Skip to content The Open University

Student and tutor module reviews

Calculus of variations and advanced calculus

see module description

  • Points: 30
  • Code: M820
  • Level: Postgraduate

Student reviews

This was my first OU module and a pure pleasure. The survey of differential equations at the start reinforced and significantly extended my undergraduate knowledge in many respects, and was an excellent start to the module. The course notes were excellent, as was the glossary of concepts. The tutor was highly supportive, providing much useful input and feedback, as were the tutors on the superb and highly useful interactive tutorials and the study weekends.

I still have much to learn from this module, the notes and exercises were so extensive; so despite doing well on the module, I think I got more than my money's worth! A lot of really interesting work, a great start to the MSc, and an opening to some extremely interesting mathematical physics. Thank you all.

Course starting: October 2014

Review posted: June 2016

My tutor was great. eTutorials and specimen were helpful on solving the problems. However, I must say, it would be much better to elaborate on the why part.

Li Jie

Course starting: October 2013

Review posted: March 2015

This was my first module on the MSc after many years away from the study of mathematics. It took me, it has to be said, many hours of study to refresh my skills in the techniques of analysis and algebra required as background to the material, although I would imagine that someone coming fresh from a degree in maths would be able to hit the ground running with this module.

I thoroughly enjoyed all aspects of the work. I had very helpful and insightful support from my personal tutor and both course organisers; the screencasts, e-tutorials and e-lectures covered all important aspects of the course and were delivered by excellent teachers to a very high pedagogical standard. The course materials are very thorough and detailed, albeit a little intimidating so on first acquaintance.

The TMAs are quite taxing and time-consuming but no more so than one would expect from study at this level. The exam was a very fair reflection of the required knowledge and techniques. I would recommend that anyone studying this module should, if at all possible, attend the two study weekends on offer which were both first class. I found them almost indispensable to my understanding of the work.

If I have a criticism it is of the MSc as a whole and it is that I think, especially in the light of the recent assessment change to 100% of the final mark being based on the exam, that it is very unfortunate that the OU chooses to restrict the past papers. I found that I ran out of revision material very quickly and I know that I would have been much better prepared for the exam had I had the opportunity for more practice on exam-style questions.

Thomas Anthony Holdroyd

Course starting: February 2013

Review posted: December 2013

After years of wondering if I could hack it at Masters level, I decided to take the plunge and tackle M820. A very enjoyable course - I would recommend it as an entry to higher level maths especially if you are suited to calculus and applied maths.

With no set book to worry about and pretty good course notes, it's just a case of getting stuck in. Some of the algebra is a bit of a slog but then again this is a Masters level course.

Very highly recommended if you like applied maths and think you can take your maths to the next level.

Mark Hobbs

Course starting: February 2011

Review posted: May 2012

This is the maths course that most postgrad students end up doing first. As such it is well presented. I found it accessible even though it was over a quarter of a century since I took my first degree. In fact there was little if anything in the content I had not met before (although most of the application was new to me (or forgotten).

Although presented as an applied course it actually compromises (or falls between two stools) the two areas. There were certainly times when I believed I would have liked to see more rigour (but in a first course after a long break many would not I am sure) and to be fair references were made if I really had wanted the rigour. On the other hand many of the applications were either trivial or somewhat glossed over (or was that just me not bothering to follow enough?)

The notes (not a set published text but course specific notes) are very good indeed (the fully worked answers particularly so). The TMAs seemed fair.
The exam requires an awful lot of algebra and is hard to do in time.

Timothy Fletcher Rogers

Course starting: February 2011

Review posted: December 2011

Good course and great Tutor. Exam was fairly written but marked a bit harshly. Recommended.

Urim Metuku

Course starting: February 2009

Review posted: June 2010

This is a lovely course. I did this as my first postgraduate mathematics course, and learned so much mathematics from it. It's challenging, especially the later chapters which get a bit detailed and technical, but worth the effort. I came at the course with an interest in optimisation, and studying this course has improved my ability to understand dynamic programming of the Bellman variety (though the course does not cover dynamic programming - it covers the precursor of dynamic programming, calculus of variations).

I also, for the first time, understood a lot of stuff I'd previously covered in calculus that hadn't really fitted together. I came away from the course wanting to continue with my study of this area.

Course starting: February 2009

Review posted: February 2010

An excellent course, with a really nice set of course notes and varied and interesting questions and assignments. A great place to start the MSc.

Course starting: February 2008

Review posted: November 2009

I enjoyed the course. The work load was as expected. The TMAs I found time consuming, so give yourself plenty of time. The exam was frightening, but fair. My tutor advised me to revise the bits I could do and not to expect to learn it all and that really helped.

Course starting: February 2008

Review posted: July 2009

After an initial revision chapter, this course quickly introduces the key ideas and techniques of the calculus of variations. It then builds up the theory to cover a wider range of problems. I enjoyed the plentiful examples of physical problems that can be modelled, such as finding the shape of a hanging rope (the catenary).

The course assumes a facility with maths methods such as integration techniques and solving differential equations, so you may need to revise them. (The revision chapter includes integration but not DEs).

I found the specimen paper was a good guide to the types of question in the exam, though I'd have liked more exam-style questions to practise on. The main challenge in the exam itself was the time pressure.

Course starting: February 2007

Review posted: January 2008

I completed this course after a considerable break from formal study. My first degree was in Physics so the mathematical formality of the text came as something of a shock to me! However, the first chapter of the course notes is an excellent introduction covering most of the calculus techniques needed to address the rest of the course.

I found having access to the computer software Maple very helpful throughout the course and particularly in the TMAs where it was often helpful to graph functions and look at their behaviour, to lead you toward a solution.

The course notes where generally good, however, in their second year, they still contain many typos and errors. The main weakness of the course is the quality of the worked solutions; these are too sketchy, often missing out difficult pieces of algebra.

The exam was reasonable straight forward and no more difficult then the specimen paper, time pressure being my main challenge.

Course starting: February 2006

Review posted: December 2006

I really enjoyed this course. It begins with a canter through familiar Calculus results from undergraduate days, and on up through the Calculus of Variations.

There is no set text to buy, it's all in the Course Notes. The style of these is easy to follow and there are plenty of examples and problems to solve as you go. I found that the material 'went in and stayed in'.

Yes there were typos in the first draft of the notes but these were only a minor annoyance. Hopefully, the second run through the course will be even better.

The examination was straight-forward, similar to the TMAs and Specimen Paper.

Course starting: February 2005

Review posted: January 2006

A good revision of techniques and introduction to the calculus of variations. The course notes were helpful generally though might benefit from a little more clarity in places and the examples tend to be too difficult too quickly. In general (given that this was the first presentation as well) a very well put together course that can only get better.

Course starting: February 2005

Review posted: December 2005


Tutor reviews

I took this course after a break of several years of studying mathematics. I found it quite straight forward in the main. The calculus techniques were 'do-able' and most of the TMA questions OK. There was no set book so all the teaching materials were in the OU unit style with sufficient examples and exercises to practise with.

However,with it being the first year of presentation, there were a couple of irritating errors in the TMA questions, and a few in the course units.

I found the main difficulty in the exam was choosing which questions to do. There was a free choice of 4 from 8, with more credit being given for full solutions. I found it hard to know at the outset of a question whether I would make it to the end.

Review posted: December 2005

Please note

Each of the views expressed above is an individual's very particular response, largely unedited, and should be viewed with that in mind. Since modules are subject to regular updating, some of the issues identified may have already been addressed. In some instances the faculty may have provided a response to a comment. If you have a query about a particular module, please contact your Regional Centre.


Module satisfaction survey

The figures below are taken from a survey of students who sat the exam/completed the end-of-module assessment for the October 2016 presentation of M820. The survey was carried out in 2017.

46 students (a response rate of 45.5%) responded to the survey covering what they thought of 10 aspects of the module.

Please note that if the percentage of students who responded to this module survey is below 30% and/or the number of responses is below 23 it means that only a small proportion of students provided feedback and their views as shown here may not be fully representative of all students who studied the module.

See this page for the full text of questions and more information about the survey.

% Count
Overall, I am satisfied with the quality of this module 93.3 42
Overall, I am satisfied with my study experience 91.1 41
The module provided good value for money 68.2 30
I was satisfied with the support provided by my tutor/study adviser on this module 84.4 38
Overall, I was satisfied with the teaching materials provided on this module 82.2 37
The learning outcomes of the module were clearly stated 86.7 39
I would recommend this module to other students 86.7 39
The module met my expectations 91.1 41
I enjoyed studying this module 93.2 41
Overall, I was able to keep up with the workload on this module 88.9 40
Faculty comment: "It's pleasing that once again students have shown their appreciation of the module. Many thanks, in particular, for the extensive comments. They're always interesting to read, and appreciated, including any criticisms. The comments feed into the development of the module. Unfortunately, the module team does not determine the module fees (the question with the lowest satisfaction rating). The module materials (the second lowest satisfaction score) are currently being revised. It was hoped to get the new materials for the next start of the module. This may not now be possible but the module team is doing its best to expedite matters and to bring the revised notes to the students as soon as possible."
Enter a module code to find a review

To send us reviews on modules you have studied with us, please click the sign in button below.