Praxis I. 

Course Highlights

  • Cold-calling businesses, companies, and communities. It can be awkward at first, but you’ll quickly become a pro and discover that it isn’t actually all that hard. This is a super useful skill that you can use for job searching and networking later too. 

  • Praxis II encourages you to explore Toronto! You will go out into the GTA, meet new people, and learn new perspectives. You will be pushed out of your comfort zone in a good way. 

  • Prototyping and testing your solutions. Not only will you learn CAD software called OnShape, but your design concepts can also be literally anything you want – as long as you can support all of your design decisions with research and verification. 

  • Praxis II Showcase! Local media have sometimes attended and featured students in their newspaper or on the radio. It is extremely fun to present and observe other teams doing the same. 

Week in the Life of a Praxis I Student

Like in Praxis I, the weeks in Praxis II can vary significantly. Here is a rough approximation of how a week will look for a Praxis II student. 

Classes

There are typically three lectures a week for Praxis II. You will learn about engineering design concepts and participate in design and thinking activities. You’ll find that the lectures are very well-integrated with the tutorials. Professors will often discuss some notable results from tutorial activities and connect them to different engineering design concepts. Additionally, some lectures will focus on engineering design tools that will be useful in the tutorial sections immediately following the lecture. 

Praxis studios occupy the same section in your schedule as tutorials. In a small class led by a couple TAs, you will be guided through engineering design activities, project help, and more. This is where most of your project-specific work and instruction will happen. Similar to Praxis I, you’ll find that the concepts discussed in studios were introduced in the lectures. This makes studios an excellent time to apply these concepts and get a deeper understanding of how they all work together. 

Similar to Praxis I, your timetable contains a 2-hour practical block during which you can meet with your team and work on your project. While the meeting time and duration is not mandatory, you should schedule regular meeting times with your team. Since Praxis is a dynamic course, you may have no meetings on some weeks, and many hours of meetings on other weeks. The key is to find times that work for your entire team, and to not leave all your work until the last minute. 

We cannot emphasize enough the importance of regularly checking in with your team. Note that the workload in Praxis II significantly increases from Praxis I, so be prepared for a lot of teamwork. Through regular team communication, you can keep track of deadlines and allocate work more effectively. Communicating with your team helps ensure that everyone is healthy and offers an opportunity to de-stress all together. 

Individual Assessments

In place of a final exam, there are two final independent assessments in Praxis II: the Engineering Handbook and the Student Engineer Portfolio.  

The handbook summarizes your personal engineering design process you developed throughout Praxis I, Praxis II and any extracurricular design activities in first year. In it, you include examples of engineering design tools, models, and frameworks that supported this process. This handbook will be very useful in your future design courses, including Praxis III in second year. 

The portfolio is a chance for you to reflect upon your engineering design work throughout first year and understand how your positionality affected/was affected by your design work. Furthermore, it offers you an opportunity to flex your engineering muscles and describe all your skills and abilities which went into these projects. Note that many companies allow prospective engineers to submit a design portfolio to display some of their work, so this assignment can be a valuable asset in the future. 

These assignments will be due on the same day, right after showcase, and right in the middle of exam season. As such, we strongly recommend that you do not leave these to the last minute. You should work on these throughout the semester. Every so often, take some time to write a page in your handbook or record some notes about what you have learned throughout the Praxis II project. 

Group Assessments 

You will spend most of your time in Praxis II working in one group. You will write the community profile, RFP, and complete the Showcase project in this group. However, there will be some individual assignments. In addition to the handbook and portfolio, your first two assignments, the community profile and positionality statement, will be independent. 

How to Succeed

Nearly all the tools you used in Praxis I will be used in Praxis II. We have listed some more tools specific to Praxis II below.

More Details

This basically means understanding what people’s body language conveys. For example, if someone keeps checking their watch while speaking with you, it could mean they are running late for something but don’t want to cut you off. This skill is useful when interacting with stakeholders.

Your team can get caught up in small details; though discussion and debate are at the heart of Praxis, ask yourself if your team’s decision will affect your design’s use and function or your ability to defend your design. If there is little impact, aim to conclude the debate by picking one of the possible options. If done correctly, it’s fine to say, “This part of the design was not significant, so we simply picked one option.”

Planning is crucial in Praxis II: there’s a lot to do and there’s limited time. Being a skilled planner will help you immensely in the course.

You should have a high-level plan before you begin working. At the beginning of each task, quickly summarize what you want to achieve and your plan to achieve it. This is especially useful when justifying your design. If you plan your argument step-by-step, you’ll have a much easier time writing clearly and concisely.

However, don’t over plan! Sometimes a detailed plan is unnecessary since you know what you’re doing. Conversely, if you’ve never done the task before, you won’t know what to include in your plan. In these cases, try to work a little first to get an idea of how long something takes or the type of work it requires – then make your plan.

In high school, you may have been used to your teacher ignoring or going easy on any obvious mistakes or weaknesses in your project if the rest of it was good. In Praxis II, the markers’ job is to be critical of your design and design process, so if there’s a clear weakness, they will ask you to address it. Thus, it’s your job to have a well-rounded design that you can fully support. If your team seems to be ignoring something about your design, bring their attention to it. Think about situations in which the design can fail, and then build some arguments for why those situations are unlikely. A little self-criticism goes a long way in Praxis!

Praxis II is a course that really benefits from your engagement and enjoyment of the work. Since you have a lot of choices in picking your engineering opportunity, look for communities and situations that you’re personally interested in and care about. Having a genuine interest in your work will help you in lots of ways, especially by motivating you to do the little extra research or experimentation that can turn your design from good to great.

Throughout the semester, you will be given feedback from TAs and profs through many different mediums. This includes activities during studios, TA meetings, and “holistic” or written feedback on assignments. Feedback is personalized and is designed to help you become a better student engineer, so don’t neglect these resources.

You will be working with the same team for four months, so get to know them. What do they like? What do they dislike? Do they have pets? Why are they late every day? Did they commute in the morning? What do they want to get out of this team? What are your team goals? The key to individual success in Praxis is to be successful as a team.

Praxis II is one of the most unique and engaging courses you will take during your first year in Engineering Science. The amount of trust and responsibility given to students is almost unparalleled. Enjoy your time in Praxis II and try to get the most out of it! You could learn skills that you use throughout your life.

What Will You Take Out of It?

  • Like Praxis I, Praxis II gives you the opportunity to turn your personal interests into engineering opportunities. You will have the opportunity to do what you excel at or to learn something brand new! 

  • You will get the opportunity to build on and apply the Engineering Design principles taught in Praxis I, including the FDCR principle and Toulmin model of arguments. 

  • In Praxis II, there’s more time to spend on prototyping and testing. Use the course as an opportunity to pick up some hardware or software skills. 

  • You’ll be designing a solution for an opportunity to support a community. This is a great way to learn about the human components of engineering, like communicating with your stakeholders, accounting for accessibility, and verifying your design. 

  • The design skills gained in this course will serve as a basis for second-year EngSci courses such as ESC204 as well as upper-year design courses in almost all of the majors. 

Praxis Showcase in the News

Media have attended some of the Praxis Showcase events. The stories in the links below detail some of the past student projects. 

Praxis Showcase 2019 Featured in U of T News
Praxis Showcase 2018 Featured in The Star

Interview with Professor Philipp Seiler

Posted on by orientation

Could you tell us a bit about yourself?

My name is Philipp Seiler. I studied Mechanical Engineering and Mechatronics in my undergrad in Germany, at the TU Braunschweig. I did my PhD in a completely different topic, in Material Science. After that, I went to the US, where I went to Purdue University to do a post-doc, then to the UK where I was a research associate at the University of Cambridge for 6 years. After that, I became a lecturer (assistant professor) at the University of Kent. I transferred very recently to Canada.

In my research, I work on materials under extreme conditions – for example, materials for rocket engines or gas turbines. I would like to answer questions like how we can design systems that can withstand very high temperatures. The other part of my research is about lightweight materials: how can you make these material structures light weight, but still make them very strong, stiff, and tough. For that, linear algebra is very important.

Professor Philipp Seiler [Source]

“I don’t think there is a single day where I don’t use linear algebra.”

There are many tools, such as Finite Element Analysis (FEA), a tool that can predict stresses and strains that use linear algebra. This tool basically solves a system of differential equations. But instead of solving two or three equations, you’re looking at a system of millions of equations. So, it’s very important to know the underlying physics as well as the algorithms used, to understand and interpret the results.

Could you describe your teaching style and your favorite part of teaching?

CC BY-SA 3.0, via Wikimedia Commons

Teaching is an integral part of being a professor. I like interacting with students, and I really enjoy seeing students grasp complex concepts during a lecture. It is amazing to meet former students a few years later and see them on track to get into their dream career.

I have an active teaching style, even with a large cohort size.

“I like going on academic detours – I would change the lectures when I see what students are interested in a certain topic.”

I do not plan lectures down to the minute. I come to lectures with a brief outline, then I see how the students follow and react. In particular, teaching linear algebra is like teaching a programming language. I start with the basic “commands,” such as vector spaces, vectors, matrices, etc., and then I apply these tools to solve equations in real world problems.

Why do engineers need to learn proofs, and do you have any tips for mastering them?

If I were to simply teach how a tool like matrix multiplication works, e.g. just by following an algorithm, students would quickly forget it. By knowing the proofs, you can understand why and how matrix operations work. Even if you forget the details, it will be easier to relearn it. Moreover, proofs can help students understand linear algebra conceptually.

“I want students to understand why certain concepts are true and why they work.”

Reading the textbook over the whole term is very important, so don’t just start before any midterm or exam. Also, continuously put work and effort into learning and following the lectures. While the learning curve isn’t steep in the beginning, it picks up very quickly, so you have to be on top of things. If you have questions, come to office hours or ask me after the lectures. I hope students are engaged and ask as many questions as possible.

Example of a Linear Algebra Proof [Source]

What can students expect from this course, and what is the key takeaway you want them to learn?

“I would like students to forget what they learned in high school”.

One by one, I will introduce the necessary concepts for them to understand what matrices are. Lectures are typically based on proofs, where I introduce a tool and explain why it works. Lectures are in general more theoretical, but there are plenty of opportunities to get examples, exercises, and additional material.

[In terms of takeaways, ] they should know the fundamentals – what a matrix is, what a vector is, what are vector spaces, and how to use them. If I teach you the concept, that way you can learn to use it and apply it to different applications.

How does linear algebra connect with your work, research, or engineering in general?

Colored finite element analysis (FEA) plot of a gear shaft, illustrating stress distribution. The legend indicates varying stress levels from blue (low) to red (high).
CC BY-SA 4.0, via Wikimedia Commons

Novel methods of artificial intelligence are typically highly non-linear. The question becomes, why is linear algebra still important? Linearizing a system of equations is still very powerful.

“Even machine learning technologies are all based on linear algebra.”

As I mentioned earlier, I’m doing research in materials science. If you are designing structures or materials, you are typically interested in predicting stresses and strains. One tool we use for these predictions is FEA and this is nothing but solving matrix equations. Here you could have a million-by-million matrix. Methods of linear algebra are used to efficiently solve these systems of equations. Nowadays, I don’t solve these systems by hand, but I should know how the results will look like and be able to interpret them. FEA produces colorful pictures, but just because they are colorful doesn’t mean they are true. You need to understand how stresses are computed and how the numerical solver works.

A second application of linear algebra is robotics. Let’s say you want to model a robotic arm by direct kinematics. Again, you are using matrix operations to describe the robotic system. For example, each joint of the robotic arm can be described as a matrix, representing translation and rotation. By using a matrix multiplication of the matrices of each joint, we can calculate the behaviour of the whole robotic arm.

Any other comments or thoughts to share?

For this course, ChatGPT is not a very useful tool to understand the proofs in the textbook. Currently, problems solved with ChatGPT can be false while still looking plausible.

ECE159: Fundamentals of Electric Circuits

Posted on by orientation

When people find out I’m not very good at building circuits, they’re shocked! 

Circuits are the basic building blocks of all electrical devices – including the computer on which you are reading this right now. In EngSci’s introductory circuits course, ECE159, you’ll be introduced to circuit properties such as current, voltage, and resistance, as well as circuit components like sources, resistors, capacitors, inductors, and Op-amps. You will learn about DC (direct current) and AC (alternating current) circuits, and will use techniques like mesh analysis, nodal analysis, Thevenin equivalents, differential equations, and complex numbers to analyze circuits. 

The goal of the course is to solve circuits for their properties by understanding how their components interact. These interactions are expressed mathematically, so a large portion of this course is solving systems of equations. Succeeding in the course requires understanding the theory behind circuit analysis, being able to build circuits in real life and, most importantly, knowing how to apply the right formulas in the right situations. Are you ready to learn the fundamentals of harnessing electricity? 

From Israel Palacio on [Source]

Some students find ECE159 difficult, and some find it easy. While a high school circuit course under your belt can help you succeed in ECE159, it is not necessary, as concepts are explained very clearly and with a lot of depth. Practice and regular review will be your best friend in this course. The key is to practice the steps to answer every type of question, as there are only a handful of distinct questions that can be asked on a test. Also, although electricity can be more difficult to comprehend than larger, mechanical systems, try your best to develop intuition for the concepts in a way that works for you. 

Professor

Professor Stickel [Source]

Professor Micah Stickel

Professor Micah Stickel is a Teaching Stream Associate Professor in the Department of Electrical and Computer Engineering. He completed his Undergrad, Masters, and PhD at U of T with a focus on electromagnetic networks and developing new devices for high-frequency systems. He is a returning professor for this course and is well-known for his incredibly clear and engaging presentation, his insightful worked examples, and the occasional joke in lecture! In general, Prof. Stickel lectures are well worth attending as they teach exactly what you will need to know to succeed, in a way that everyone will be able to understand! 

Professor Interview

“The heart of the course is really about problem solving […] It’s really about understanding how circuits behave with the hope that once you develop the ability to analyze circuits, then you can design circuits, and that’s the power that math and science together bring to engineering.” 

“For [students] who go into [mechatronics, robotics, or any combination of software and hardware], the core ideas [of circuits] will come back. […] They’re really critical ideas.” 

“I’ve described engineers as master approximators. […] To analyze [an electric circuit] we’d need Maxwell’s equations, the fundamentals of electromagnetics, and vector calculus, which [results in a] difficult problem. […] We don’t need to think of [the circuit] at an atomic level [and can] approximate it with a resistor, capacitor, or inductor […] Electric circuits are fundamentally just approximations of a real-world system” 

Course Highlights

  • Labs! Every other week you’ll have the chance to create circuits on breadboards. Be ready not only to build circuits but to have fun. 

  • Have you ever looked at a circuit diagram and thought, “I wish I knew what this all meant”? Well, you will be able to interpret and analyze many different types of circuits after ECE159! 

  • This course will introduce you to using complex numbers to model real systems!  

Week in the Life of an ECE159 Student

Classes

There are typically three hours of ECE159 lectures a week. Be sure to pay attention during these lectures: this is where you learn about the circuit laws you will use to solve problems on assignments. In lectures, your prof will conceptually explain circuit topics, as well as go through many examples of circuit analysis. Note these examples, as they serve as models for midterm and exam questions. Similarly to MAT185, you must watch a 20-minute video and complete an online quiz before attending each lecture. Make sure to do these, as they are crucial to developing intuition, and lectures will be much more fast-paced and in-depth. They are also worth marks! 

Ensure you attend every lecture, as throughout the semester, there will be multiple in-class quizzes which will require you to solve a couple of assignment-style questions. 

There is one hour of ECE159 tutorials built into your weekly schedule. During the tutorial, the theory of the course will be briefly summarized. However, the emphasis during the tutorials is on learning how to problem-solve. Your TA will work through lots of different examples, and we recommend taking notes of their problem-solving steps. ECE159 TAs are extremely helpful, so make sure to pay attention! 

ECE159 labs are held biweekly. Make sure to do the pre-labs before every lab session, as they are worth marks but are also crucial to your ability to understand the lab. They can be a time crunch because the whole lab is done in a three-hour period. During this time, you’ll build circuits in the lab and observe their properties with different electrical instruments such as oscilloscopes. 

Assessments

Throughout the semester, you will be assigned five online problem sets consisting of topics covered during the previous two weeks of class. These questions can become difficult, but they are excellent practice for the exams. Every week, you will also be provided with some textbook problems for additional practice.  

ECE159 has a midterm and a final exam. They consist of five circuit analysis questions, and each question can be thought of as multiple difficult assignment questions packed into one. For both exams, you will be permitted to bring a single double-sided handwritten aid sheet. 

How to Succeed

Quick tips and equations

  • Passive Sign Convention: if positive current flows out of the positive side of a voltage, then the element is delivering power. Otherwise, it is absorbing power. 

  • Consider the hydraulic analogy, where voltage and current are analogous to water pressure and flow of water, respectively. 

  • V = IR (Ohm’s Law) P = VI (Electric Power)

  • Any voltage or current in a circuit can be written as:
    • v(t) = v(\infty) + [v(0) - v(\infty)]e^{-t/\tau} or
    • i(t) = i(\infty) + [i(0) - i(\infty)]e^{-t/\tau} 
Common electric circuit component diagrams
  • You will learn how to use complex numbers to model AC circuits. Normally, this would involve many difficult computations. However, certain types of Faculty-approved calculators can perform almost any complex calculation for you! 

  • Remember that circuit analysis is a mere representation of the physical world; if during a lab your data is not exactly as you had expected, do not worry! Small sources of error are common. 

More Details

Technically speaking, you could get through this course just by knowing nodal and mesh analysis. However, you will waste considerable time on questions if they’re all that you use. Pay attention to concepts that can speed up your problem solving. Examples include the fact that parallel branches have the same voltage, or that certain Op-amp configurations are designed to perform addition, subtraction, differentiation, and integration.

The best way to remember the equations and how they connect is by writing an equation sheet as the course moves on. This will also be a helpful resource when you work through the homework problem sets, and on the exams, you will be allowed a single double-sided handwritten aid sheet!

This course is about problem-solving, which means the more questions you practice, the more you will succeed. The lectures are also designed to be very interactive and will focus on working through lots of examples. Find past ECE159 midterms and exams on courses.skule.ca.

Like classical mechanics, which you’ll learn in PHY180, introductory circuits is a very old and standard course. There are many online videos and textbooks that you can use if you’re struggling with a concept and need a new perspective.

Beyond First Year

  • You’ll get crucial experience in building circuits, which is important in engineering prototyping (you will likely need this in Praxis III, in your second year, and you can use these skills on design teams and for personal projects). 

  • This course will provide a foundation for all upper-year electrical engineering courses and the coursework for majors such as ECE and Robotics. 

  • Even if you don’t find electronics interesting, the problem-solving skills you develop in this course will be used heavily in future courses with many connected concepts and equations, such as thermodynamics. 

MAT185: Linear Algebra

Posted on by orientation

Why were the Wright Brothers linearly independent vectors?

Because two of them made a plane!
Photo by Joshua Sortino on Unsplash

Linear algebra is a field of math that is used in many engineering and science fields. In fact, the first step in solving many engineering problems is to make it a linear algebra problem. It’s no surprise that almost all engineering and science programs teach linear algebra early on. 

MAT185 is loosely a continuation of ESC103. It teaches linear algebra from a first principles, ground-up approach. You will learn the reasoning behind mathematical ideas and rigorously prove that they are true. You will cover some concepts that were introduced in ESC103, such as vectors, matrices, and differential equations, and many new concepts including fields, vector spaces, bases, coordinates, linear transformations, and eigenproblems. 

However, unlike ESC103, there is little computation in this course. This is a proof-based course, so you will be tested on your ability to connect concepts and use linear algebra principles to prove and disprove general statements. MAT185 is taught as if you have never taken a proof-based course before, so don’t worry if you are new to this: it’s time to learn! Students have varying experiences with this course. Some find it reasonable while others find it very difficult. There is little correlation between how you felt about ESC103 and how you will feel about MAT185. Although they both cover some pure math and linear algebra, the questions you are asked, the perspective from which you learn, and what you are expected to understand are completely different. 

Professor

Professor Philipp Seiler [Source]

Professor Philipp Seiler

Professor Seiler completed his Bachelors in Mechanical Engineering and Mechatronics from TU Braunschweig, in Germany. He then completed his PhD in Material Science. He recently transferred to be a Professor at U of T but has been teaching for many years as an assistant professor at the University of Kent in England. His research focuses on materials under extreme conditions, such as materials for rocket engines or gas turbines and lightweight materials. 

Professor Interview

Snippets from our interview with Professor Seiler:

“In my research, […] I don’t think there is a single day where I don’t use linear algebra.” 

“I have an active teaching style. I like going on academic detours […] I do not plan lectures down to the minute. I come to lectures with a brief outline, then I see how the students follow and react.” 

“One by one, I will introduce the necessary concepts for [students] to understand [linear algebra] […] If I were to simply teach how a tool like matrix multiplication works, e.g. just by following an algorithm, students would quickly forget it. By knowing the proofs, you can understand why and how matrix operations work. Even if you forget the details, it will be easier to relearn it. Moreover, I want students to understand why certain concepts are true and why they work. Therefore, proofs can help students understand linear algebra conceptually.” 

For more, check out the Interview Transcript here.

Course Highlights

  • The course textbook. We don’t want to spoil your fun, so read it for yourself!

  • Not only will you learn new theorems, but you will learn how to prove them so that you know they are true! 

  • A lot of math symbols. (Don’t worry, the professors will walk you through them.) 

  • The pure satisfaction you gain from proving difficult mathematical statements by using fundamental linear algebra concepts. 

Week in the Life of an MAT185 Student

Classes

There are three hours of lecture per week in this course. Lectures cover proofs, explanations of theorems, and concepts. The professor is usually very clear with his writing on the board, and everything he writes will be relevant, so take notes. There will be some examples, including graphical explanations and engineering applications to linear algebra, but ensure you do additional practice in tutorials or on your own time. If you have questions, don’t hesitate to ask the professors after class. 

Before every lecture, you will have to complete a textbook reading along with an online quiz. Ensure that you do these, as they are crucial to understanding the concepts that will be covered more in-depth during the lecture (they are also worth marks)! 

There is 1 hour of tutorials per week in this course. In tutorials, you will be given practice problems, and the TA will help you solve them. This is a useful tutorial where you can get a lot of practice, but it is only as good as you make it. 

Assessments

Approximately every month there is a problem set consisting of 3 questions. You are usually asked to prove or disprove some statements. The problems are relatively difficult, but you get a week to think about them and work on a solution. Try your best and these problem sets will be valuable practice. The problem set contents are also similar to the more difficult exam questions.  

In addition to these problem sets, the professors will give you a list of recommended problems for every week. Do these. They are not marked and are technically optional, but you will not succeed in this course without them. If you can’t complete all of these recommended problems, solve as many as you can. 

This course has two midterms and a final exam. To study for these assessments, complete many homework and tutorial problems, and past exams. Once you understand how to think about problems in this course and have seen sample solutions, you will begin to adopt the right problem-solving mindset and develop intuition as to when you should apply certain linear algebra principles. Note that you will not succeed in this course just by completing a few past exams. You will need to practice regularly and truly attempt to digest all of the content. 

Find past MAT185 Exams on courses.skule.ca.

How to Succeed

Quick tips and equations

  • Understand the concept of vector spaces. As you’ll learn soon enough, vectors are more than just “pointy arrow thingies!” Know the proof for vector spaces by heart.

  • Know the difference between \bigcap and \bigcup , as well as \subseteq and \subset .

  • \text{rank}(\textbf{A}) = \text{dim}(\text{col}(\textbf{A})) = \text{dim}(\text{row}(\textbf{A}))
  • The rank-nullity theorem: \text{dim}(\text{null}(\textbf{A})) = n - \text{rank}(\textbf{A}) , where \textbf{A} is an m x n matrix with real values.  

  • \text{det}(\lambda\textbf{I} - \textbf{A}) = \textbf{0} : Characteristic equation of matrix \textbf{A}

More Details

MAT185 builds upon concepts from ESC103 such as vectors and matrices and requires you to use them for proofs instead of computations. Therefore, you should thoroughly understand all the content from ESC103; concepts in MAT185 are VERY connected, so a shaky foundation will make your semester more difficult later.
As mentioned earlier, practice is necessary for success in MAT185. Solving a variety of problems will help you learn different problem-solving methods. You will become more comfortable with proofs and will build your linear algebra intuition – both critical in this course.

Sometimes, it’s difficult to even start a problem in Linear Algebra. Don’t cave in and look at an answer key right away: this practice will hurt you in the long run. If you don’t know how to start a problem, write down what you know about it, such as relevant equations, facts, and theorems. Once these tools are laid out in front of you, it’ll be easier to connect the dots and develop a solution.
Even if you do think that you know how to solve a problem, ensure that you can solve it with a formal and rigorous proof! That being said, do not waste your time creating a very sophisticated proof for every single easy question.

In this course, your main job is connecting different facts and theorems to prove and disprove statements. Physically organizing and writing down theorems and equations will help you get organized in your head and understand how they connect.

Linear algebra is not a new subject. If you have trouble understanding a concept, there are a lot of online resources through which you can gain intuition and look for different perspectives. These different interpretations are what make linear algebra great: sometimes a physical, geometric interpretation makes the most sense. Other times, equations will just congregate together in your head. Experiment and find out what’s best for you.

Beyond First Year

  • This course will give you lots of problem-solving experience. Linear algebra is a very abstract and general topic in math; there are often many ways to approach a problem, and you’ll get to experiment with this. 

  • Linear algebra has applications all over engineering and science. For example, most circuit problems are solved using matrices. Quantum mechanics make use of special matrices to determine what is possible for a particle. In computer science, vectors can be used in gaming and graphics. Google uses eigenvectors to determine the ranking of pages in a search. Linear algebra is a necessary tool for robotics, machine learning, and for any field you’re interested in. 

  • Many of your upper-year courses will require strong knowledge and frequent usage of linear algebra! 

Interview with Professor Scott Ramsay

Posted on by orientation

Can you share about yourself and what students can expect from MSE160?

I am from Vancouver originally. I did my undergrad at UBC, and did grad school at U of T, with a PhD in Materials Science and Engineering. In terms of my academic appointment, I’m a teaching stream faculty member, so my primary appointment is to teach. The only research that I do is pedagogical.

“[MSE160] is meant to be a course that will be useful for you as an engineer, regardless of your future specialization.”

It’s about understanding solids, and we go through everything from mechanical to optical, electrical, and magnetic properties. There is some thermodynamics in there as well, and we try to show how all the topics are interrelated. We start with one topic, and after we build up more about it, we connect it with the next topic, so hopefully by the end of it, people have a good understanding of solid materials, how they work, and the underlying structure property relationships.

Professor Scott Ramsay [Source]

We want this course to help you choose the most appropriate material for a design, or understand how, for example, temperature will affect the properties of material, if you ever need it later on in your engineering career. You either know it or you know the fundamentals to go and figure it out later yourself.

How can students succeed in this course?

CC BY-SA 3.0, via Wikimedia Commons

It depends on the educational system that students have come from. I think most people have seen the structure of the atom and electron configuration, so we go into that fairly quickly and we try to build on new concepts for most people, like the band theory of solids and semiconductors. Then there’s a little bit of reviewing. Some people have done crystal structures or thermodynamics in high school. We don’t assume that people have the knowledge, but we will go a little bit more quickly for some parts if we feel that most students have some background in it.

To sum it up, there’s a lot of topics that build on things that students have seen before. As for doing well, I would say probably one of the most important things is to keep up. There’s a lot of topics that are covered as I mentioned, so if you fall behind, it becomes more challenging. Also, you sometimes lose the ability to make those important connections I was talking about earlier.

What is your teaching style and favourite part about teaching?

I try to be engaging, and I like lecture demonstrations. What we have been doing every week is to build up to a good-sized lecture demonstration, probably on Friday. Hopefully that makes it memorable and reinforces concepts from the lecture.

“I suppose my style or philosophy is to convey excitement I have about the subject material and convey a sense that you can figure out so many things if you understand these underlying concepts.”

When I see a student get inspired, see a connection, or even have a Eureka moment. When they say “I understand this” or “I see how this relates to something in my life” or “that broke and I fixed it.” Those moments of learning or sudden realization of something that students have are probably my favorite.

How does this course connect to your research?

Currently, I’m not directly involved in discipline-based research like engineering research. I had a master student a few years back and she did an engineering design project, but the data we collected was more pedagogical in nature. We collaborated with some people growing lung tissue using a machine she designed. MSE 160 is really about fundamental topics. It is the basis for understanding so much of the world using bits of Physics and Chemistry.

“It’s all this structure/property relationship that really helps us understand so much of what’s key to engineering.”

Any advice or comments for incoming first-year students?

I have really enjoyed teaching EngScis in the past three years. They are a fantastic group, and I’m always impressed with how even from 3:00-4:00pm on a Friday afternoon, they seem energized and they’re happy to come to class and be polite and professional. It is really nice to get to know the EngScis and I look forward teaching them. I’m excited and looking forward to meeting everyone.

ESC180: Introduction to Computer Programming

Posted on by orientation

99 little bugs in the code

99 little bugs

1 bug fixed, run it again

100 little bugs in the code
Photo by Emile Perron on Unsplash

ESC180 is an introductory computer programming course. The course is taught with the assumption that students have no prior experience in programming. Python will be the only programming language used for this course.

You’ll start by covering fundamental programming concepts, including functions, conditional statements, syntax, and loops. You’ll use these basic concepts to create simple programs, ultimately learn more advanced concepts such as Python data structures and recursion and be introduced to features of computers such as memory storage and time complexity. For assignments, you’ll be writing your own code for interesting applications, practicing the skills and theory from class.  

For experienced programmers, much of this course will be repetition. For newer programmers with less experience, this course will require regular practice to build a new skill set.  

Professor

Professor Michael Guerzhoy [Source]

Professor Michael Guerzhoy

Michael Guerzhoy (pronounced “GER-joy”, with a hard “g”, and with the “j” pronounced like the “s” in “measure”) is teaching both ESC180 and ESC190 this year. He graduated with an Honours Bachelor of Science from the University of Toronto in Computer Science, Mathematics, and Statistics. He went on to earn a Master’s degree in both Computer Science and Statistics. Professor Guerzhoy has taught courses at the University of Toronto for quite some time, including this course in multiple years. He then moved to Princeton where he worked as a lecturer in the Center for Statistics and Machine Learning. In 2021, he returned to teach computer science in EngSci. 

Course Highlights

  • Discovering Python is not a snake; it’s the programming language you’ll be using for this course.
  • That eureka moment when your program works after spending hours debugging it.
  • Generating code that solves a big, real-life problem with very basic concepts. 
  • Figuring out how recursion works!
  • Participating in some programming competitions hosted by Prof. Guerzhoy!

Life of an ESC180 Student

Classes

There are typically three hours of ESC180 lectures per week. There are no tutorials, so be sure to pay attention during lecture! The professor will explain programming concepts and go through example code. Ensure that you attend every lecture, because there will be multiple quizzes throughout the semester! 

There are no tutorials for this course. ESC180 practicals are weekly 3-hour slots held in the Engineering Computing Facility (ECF) Labs. Here, you will work in pairs on assigned programming labs, getting feedback from TAs if needed. 

There are recommended exercises for beginners, which you really should do if this is your first time coding. They will help you catch up with coding in no time. For now they are optional, but they may become mandatory.

Assessments

ESC180 has two types of assignments: labs and projects. 

Labs are released weekly, and you have three hours to complete them. You will be challenged to program functions that complete specific tasks. The labs can be long and difficult, but they are very beneficial. Try to complete all of them: it is the best way to prepare for the midterm and final exam. They will give you an opportunity to practice coding and build on your programming skills. All labs are graded by TAs, who are also there to help if you get stuck. Don’t be afraid to ask for help, especially if this is your first-time programming. According to the syllabus, “teams that make their best effort toward completing the lab will be awarded full credit.”  
 
Projects are longer than labs and are typically assigned 3-4 weeks before the due date. They are more difficult because their scope is larger. Instead of writing one standalone function, you need to write at least 4-5 functions that accomplish a broader goal. For example, you might need to track a fictional person’s physical activity and happiness levels or build a program that predicts its opponent’s moves in a board game. You may choose to work with a partner on projects. Projects will be automatically graded on Gradescope based on many programming test cases.  

ESC180 usually has a midterm and a final. In these exams you will be asked both conceptual and programming questions. For questions that require you to write code, you will have to do so using pen and paper. The code you write in the exams will be more conceptually challenging, although it will not be as long as code from labs. The challenge is writing it quickly and without external aids. Keeping up with the labs and practicing throughout the semester will reduce your prep time, and past exams are a great source of practice problems.   

How to Succeed

Quick Tips & Equations

  • Know your “if” statements, “for” loops, and “while” loops

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

  • For assignments (and programming in general) ensure that you have thoroughly debugged and considered boundary cases. If your program produces an error on a boundary case, you will likely fail that particular case, and if your program does not compile at all, you will not receive any marks for the assignment!  

More Details

It is totally okay to come into EngSci not knowing how to code yet! Even if ESC180 is your first exposure to programming, you can do well in the course. You will not be alone, and there are many online resources, as well as upper years/peers who will want to help you.

We recommend starting ESC180 projects as soon as they are released. They require a lot of thought and iteration; they cannot be completed in one go, the night before the due date. You will need to brainstorm a solution, try it out, debug, and probably try again. Don’t be fooled by the “simplicity” of the problem statement: even if a function seems easy to write, it might take you several hours to debug.

Some experienced programmers can write their code immediately after seeing a problem. However, we recommend that beginners write an outline in pseudo-code before writing any code. Pseudo-code refers to an informal version of code, written in words explaining what your program does. Plan how your functions will interact and what they need to do to achieve your desired result. This way, you’ll avoid making mistakes, writing unnecessary code, and confusing yourself. Planning and sketching things out on paper is especially important when tackling projects.

Complex programming problems are often difficult to solve using one function. However, they become significantly simpler if you break the problem into smaller sub-problems. You can solve each of these sub-problems with different functions, called “helper functions.” You can then put everything together to obtain a final solution.  Helper functions might be very useful on ESC180 projects!

Everyone wants to write short and efficient programs. However, focusing too hard on elegance or efficiency can stop you from making working code. Always make a program that can produce the results you need before you take it apart to make it more efficient or less ugly. Even professional software developers often show that their initial method works before making small improvements. 

Labs will be released a few days before the practical, so you get a chance to attempt them before asking your TA questions. Always attempt the labs! If you’re stuck on one for too long, take a break and ask your TAs and peers for help. They’re meant to be finished within a certain time frame (about three hours) but getting stuck is completely normal. Sometimes it can be a simple error or a trick you don’t know that prevents you from completing them. If you miss a deadline, don’t stress. Labs are great practice, but you have five other courses with larger assignments to manage. Use your judgment!

Aside from the midterm and the final, you will almost always write and practice coding on an IDE (Integrated Development Environment). While you may become very good at writing, debugging and running code this way as you do the labs, solving problems with just pen and paper without being able to test or debug them on an IDE is a completely different experience. During labs, you may get into the habit of writing, running, and debugging code line-by-line; however, during exams, you will have to go through the program you have written line-by-line in your head and identify the errors yourself. So, it is important to practice without an IDE regularly, so you are better prepared for written assessments along with the labs and projects.

Like any other skill, it will take time and practice to become comfortable at programming. You’ll make mistakes and feel frustrated when you don’t know what to do. The key is regular practice. Looking at code will not be as useful as writing code on your computer. Without actual practice, it’s impossible to improve. Experimenting is the best way to learn coding. You’ll learn to use many useful methods and tools by playing around with code.

Beyond First Year

Through ESC180 you’ll learn how to think like a programmer. You will be introduced to several programming problem-solving techniques. These include sequential, functional, iterative, and recursive programming.

  • Sequential: In basic programming, the computer follows a set of instructions one after the other. By thinking sequentially, the programmer tells the computer what information to save when moving between steps and in what order.

  • Functional: You’ll often need several small, independent functions in your program that come together to solve a problem. Thus, you need to think about the individual components of your problem and how multiple smaller functions can be combined to solve it.  

  • Iterative: By using loops in programming, you can repeat an action as many times as you need to solve a problem. You must therefore understand how to create solutions using these iterative techniques.

  • Recursive: In some cases, it is impractical to solve a problem iteratively. That’s when recursion comes in handy. Recursion is a method in which you break down a larger problem into its smallest subproblem that has a direct solution. Since the solution to the larger problem depends on this direct solution of the smaller subproblem, your program breaks down the large problem, and once it finds the smallest subproblem, it works its way forwards with the solutions from each step. You have then found a solution!
“Good code” by xkcd

Programming is one of the most essential skills in science and engineering today. Many technical courses will either use programming or teach you to program, and you can always use programming to simplify calculations in assignments and labs. Many internships and jobs require programming experience, so it’s great that EngSci provides a solid introduction in first year. 

Note: The course code for Introduction to Computer Programming used to be CSC180. You may still see it referred to as such on some websites (e.g. courses.skule.ca). 

CIV102: Structures and Materials

Posted on by orientation

A uniform beam walks into a restaurant…

The waiter asks, “What would you like?”

The beam replies “Ummm… just give me a moment.”

Welcome, young civil engineer! CIV102 is one of the most iconic and most difficult courses in Engineering Science. It even contains material normally taught to upper-year Civil Engineering students. But we promise we aren’t trying to scare you away; in this course, you will learn a lot and have a lot of fun. 

CIV102 gives you an overview of civil and structural engineering and covers topics such as static systems, truss bridge analysis, bending beams, and concrete. Material is often introduced in its historical context, so you get both a technical understanding of the concepts and their societal relevance. You’re taught a set of equations and problem-solving techniques for each topic and are assessed with problems that ask you to apply these equations in new scenarios. The trick with this course is understanding how and where to apply your equations and rules, not necessarily how the equations and rules were derived.  

Giant version of the old CIV102 notebook, located in the EngSci Common Room.

Professor

Professor Evan Bentz [Source]

Professor Evan Bentz

CIV102 is taught by Professor Evan Bentz. He is an expert in structural software; in particular, he explores the best methods for the upkeep, repair, and maintenance of structures before critical failures occur. Professor Bentz completed his PhD here at U of T and has been teaching CIV102 for two years. He brings a tremendous amount of experience and knowledge from his many years working in the field of civil engineering while providing a unique perspective on structural engineering to EngSci students. 

Interview

“All of engineering is […] about managing uncertainty […] [We have to] make sure that things are safer than they need to be — not too much safer, or else we can’t afford to build it, or indeed the environmental consequences are too big — but appropriately safe given the statistical variation of all the things we have happening.”

“Hold on tight, it’s going to be an exciting time – it’s a development towards the next phase of your life and you’ll see that there’s a lot of people around here that are really sharp, and initially you’re going to say, “Geez, do I belong here?”. And the answer is, yeah, you do. If you’re getting in, you’ll succeed at it.”

Course Highlights

  • Matboard Bridge Competition! For this extremely challenging and rewarding project, every team is given a limited amount of a cardboard-like material called “matboard” and glue (contact cement). Your job is to design a bridge to sustain as much weight as possible, applying your civil engineering knowledge, and utilizing MATLAB, Python, and engineering design best practices. The best designers win special prizes from professors and, more important, eternal bragging rights (especially if you make the “KiloNewton Club”). See this video from a past competition. Note: the course project may change for the 2024 academic year. 
     
  • Nothing will bring you closer to your peers than the legendary weekly problem sets. The questions are challenging but deal with some really interesting course concepts. 

  • Demonstrations and experiments are run by the instructors. We saw wood beams getting crushed and heavy weights dropping on the floor – don’t worry, we were safe… we think… 
  • Stress will gain a whole new meaning, and you’ll have great positive moments! 🙂

Week in the Life of a CIV102 Student

Classes

CIV102 lectures usually happen three times a week. They cover mathematical and physical concepts behind structures while providing historical background as to how these structural properties were discovered and used. These historical anecdotes will help you understand the societal implications of an engineer’s work, especially in civil engineering.  

While there are no dedicated Tutorial slots for this course, practicals are two hours long and are where students usually get the most value from CIV102. They vary weekly but typically consist of a material or design demonstration from the professors followed by a lab, or a teaching session and a 30-minute quiz. In a lab, you will need to build testing structures and analyze material properties you are learning in the course. In weeks without labs, a TA will walk you through course material and worked examples to help your understanding. Then, you will be given a quiz on the material. Your quiz marks add up by the end of the semester, so make sure you review your CIV each week. If you need help outside of practicals and tutorials, there are also plenty of extra TA office hours throughout the week. 

Assessments

The ✨legendary CIV102 problem sets✨ are a staple of any EngSci’s Fall semester. You will analyze stress, strain, concrete, beams, and more. Working through the problem sets will help you understand course concepts and succeed on quizzes and the final exam, so make sure to stay on top of them! Upper-year EngScis may tell you about the stress these problem sets caused them. Nevertheless, the material is very interesting, and assignments are more manageable when you’re working alongside peers. 

There are no midterms in CIV102. No checkpoints. Nowhere to test your skills (except quizzes, problem sets and past exams). There is only a final. This is a difficult cumulative assessment. Because of the single-exam nature of this course, students often neglect it during the semester thinking, “I’ll cross that bridge when I come to it.” However, you will not succeed in crossing the CIV102 bridge (like this one right here) by studying only for the final. Study for this course as if you had midterms – use the problem sets, quizzes, and past finals available to you.  

Find past CIV102 exams in the Skule exam repository.

How to Succeed

Quick Tips & Equations

  • Start the problem sets early! They cannot be completed in the 2-3 hours right before the deadline – truss us…

  • \sigma = E\epsilon [Stress = Young’s Modulus * Strain] 

  • \epsilon = \frac{\Delta L}{L} [Strain = Change in Length/Original Length] 

  • \sigma = \frac{F}{A} [Stress = Force/Area] 

  • A bending moment diagram (BMD) is represented as the area under the shear force diagram (SFD)

  • Know every equation related to reinforced concrete. There are so many that we can’t write them all here!

    • More Details

    Every assessment in CIV102 is open book. You are allowed to bring in the notebooks you used throughout the semester, equation sheets, and whatnot*. Pay attention and take detailed notes in class to stay on track. Don’t rely 100% on your available resources during an assessment as you only have a set amount of time to complete it. Advice from us as your blog admins is that your resources are there as aids; do not underestimate the amount of studying needed.

    *There may be restrictions on the material allowed (such as “no electronic devices”) so make sure you confirm with your professor/TA beforehand.

    CIV102 lectures include lengthy and complicated mathematical derivations of structural engineering concepts. Although you are not expected to know these, attempting to understand where certain equations come from can enhance your overall understanding of the content. In case you missed something, the official course notes are your friend!

    The TAs for this course are some of the best you’ll have. They are either past EngScis who know exactly what position you’re in or very experienced civil engineering graduates. Office hours are extremely valuable; TAs will answer your questions, especially when you need some one-on-one time before quizzes, exams, and problem sets.

    When answering a question on a quiz or an exam, be clear about what you know. Describe your process and don’t give up! If you answer the majority of the question properly but cannot produce a final answer, you could still receive 8-9 out of 10 marks.

    Beyond First Year

    • You will understand the physical world around you in terms of fundamental concepts. These can then be applied beyond the field of just civil engineering. For example, airplane wings act like cantilever beams. The former flies while the latter supports weight on the ground, but the basic principles of the two structures are the same. 
    • Being an engineer comes with a set of responsibilities, and this will be emphasized quite a lot in this course. As an engineer, you need to be aware of people’s safety, a priority in all your designs. 
    • Several concepts from CIV102 will show up in courses in the Aerospace Engineering, Engineering Physics and the Robotics Engineering majors. 
    From David Martin on Unsplash

    PHY180: Classical Mechanics

    Posted on by orientation

    Q: Why did the chicken cross the road?

    Aristotle: It is the nature of chickens to cross roads.

    Isaac Newton: Chickens at rest tend to stay at rest, chickens in motion tend to cross roads.

    Albert Einstein: Whether the chicken crossed the road or the road moved beneath the chicken depends on your frame of reference.

    Werner Heisenberg: We are not sure which side of the road the chicken was on, but it was moving very fast.

    Wolfgang Pauli: There already was a chicken on this side of the road.

    Photo by Sunder Muthukumaran on Unsplash

    Welcome, young physicist! Classical mechanics is one of the most fundamental topics in physics, and this course will set you up for success in your upper years. Everything from flying planes to walking robots can be explained through concepts taught in PHY180. 

    The goal of PHY180 is to teach you about the equations and principles used to model a variety of real-world situations. For example, you might model the flight of a rocket to determine its energy and velocity at a given time. You’ll also use tools from other courses, like differential and integral calculus from ESC194, to model more advanced systems as you progress throughout the course including rotating objects and systems where energy is dissipated.  

    Professor

    Professor Brian Wilson [Source]

    Professor Brian Wilson

    Professor Wilson Brian Wilson is an assistant professor, teaching stream in the Department of Physics. His focus is on general relativity, looking into exact numerical solutions. Since 2018, his research has focused more on pedagogy – how students learn. For the PHY180 course, Professor Wilson focuses on labs and the practical side of things, which is very important for preparing EngSci students for second year physics labs and potentially upper-year labs! 

    Interview

    “[The pendulum lab] is not like a high school recipe, where you [must follow specific steps]. It’s much more like ‘these are your goals, and you must devise a strategy to get to these goals.’ The goals are basic science-y stuff like controlling variables, and then there’s also a big element of uncertainty.”

    “What distinguishes science from philosophy is that [in science], every time you have this brilliant idea, you need to test it. Testing is the core of science […]  I’m hoping to get towards the understanding from the engineers that when you trust that the scientists have figured something out and then implement it, it would be good if you understood what exactly scientists mean when they say ‘we understand something’”

    Course Highlights

    • Labs are a great opportunity to connect the math and theory of the course with the real world. You’ll quickly see that the equations taught in the course can model the world around us.   
    • This course will teach you the fundamentals behind the motion of an object. Soon, you’ll be able to simplify many complicated physics problems to the basic equations taught in this course. 
    • Learning physics from a more mathematical approach! You’ll learn how to derive physics equations from first principle and then apply calculus and mathematical concepts to solve physics problems using those equations. 

    Week in the Life of a PHY180 Student

    Classes

    This course has a total of three hours of lectures a week. They will cover concepts such as Newton’s three laws, kinematics, forces, oscillations, momentum, angular momentum, and energy. 

    The best tip for PHY180 lectures is ensuring you understand each fundamental idea before moving on to the next one since the concepts in the course will continue to build upon one another. Most lectures will involve derivations and theory. If you understand the derivation techniques used and apply the theory learned, you will implement your knowledge more effectively during independent study and when taking assessments.  

    For some of you, the content covered in lectures may be a review of high school physics. Nevertheless, it is still important that you pay attention to lectures and take notes because the derivations are likely more advanced than what you have seen in the past. For those who have not seen the content before, do not worry; the course starts from the basics, and everything is derived from first principles.   

    While there are no dedicated tutorial slots for this course, you will get to interact with your TAs during practical sessions. Practicals are weekly two-hour sessions run by TAs. During the first hour, you will solve midterm-level questions in groups using topics discussed in lecture. This is great preparation for the midterms and finals and allows you to integrate all concepts you learned so far! The second hour is Q&A time for students to ask questions about the content and the pendulum project, which is your main assignment throughout the course.  

    Assessments

    There is typically one main assignment. The Pendulum project is a term-long experiment focusing on analyzing its harmonic motion. It involves building an oscillating pendulum at home, recording data from observing its motion, analyzing its amplitude over time, and improving the accuracy of your setup and methods. This culminates in a series of 2 intermediate lab reports and 1 final report. This project gives you good exposure to setting up experiments with minimal assistance, observing results by controlling variables and finally writing lab reports and communicating your results, which is great preparation for all the labs you will do in second year! 

    You may be asked to build another simple physical set-up like the oscillating pendulum this year. However, it is important to note that the pendulum project is relatively time consuming. And while the report submissions are spaced out throughout the semester, make sure you allocate sufficient time on a weekly basis to work on it to avoid cramming at the end! 

    PHY180 features weekly problem sets that require you to use and derive equations based on course concepts. The questions usually focus on concepts learned that week. They may also incorporate content from previous parts of the course. There are two term tests. Use these as checkpoints to test that you are staying on top of the material. Each test only has a few questions, but they are more challenging than textbook questions and require you to connect concepts from different parts of the course. They are almost all computation-based and can involve advanced mathematical derivations.  


    Find past PHY180 exams in the Skule exam repository.

    How to Succeed?

    Quick Advice and Equations

    Energy: E = \frac{1}{2}mv^2 + mgh + \frac{1}{2}kx^2 – Total mechanical energy of a system is equal to the sum of its kinetic energy (motion energy) and potential energies (e.g., gravitational and elastic potential energy; potential energy from height and in a spring, respectively). 

    Angular Momentum: L = mrv\sin\theta – Angular momentum L is the momentum of an object moving in a rotational path of radius r. 

    Hooke’s Law: F = -k\Delta x – Hooke’s law, which states that the deformation in a spring is directly proportional to the deforming force. And the constant of proportionality is the stiffness of the material, K, better known as the spring constant. Fun fact, everything from concrete to glass has a spring constant! 

    [Source]

    More Details

    PHY180 moves quickly, so make sure you keep up with the material. Ask professors, TAs, upper years, or your peers if you are confused about a certain topic. Because the material builds on itself, it is important to cement your understanding as concepts are being taught. If you have holes in your understanding, it will be difficult to learn new concepts well.

    While we encourage you to know the equations and how they work together, we also want to stress that knowing why something works is also very useful in classical mechanics. If you can understand how the concepts work on a theoretical level, you are better prepared to answer more difficult, concept-focused questions than you would be otherwise. In our experience, the best way to achieve this understanding is to ask questions about why these concepts work wherever possible. Asking these questions in lectures, tutorials, office hours, and on Piazza will help build your understanding of what these concepts really mean. Classical mechanics is arguably the oldest science ever taught, so there exist tons of resources that can help you learn.

    Mastering the theory behind problems will require a lot of practice. As you do more questions, your understanding of the material will improve, and you’ll model situations with fewer mistakes.
    The midterm and exam will have no “easy” questions, so there is no point in repeating problems you can easily do! We suggest making a list throughout the semester of questions you struggle with. Then, before the term tests and exam, work through the questions. Try to do them without looking at the answers to ensure you know how to solve the problems.

    This course has a lot of equations, and many of them can only be used in very specific conditions. We recommend making a list of equations—and when to use them—as you go through the semester. Seeing them in an organized way will help you memorize the trickier ones and remember how they connect. However, you won’t be allowed to bring anything into the exam.

    Before jumping into calculations for a physics problem, sketch out the situation and draw a Free Body Diagram (FBD). This will help you understand the problem and keep track of system components.  

    You may be able to solve some physics problems mentally. However, PHY180 problems can get quite complex, especially when you need to consider different time intervals. With a simplified diagram, you can connect physics concepts to a system without needing to remember every part of it. After you’ve visualized the problem using diagrams, you can focus on identifying and solving for your unknowns.

    Additionally, diagrams can help assessors understand your solution, as they have a visual aid to guide them through your calculations.

    Problems will often present you with information about a system of objects in motion and ask you to find a particular variable. If you are struggling to determine which equation to use to find this variable, it’s helpful to list all known and unknown information from the question in the solution space first. This will allow you to run through the equations in your head and find the most relevant ones to use. This is especially helpful during term tests and the final exam to break down complex problems into simpler steps and solve them faster.

    Deriving equations from first principles may be new for some of you, compared to what you have seen in high school physics. Since there are a limited number of them covered in PHY180, it may be tempting to memorize them step-by-step. However, it will benefit you more in upper year courses if you take the time now to understand the thought process and techniques behind these derivations rather than committing them to memory.

    Beyond First Year

    • Classical mechanics is the root of most other science and engineering fields. The equations and concepts you learn in this course will become second nature by the time you graduate. Understanding these concepts is necessary to progress through engineering, and for success in later courses during your degree.   
    • One classic problem-solving technique in physics is modeling. This course will teach you how to model a situation and how to apply the equations to solve for what you need. Many other courses you take will use this technique! 
    • The materials covered here will serve as the basis for several 2nd year EngSci courses such as PHY293 and AER210 as well as upper year courses in the Aerospace Engineering, Engineering Physics and the Robotics Engineering majors.  

    ESC101: Praxis I

    Posted on by orientation

    To the optimist, the glass is half full

    To the pessimist, the glass is half empty

    To the engineer, the glass is twice as large as it needs to be
    Primary Engineering Design Framework used in Praxis I and II
    Primary Engineering Design Framework used in Praxis I and II

    Praxis I is an introduction to engineering design processes and theory. The course focuses on communication, teamwork, research (a lot of it), and prototyping – all crucial and connected parts of engineering design. An overarching theme is developing an engineering identity – something that unites all parts of the course and that you can carry and develop throughout your career. .

    At the start of the course, you will learn about design theory which is based on the concept of engineers formally and rigorously documenting and supporting their designs. “Supporting your design” means finding research that supports your decisions and testing your design to ensure it will perform correctly. Documentation involves tracking materials, ideas, and information that went into developing your design. Along the way, you will learn to communicate your design process and products to wide audience.

    You will learn all about, and apply, the Frame, Diverge, Converge, and Represent (FDCR) engineering design process that is at the foundation of Praxis I and II. First, you’ll find and frame an engineering opportunity by talking to and observing stakeholders around you. Then, you’ll develop ideas for tackling the opportunity and begin to challenge and test these ideas. This process will culminate in developing a report and several prototypes of your solution.

    Professors

    Professor Roger Carrick

    Professor Roger Carrick

    Professor Roger Carrick is an Assistant Professor, Teaching Stream, in the Division of Engineering Science and the Department of Mechanical & Industrial Engineering. Professor Carrick has a background in mechanical engineering. He completed both his undergraduate and masters education at the University of Waterloo. Before joining the Praxis team, he served as the Designer-in-Residence in the Department of Mechanical Engineering at York University, where he helped set up the Engineering Design curriculum. Through this role, he enjoyed teaching and completed his PhD there. His research interests include project-based learning, knowledge integration through design, and integrating CAD training in engineering curriculum.

    Professor Jennifer Lofgreen

    Professor Jennifer Lofgreen

    Professor Jennifer Lofgreen, who goes by Jenny, completed her PhD in Chemistry at U of T, while working on writing instruction for chemistry students and TAs. In fact, she used to be a TA herself for this course! She spent the past eight years in Sweden teaching academic writing for PhD students. During her time there, she started a second PhD focusing on integrating science philoshophies into engineering education. She focuses on the communication half of Praxis I – which is all about arguments and building strong claims!

    Interview

    “There is a lot of theoretical understanding around engineering design and engineering communication, and learning that theoretically doesn’t really help you understand how to make use of it. You actually have to spend a lot of time practicing, iterating, running through stuff, trying things out, not quite succeeding, doing it again […] We move back and forth between a theoretical perspective and a hands-on practical application.”

    Course Highlights

    Primary Engineering Design Framework used in Praxis I and II
    Praxis students prototyping designs in the Myhal Light Fabrication Facility. (It’s worth noting that “Light Fabrication” is “Light” as in “Not Heavy Fabrication”. They do NOT make light in this facility. Making light would be, strangely enough, “Heavy Fabrication”, not Light Fabrication at all.)
    • Brainstorming many different ideas, and then prototyping and testing them. Dollar stores are your friend! 
    • Learning to make strong arguments and support them with evidence (your own testing or from other sources).
    • Exploring the campus and asking students about their lived experience (as non-awkwardly as you can: make it a challenge). Then, finding a group within U of T, and trying to improve the lives of a group of students on campus, using your newly learned Engineering Design abilities! 
    • Writing your first report! In Engineering, communication is as important as design. No single engineer can be responsible for a product, from the planning and design, to manufacturing and distribution. Therefore, it is good practice to formally communicate ideas and information in a written manner. 
    • Developing and building an amazing invention that improves the lives of many people! 

    Week in the Life of a Praxis I Student

    Praxis I is a versatile course that changes significantly from week-to-week. Here is a rough approximation of how a week will look for a Praxis I student.

    Classes

    There are typically three lectures a week for Praxis I. You will learn about engineering design concepts in lecture and participate in design and thinking activities. You’ll find that the lectures are very well-integrated with the tutorials. They will often discuss some notable results from tutorial activities and connect them to different engineering design concepts. Additionally, some lectures will focus on engineering design tools that will be useful in the tutorial sections immediately after the lecture.

    Praxis studios occupy the same section in your schedule as tutorials. In a small class led by a couple TAs, you will be guided through engineering design activities, project help, and more. This is where most of your project-specific work and instruction will happen. You’ll find that the concepts discussed in studios were introduced in the lectures. This makes studios an excellent time to apply these concepts and get a deeper understanding of how they all work together.

    Your timetable contains a two-hour practical block during which you can meet with your team and work on your project. While the meeting time and duration is not mandatory, you should definitely schedule regular meeting times with your team. Since Praxis is a dynamic course, you may have no meetings on some weeks, and many hours of meetings on other weeks. The key is to find times that work for your entire team, and to not leave all your work until the last minute! We cannot emphasize enough the importance of regularly checking in with your team. Through regular team communication, you can keep track of deadlines and allocate work more effectively. Communicating with your team helps ensure that everyone is healthy and offers an opportunity to de-stress all together. 

    Assessments

    There is typically a midterm and final exam in Praxis I. This will test you on the engineering design theories and concepts you have learned, as well as your ability to apply them. Based on our experience, understanding how the course concepts connect to each other can be a useful tool when studying. To find past exams and tests, visit the Praxis I page on courses.skule.ca.

    Overall, the course project consists of identifying, framing, developing solutions, and verifying design concepts for an engineering opportunity within the U of T community. You will have several independent reports and team projects, reports, and presentations due throughout the semester. Look at the How to Succeed section below for some advice on completing these. 

    How to Succeed

    Quick Tips & Equations

    • The Toulmin model for arguments (feel free to argue in Praxis! It’s not rude, it’s constructive).
      • Learning to make an engineering argument is one of the most important fundamentals in Praxis (and engineering in general), whether you are backing up your claims with a lot of evidence or admitting you have not done enough work to know the full answer to a question. 
    • C.R.A.A.P. Test for source credibility (very useful, though you wouldn’t think so based on the name). 
      • You will likely do tons of research in your engineering career and this test serves as a checkpoint to make sure the sources you are getting information from are reliable. 
      • C = Currency
      • R = Relevance
      • A = Authority
      • A = Accuracy
      • P = Purpose
    • Requirement strings outline what a solution to an engineering opportunity must (not) accomplish. They are built as such: 
      • Objective 
      • Metric 
      • Constraint 
      • Criteria 
    • Measurement matrices and Pugh charts organize the results from your design testing and can help you identify which design concepts are stronger than others in which specific areas (and can therefore allow them to be further improved). 

    More Details

    Much of Praxis I is done in teams to which you’ll be assigned using an algorithm. This is a chance for you to get to know more of your peers and learn from diverse viewpoints. Try to learn each other’s habits and how everyone likes to operate, like who’s an early bird and who’s a night owl. Agree on simple rules: “If someone is late, they will buy Timbits for everyone,” or, “We will not just shoot down others’ ideas: we’ll give a reason we don’t agree and be open to debate.”

    Many teams will wait a few days after an assignment is given to plan and allocate work. Upper-year students recommend planning early so everyone can do their individual portions as soon as possible. This gives plenty of time for group review and for the collaborative portions of the assignment. Waiting too long before planning will just push work off, leaving you with less time to review. If you find a particular teamwork strategy is not working, try something different. Above all, don’t forget to communicate!

    Writing is a key part of professional communication, and you’ll be expected to write formally for Praxis I. The reports can be long, so don’t review them entirely in one go; you’ll find that fatigue impairs your reviewing and editing ability. Also, do not forget about your citations, which must be formatted with APA/IEEE guidelines, and include images/screenshots (extracts) of the information you took from the source. Citations always take longer than you expect, so do them as you go.

    Having a good understanding of the course material goes a long way to quickly generating reports that are professional and well-supported using models and evidence. Additionally, engineering design builds upon itself, so if you don’t review core “simple” concepts early on, you will find it difficult to follow processes later in the course.

    As with all other courses, ask questions! The teaching team will answer any of your questions about assignments, concepts discussed in lecture, engineering, communication, and much more. You will have about 5-10 minutes before and after the lecture to ask quick questions. You can also always email professors for more personal questions or attend their office hours.

    You will receive holistic feedback from TAs, professors, and teammates during studio activities along with written feedback on assignments, and teamwork evaluations. Feedback is personalized and is all designed to help you become a better student engineer, so don’t neglect these resources.

    Beyond First Year

    • You’ll learn how to design creative solutions to design challenges! This skill will be useful in future design courses and in your engineering career.
    • Completing an engineering design process for the first time is a great learning experience for most students. It’s very rewarding to find a problem, frame it, develop a concept solution and then prototype it through to functionality.
    • As a future engineer, you will need to make engineering decisions based on strong arguments and credible, relevant evidence, and think with a sense of logic and rigor.
    • The research and citations that you do for the course may seem tedious at first, but they’ll prepare you for future design projects and courses by introducing you to the research tools necessary for professional engineering.

    person holding black marker pen
    Photo by Kelly Sikkema on Unsplash

    If nothing else, this course will give you confidence in your problem-solving abilities. Overcoming the wide variety of challenges will be a source of confidence for you in your engineering design and problem-solving abilities. Additionally, the engineering design frameworks and techniques that you will learn in Praxis I will be the foundations in Praxis II, where you will focus on applying these skills to a larger scale project!