MATH10222: Calculus and Applications -- Part 1: ODEs

This first half of the course, dealing with ordinary differential equations (ODEs), is taught by Prof. Matthias Heil. The second half, dealing with mechanics, is taught by Dr. Rich Hewitt who provides a separate page for his course notes. This page provides online access to the lecture notes, example sheets and other handouts and announcements. Most of the material will be taught in "chalk and talk" mode. If OHP transparencies are used, copies will be made available (after the lecture) on this page.

Please note that the lecture notes only summarise the main results and will generally be handed out after the material has been covered in the lecture. You are expected take notes during the classes.

The Riot Act -- Please Read

The lecture course (four hours a week) is accompanied by weekly supervision classes during which you will get a chance to discuss the material in small groups, and to resolve any problems. The course is a "methods course" and I can assure you that the only way to understand the course material is to work your way through LOTS AND LOTS of examples. Suitable example sheets will be made available (in pdf format) on this page. You MUST attempt the questions on these sheets and hand them in before your weekly supervision. (Your supervisor will arrange details with you.) He/she will mark the most important questions (as identified by me) and give you feedback during the supervision.

The supervisions are for YOUR benefit -- if you have any problems with the material, YOU have to take the initiative and raise them during your supervision class. You will be expected to have at least tried to solve the problem so that you are in a position to ask specific questions. Most of the problems are extensions/modifications of examples presented in class, so it's a good idea to have a look through your lecture notes before attempting the questions on the example sheets. The following exchange tends to take place at the beginning of most of my lecture courses:

Student: "I can't do that question"
Lecturer: "What exactly is the problem? How far did you get?"
Student: "I don't even know how to start"
Lecturer: "Well, this is essentially the same example that we did in class; have you looked at your lecture notes?"
Student: "No, I can't find them" [or "No, I didn't go to the lecture", "No, why should I?", etc...].
Lecturer: "[censored]".

To be absolutely clear: If you can't do a question even though you've tried really hard [see below for a definition of "really hard"], and you have consulted all the available material, I'll be delighted to help you -- that's my job, after all. However, if you expect me (or my colleagues) to turn supervisions into repeat performances of the lectures because attending them would interfere too much with your social life, or if you can't be bothered to read the handouts, I will have very little sympathy.

I will distribute detailed solutions (again in pdf format on this page) after the material has been covered in the supervisions but these should only be used to check your solutions. Do not make the mistake of assuming that it'll be sufficient to look at somebody else's solution to understand the material! "Maths is not a spectator sport!".

While I'm having a general rant, let me address another frequently-asked-question:

How much time should you expect to spend on this course?
As I said above, you are expected to attend the lectures and the weekly supervision classes. However, you will obviously have to dedicate a considerable amount of additional time to understanding the material that's been covered in the lecture. As a rough guide, I'd say that the absolute superstars amongst you (if in doubt, assume that this does not include you) will need about an hour of private study per lecture to really understand the material, and to work your way through the example sheets; two hours is likely to be more realistic for the mere mortals amongst you. If you decide to cut corners you will pay the price, not only in this year's exam but also in all subsequent ones, because second- and third-year courses build on the material taught in this course.



There is no textbook for this course. All you have to do is to attend my lectures and download the notes from this webpage. The example sheets will provide plenty of problems to work through. If you need more, there are literally hundreds of good textbooks out there -- go to the library and browse around to see which ones you like. I personally quite like any from Schaum's Outline series, e.g.

Schaum's Outline of Differential Equations, 3rd ed [Paperback] Richard Bronson, Gabriel Costa.
[The link is to Amazon -- I suggest you use it for the "look inside" feature and then get the book from the library or if you really want to own it (it's actually very cheap) from a reputable book shop.]

It provides a very succinct overview of the theory and methods (methods being its real focus) and lots of worked examples. Note that the book covers a lot more material than I can accomodate in this course!


Feedback supervisions will provide an opportunity for students' work to be discussed and provide feedback on their understanding. Students can also get feedback directly from me, for example during my office hour.

Material for supervisions:

"Synchronising" the example sheets with the lecture is slightly non-trivial since supervisions are being held throughout the week. As a result, you may occasionally come across a question that deals with material that has not yet (!) been covered in the lecture. Since this tends to cause instant panic amongst students, I propose the following procedure: Example sheets will be made available as soon as possible and you should check this webpage frequently for any new material. I will update the box below after every lecture to state which questions I regard as "do-able". Being keen students, you will then immediately start to work on these to make sure that you can bombard your supervisor with questions if you encounter any problems.

Example Sheets:

Solutions to Example Sheets:

Do-able questions:

Date Topics covered Do-able questions
Week 1 We haven't done anything yet! However, tutorials will already take place during week 1 and some of you may have your first tutorial before the first lecture. Don't panic: The "warm up" exercises on Example Sheet 0 should all be do-able, provided you remember your A-Level maths and have your brain switched on.... Example sheet 0 (all questions!)


The course will be examined in a three hour exam in May/June.


[Note: Students requested that all the course material will be made available in advance so here it is... It's (still) listed in the order in which we'll encounter things in the lecture and I will update the marker that indicates which parts have already been covered in the lecture.]

Please note a few corrections for previous handouts (the files above have already been corrected).

Exam feedback:

I'm supposed to provide "feedback on the exam", so, for what it's worth, here's what I thought after marking the exam. However, rather than wasting your time reading this (in an attempt to improve your grade by "improving your exam technique"), I suggest you have another read through the Riot Act above. Concentrate on actually understanding the material rather than trying to memorise likely exam questions and how to tackle them. Pleeeeease!

Feedback on your Feedback (yes, really!):

The most recent gimmick is that we have to give you feedback on your feedback. Here it is (executive summary: "Thank you, I enjoyed it too!"):
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Page last modified: January 10, 2019

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