MTH2010: Multivariable Calculus

5 quizzes worth 1% each
4 assignments worth 5% each
1 midsemester test worth 10%
Lecture poll participation and applied class participation worth 5%
Exam worth 60%

This subject was really great. It explores calculus in 3 or more dimensions, looking at vector functions, multivariable functions, and vector fields. It's a natural extension of the calculus already learned. This subject uses some more complex integration strategies (mainly substitutions, trigonometric identities, and a little integration by parts) but complex strategies are either shown in the lectures first or hinted at. The lecturer would often encourage us to "integrate like a champion", thinking of u substitutions as a backwards chain rule.
The lecturer is excellent. Norm is very engaging and focuses on an intuitive understanding behind the mathematics. It was his first time teaching the subject and so he would be writing the notes while he taught us the content. This helped the lectures to be well-paced. Unlike past lecturers, Norm did not focus on proving any of the theorems, making the unit more accessible to people with all sorts of mathematical backgrounds.
The applied class involves working with a group to solve problems on a whiteboard, and is usually pretty helpful in understanding some of the more difficult concepts.

The quizzes were done on paper and usually were pretty easy to do, often taking a similar style to questions done in the applied class.
The assignments were more challenging, sometimes extending the questions beyond what was on the applied class material, but many were similar and used similar strategies.
5% of the mark was split between answering lecture polls and participating in applied classes. You had to correctly answer 75% of the flux poll questions asked on the lectures, with there being a 48 hour time period after each lecture to answer it. I thought this was mostly pretty reasonable. You had to attend and participate in 8 of the 11 applied classes to get the marks.
The midsemester test was pretty easy. A practice test was given and the actual test was very similar, just with a few numbers changed around.
The exam was also not too hard, also being very similar to the sample exam. Basically, to do well on the test and exam, ensure you can do the practice test really well and understand everything.

Overall it was a really well run unit and very enjoyable. Some of the integration towards the end was more challenging but it ultimately was all accessible.

Norm Do

2 sample exams, one from 2020 and one written for 2021.

5 out of 5

Yes, lectures were done over Zoom so the Zoom recording with screensharing was uploaded.

Calculus, Metric Version (8th edition) by James Stewart
Not really necessary. The lecturer uploads weekly extra problems without answers, but the answers can be found in the textbook. That's really the only use for it, unless you have a specific interest in looking up proofs.

3 x 1 hour lectures
1 x 1.5 hour applied class

2021 Semester 1

97 HD

Lecture participation (4%)
Most lectures contained an active learning component, where students would be given time to complete a question relating to the topic being taught. We would then submit submit our answers via an MCQ on an online Google survey form, which recorded our answer and also our student IDs. The lecturer would then go through the question. Marks were only required for participation (not necessarily a correct answer, leading to many students randomly selecting answers just for the marks). The Google forms were typically left open for 24 hours, after which they were closed and you would no longer be able to complete them to obtain the associated marks. The contribution of each question to the overall mark, or the number of questions needed to obtain the full 4% was unknown, and there was also no way for us to track our progress on this assessment (which was slightly annoying). Still, it was an interesting concept and I felt it was useful in engaging students in the learning process.

5 x quizzes (1% each; 5% total)
The quizzes were small assessments, containing 2-3 basic questions regarding recently learnt content. These were take-home, and submitted to your tutor, either in your support class, or via their submission box. The quizzes were due in weeks where there was no assignment due, and were spaced evenly throughout semester. The marked quizzes were generally returned within 2 weeks.

4 x assignments (4% each; 16% total)
The assignments consisted of short answer questions related to recently learnt content. Considerably more work was required for these compared to the quizzes, and many students went to the Maths Learning Centre for assistance with some questions which were particularly difficult. However, the information from the lecture notes were sufficient to be able to complete all the questions. There was also a significant focus on communication in these assignments - we were expected to (briefly) justify the use of any new concepts or formulas. My tutor was especially strict in this respect when it came to marking. The assignments were due in weeks where quizzes were not, and were spaced evenly throughout semester. They were submitted in the same manner as quizzes, although required an additional cover sheet. Marked assignments were generally returned to us within 2 weeks.

Mid-semester test (15%)
This was a paper short answer test, consisting of 6 questions (50 marks) in 50 minutes. It was held in week 7, and covered the first 4 weeks of content. The questions were fair - they were all modified versions of questions we came across in lectures, assignments, problem sets, or quizzes. I personally found that I was pressed for time in this test, so it is wise to use your reading time efficiently to allocate your time between questions. The marked tests were returned to us within 2 weeks.

End of semester exam (60%)
The end of semester exam was 3 hours long, and consisted of 10 short-answer questions (90 marks). Like the mid-semester test, I found that most of the questions were modified versions of questions which were encountered at some point in semester, so my advice would be (optimally) to re-complete all questions from the lectures, tutorials, and assessments, as well as complete and study the questions from the past exams. There were also a few questions which required deeper thinking, so it's important to actually understand the concepts, and seek help where required. Beyond the lectures notes and textbook, there are a multitude of resources online to assist you, including Paul's math notes, and Khan Academy. Yann, Todd, and Simon all held consultation hours leading up to the exam period, and Yann was also very responsive to Moodle posts. Hurdle requirement of 40% (on the exam) to pass the unit.

This unit is hard. It takes calculus to the next dimension (literally) and beyond. All the concepts which were taught in high school and in previous units (MTH1030 and MTH1020) are extended and expanded on into the third and higher dimensions. What I encourage you to try to realise and understand that much of what you learn in this unit is an extension of what you already know (for example, instead of a single integral, you will learn to evaluate double and triple integrals).

In terms of assessment, there was something due basically every week, so it is very important that you keep up to date with the content - there is a lot of know, and can quickly become overwhelming as assessments build up. However, it is possible to do well in this unit. Don't be afraid to seek help - from your peers, tutors, or the math learning centre. In particular, I recommend attending the support classes, where you get to apply the knowledge, and discuss the concepts with peers.

The concepts learnt in MTH2010 can be grouped into 3 overarching themes:
1) Partial Derivatives - multivariable functions, limits and continuity, partial differentiation, the multivariable chain rule, directional derivatives and gradients, tangent planes, finding maxima and minima
2) Multiple Integrals - change of variables, double integrals (including in polar coordinates), triple integrals (including in spherical and cylindrical coordinates), finding areas and volumes using integrals
3) Vector Calculus (the pointy end of semester, which is what most of the previous topics lead up to) - vector fields, line integrals, Green's Theorem, curl and divergence, parametric surfaces, surface integrals, Stokes' Theorem, Divergence Theorem
It may all sound daunting for those who are considering completing this unit, but it's definitely achievable to learn all of this in a semester!

This unit is also the gateway to all higher mathematics. What you learn here is important, and many of these concepts will be built on further in later units (if that's your thing ).

Yann and Todd had slightly different approaches to teaching. In particular, Todd liked to dicuss the n-dimensional generalisations of the concepts, while Yann tended to only briefly mention these, and focused on the core concepts (which were more relevant to the assessments).
- Dr Yann Bernard (Weeks 1-7) - also unit coordinator for weeks 1-6. The mid-semester test and final exam were written by Yann.
- A/Prof Todd Oliynyk (Weeks 8-12)
- Simon Teague - unit coordinator for weeks 7-12. While he did not actually give any lectures, Simon was a support class tutor, ran an exam consultation session, and also wrote some of the quizzes and assignments.

Yes - semester 2, 2017 (with answers), and semester 1, 2018 (without answers). I highly recommend that you work through both of these, and compare/discuss your answers with other students.

4 out of 5. Assessments were fair in terms of weighting, and well-spaced out throughout semester.

Yes, with screen capture. Live-streaming available via Panopto and Echo360.

- Recommended: Calculus, Metric Version (8e) by Stewart, Thomson. The lecture notes follow the topics of this textbook, so it is a great first resource to use if you require extra clarification or detail. The problems from the support classes are also taken from here, and so the remaining questions can serve as good extra practise. This text was also recommended in MTH1030 and MTH1020.

Per week: 3 x 1-hour lectures, 1 x 2-hour support class

The lectures consisted of the lecturer going through skeletal notes posted on Moodle, and filling in the gaps. The gaps included proofs, examples, and questions. Completed notes were uploaded after each lecture. Most lectures involved an active learning component, whereby we would be given time to attempt a question and then submit their response online (see assessments below).

The support classes are your stock standard mathematics tutorial. We would work in groups on problems related to the previous week's content, in the presence of a tutor to assist if required.

Semester 2, 2018.

Not yet available

-5 quizzes (5%)
-3 Assignments (15%)
-Mid Semester Test (20%)
-Exam (60%)

There are 3 assignments across the semester and each worth 5% for a total of 15% of your total unit grade. They would usually be on the harder side, but you get a few weeks to complete them and usually a lot of people will work together and also ask tutors for assistance which probably justifies their difficulty. I found that the difficulty is due to us not having probably learnt and consolidated the material before doing the exam, so we were sometimes doing the assignment whilst doing the learning. These assignments were required to be handed in during the first 5 minutes of your tutorial of the week that they were due. Overall it is quite easy to do well on the assignments for the aforementioned reasons and good scores on these are a great boost to your score easily.

I probably should preface this with the fact i'm a biomed student who did this unit as an elective so my experience may differ from a science student.

As the subject name suggests it was all about multivariable functions (e.g. f(x,y))which may seem daunting at first but once you realise that a lot of what you are learning analogous to univariable functions (e.g. f(x)) it makes it a whole lot easier to understand and remember the content. Overall the subject content was not too difficult if you had a decent mathemtical foundation going into the unit.

The main topics we studeid were, revision of vectors from first year/specialist maths, basics of multivariable functions, partial derivitives, tangent planes, linear approximations, total differential, chain rule, implicit differentiation, directional derivitive, gradient vector, max/mins, iterated integrals, double integrals, double integrals in polar coordinates, applications of double integrals, triple integrals, triple integrals in cylindrical and spherical coordinates, vector fields, line integrals, Green's theorem, curl/divergence, paramterisation of surfaces, surface integrals, Stoke's theorem and Divergence theorem.

Whilst doing most of the questions isn't too hard the real difficulty lies in understanding the content properly which is needed to do the harder problems. Your best bet would be trying to get exposed to a lot of questions before the exam.

It is worth 60% so you are really working towards this the whole semester. It was 9 extended response questions for a total of 123 marks. In contrast to the MST the exam was more about procedural working rather than proofs. There were no real surprises in the exam either but by no means was it "easy". All the questions were comparable to the exams provided albeit may be a little harder. As revision I would be doing and redoing the exams that you are provided with and any resources from any revision lectures.

A/Prof Todd Oliynyk
Dr Yann Bernard

It is worth 20% so a huge chunk of your total score. It was 40 marks and covered the first 4 weeks of content and was during week 6. I think the MST was harder than they had intended which resulted in a lot of people feeling that they had been cheated especially since there was many proofs on the MST. Overall, I thought the MST was on the easy side, no real tricks, but only because I had put the time in to learn the proofs for everything we learnt. There may have been a little lack of time since I wasn't able to double check my whole test.

Overall a nice unit to do if you enjoy maths. The lecturers aren't compulsory or necessary imo I found that I learnt better by doing questions and watching videos on YouTube (khan academy, Professor Leonard, Krista King maths etc) were much more beneficial to my learning and a lot less time consuming. I also found Paul's Online Maths Notes to be very helpful to explain any topic from he unit. I would still read through the lectures and practice all the proofs since they do come up.

Yes, two exams. One with solutions and one without solutions.

None

There were 5 quizzes across the semester each worth 1% for a total of 5%. These were basically less formal assignments and all 5 quizzes probably totalled to a single assignment. These were on the harder side of what you would expect to see on the MST or the exam but very useful for consolidating your understanding. It is very achievable to full mark these since you have a week to do them at home and hand them in the first 5 minutes of your tutorial during the week it was due. Which is different from past years which were done during the tutorial.

4 Out of 5

Calculus : Early Transcendentals 8ed International Metric Ed
(not 100% required as a suitable amount of questions were already avaliable but if you are struggling early it might be good to get a copy for some extra practice)

Yes, with screen capture.

Basically a 2 hour session every week where we would work on a problem set on whiteboards with other students. A tutor was available for help if needed. These aren't compulsory but would suggest going since I found that this was the most useful part of the unit. If you can't go to your tutorial you need to complete the worksheets since they form the basis of your understanding and learning from doing is the usually the best for maths. My tutor, Simon Teague, was extremely helpful with tough questions and how to study for the MST and exam.

Weekly 3 x 1 hour lectures, 1 x 2 hour computer labaratory (no computers involved just a tutorial where we would work on a problem set with others)

2017, Semester 2

TBA

Starting from week 3 I believe, we had an assignment every second week, and a 25 minute test every other second week, which were done in tutorial classes.

I really enjoyed this unit. The content I found to be thoroughly interesting, it began with extending derivatives and integrals from single variable calculus into xyz space - partial derivatives and multiple integrals - then we moved onto Vector Calculus which is essentially a generalization of all calculus. Steve is a brilliant lecturer, he kept everyone interested with his enthusiasm and self proclaimed loud American voice, and is never afraid to crack a joke or to rip on engineers just for being engineers (For some reason he likes 'swearing at engineers' lol ).

The tutes are not compulsory but are well worth it, basically my tutor would go over all the content that Steve did in lectures but in a fair bit more detail and depth. I would highly recommend always showing up to tutes for this unit. Every second week there was a test which ran for 25 mins in tutes. They had generally 3 or 4 questions on them and were worth 5% each. They were always very doable, and if you had done all the problem sets before hand then there is no reason you couldn't get close to 100% on them every time - the questions were never anymore difficult than what was in the problem sets (sometimes it was even the same question). The assignments were every other second week and also worth 5% each.

If you enjoy Calculus - particularly if you enjoyed specialist maths - then you I think you will really enjoy this unit, as it basically completes elementary calculus and generalizes it quite nicely - although you will only do it for xyz space. If you want to do it for n space you will have to take real analysis and do some pure maths.
Also, I highly recommend anyone studying calculus use Pauls Online Maths Notes, its a fantastic resource and helped me a huge amount in this unit. I wish I had discovered it earlier. http://tutorial.math.lamar.edu/

Steven Siems

1 with solutions, 1 without

4.9 Out of 5

Yes. Steve uploaded everything he wrote down in lectures.

Stewart Calculus: Early transcendentals - basically a must in my opinion. Although Steve's lecture slides were excellent and he also uploaded a hand written summary of every topic in the unit on Moodle at the beginning of sem, the textbook is extremely well written and the unit follows it word for word basically. Another reason the textbook is a must is that your weekly problem set is a list of questions which are in the textbook, however I believe they photocopied these questions from the textbook and put them on Moodle anyway. Also, Steve pu up handwritten solutions on Moodle to all the selected textbook questions.

Three 1-hour lectures and one (non compulsory) 2-hour tutorial per week

2013, semester 2

4x20 min tests worth 5% each, 4 assignments worth 5% each, 60% exam

I really enjoyed this unit, but wished I had more time to enjoy the back end of the material properly. I didn't have much time at this stage, although that's probably more to do with me overloading than the unit itself. What you learn in MTH2010 seems to actually be useful, and in itself is interesting enough to entice you to do more tute questions (and put off other units/assignments to do them). In some of the early stages you may think that you're just learning random tools, but towards the end of semester it all ties in together really nicely, and I would say this is in my top 2 favourite units so far (I can't split this with ENG1091). Although in the odd case any of you transfer from eng to the double degree, the first couple of weeks will be a re-run of ENG1091.

One of the downsides to how the unit was run this semester was the 20 minute tests worth 5%. You normally get 3 or 4 questions, the first two tests this was doable without pushing two hard, but for the third and fourth test you really only got one shot at each question, no time to stop and think, you just had to power through it to try and get them done on time. As a result you make a lot more simple mistakes, or if you didn't see the way to do the question right away, you probably wouldn't have had time to get back to it.

Lectures are worth going to, as are tutes (although with a test one week and an assignment that has to be handed in in the tute the next you can't really skip too many, well skip showing up for at least 5 minutes anyways ). Seriously though, it's just practice, make sure you do the tute questions each week, and make sure you go over past exams from previous years during swotvac. You'll see past questions coming up again, and the others are to be approached in similar ways to other questions, (and you'll see a tute question from the semester appear in the exam every now and then).

If anyone wants to start this unit early, here are the topics covered (roughly by week)
- Vectors+Geometry of Space, Lines, Planes, Functions of Several Variables
- Limits and Continuity, Partial Derivatives
- Tangent Plane, Linear and Quadratic Approximations, Chain Rule for multivariable functions, directional derivative and the Gradient Vector
- Double Integrals, Iterated Integrals
- Double Integrals over a general Region, double ints over polar coordinates, applications of double integrals
- Triple Integrals, Triple Integrals in Cylindrical Coordinates
- Triple ints in Cylindrical + Change of variables in multiple integrals
- Vector Fields, Line Integrals, Fundamental Theorem of Line Integrals
- Green's Theorem, Curl and Divergence
- Parametric Surfaces, surface area, surface integrals
- Stoke's Theorem, The Divergence Theorem

But yeah, you'll be dealing with things like this (it's cool! )

Dr Simon Clarke

Yes, 1 exam with solutions (although you can probably dig around for others)

5 Out of 5

Yes, audio only though, although lecture transparencies are scanned and put onto moodle.

Stewart's is a pretty good resource for this unit, although not absolutely necessary. Others I know relied on it heavily, I didn't really use it much though (tute questions were scanned onto moodle). If you want to (and have the time to... this was my problem this semester) to do a little bit extra then it's probably worth it.

3x1 hr lectures a week, 2 hr tute

Semester 1 2013

95 - HD