Calculus III, MTH5102, 2011-12

Lecturer: Dr. Will Sutherland

Update: revision lecture notes now posted (see below)
Exam is Weds 23rd May, 10am . In the Octagon, or see MySIS for special arrangements.
The 2011 exam and solutions now posted (see below).

Page Update history (most recent first) :

25 Apr 2012: Added notes from revision lecture.
23 Mar 2012: Added info on revision lec & exam time. 2011 exam and solutions added.
09 Jan 2012: Courseworks 8 and 9 available for collection from Maths Office.
05 Jan 2012: Added scanned notes for Chapter 7.
16 Dec 2011: Coursework 7 available for collection. Added Coursework 8 answers, coursework 9 questions and answers.
12 Dec 2011: Added scanned notes for Chapter 6.
07 Dec 2011: Coursework 5+6 available for collection from Maths Office.
02 Dec 2011: Added Coursework 7 answers, and coursework 8 questions.
01 Dec 2011: Added scanned notes from Chapter 5.
28 Nov 2011: Added Coursework 6 answers, and coursework 7 questions.
21 Nov 2011: Added Coursework 5 Q+A, and Coursework 6 Questions, and scanned notes from Chap 4.4 - 4.7
09 Nov 2011: Added scanned notes from Monday revision lecture.
02 Nov 2011: Added scanned notes for Chap 4.1 - 4.3, answers to 2010 Test, and coursework 4 answers.
31 Oct 2011: Added scanned notes for Chapter 3.
27 Oct 2011: Added week 6/7 info.
21 Oct 2011: Added Coursework 4 questions and coursework 3 answers
18 Oct 2011: Added scanned notes for Chapters 1 and 2.
18 Oct 2011: Added Coursework 3 questions and coursework 2 answers.
10 Oct 2011: Added Coursework 2 questions and coursework 1 answers.
03 Oct 2011: Coursework 1 questions added
26 Sep 2011: Updated module information document.
15 Sep 2011: Page updated for 2011-12 course.

This module is an introduction to vector calculus and some topics in partial differential equations, i.e. Fourier series and Laplace's equation. These are classical mathematical methods, useful not only in applied mathematics but also in many other contexts.

Detailed module information is available here in PDF format; last updated 26 Sept 2011.
This page will cover: Please note the administrative announcements that follow.

Lecture times

Lectures will be at the following times:

I strongly advise students to attend most of the lectures; it is theoretically possible to follow the module using just the printed notes, but experience from previous years showed that most students who failed had not been attending lectures.

Lecture notes

Here follow the complete set of lecture notes from last year, one file per chapter. I strongly recommend reading these in conjunction with the lectures. Note I may post some minor updates as we go along, so you may want to wait before printing them out, but these cover all the module syllabus.
Chapter 1: Revision material (2010 version)
Chapter 2: Curves, lengths, surfaces and areas (2010 version)
Chapter 3: Vector differentiation, grad, div and curl (2010 version)
Chapter 4: Vector integration and Integral theorems (2010 version)
Chapter 5: Orthogonal curvilinear coordinates (2010 version)
Chapter 6: Fourier series (2010 version)
Chapter 7: Laplace's equation (2010 version)

Scanned overheads from lectures:

Here follow the scanned overheads as shown during the lectures. These are not quite as complete as the printed notes above, but have more diagrams.
Chapter 1: 1.1 to 1.5
Chapter 1: 1.6 to 1.8
Chapter 2: all
Chapter 3: 3.1 to 3.4
Chapter 3: 3.5 to 3.6
Chapter 4: 4.1 to 4.3
Week-7 Revision lecture.
Chapter 4: 4.4 and 4.5
Chapter 4: 4.6 and 4.7
Chapter 5: 5.1 to 5.4
Chapter 5: 5.5 to 5.9
Chapter 6: 6.1 and 6.2
Chapter 6: 6.3 and 6.4
Chapter 7: 7.1 and 7.2
Chapter 7: 7.3
Chapter 7: 7.4

Revision Lecture.

Coursework

Coursework question sheets will be posted here as they are issued, and answers will be posted after the relevant hand-in date.

There will be nine courseworks, with hand-in deadlines normally on Thursday, in weeks 2,3,4,5, 8,9,10,11,12.

Hand-in will be in the Green box, Basement floor of the Maths building.

As usual the tutorial classes start in week 2.

Note that in week 6 there will not be a coursework, but there will be tutorial classes at the usual time which will revise last year's week-7 test (see below).

Coursework question sheets and answers:

Coursework 1: Questions (deadline 6 Oct), and Answers.
Coursework 2: Questions (deadline 13 Oct) and Answers.
Coursework 3: Questions (deadline 20 Oct) and Answers.
Coursework 4: Questions (deadline 27 Oct) and Answers.
Coursework 5: Questions (deadline 17 Nov) and Answers.
Coursework 6: Questions (deadline 24 Nov) and Answers.
Coursework 7: Questions (deadline 01 Dec) and Answers.
Coursework 8: Questions (deadline 08 Dec) and Answers.
Coursework 9: Questions (deadline 16 Dec) and Answers.

Coursework collection: The School is investing quite a lot of time and effort in improving feedback on coursework. Please collect courseworks with feedback from the School of Mathematical Sciences Undergraduate office (Room 101, first floor). They will be in the relevant division in the filing cabinets there.

Mid-term test

The mid-term test counts 10% towards the final module mark.
Here as a sample are the 2007 - 2010 tests and their answers, including some comments on students' responses.

Note that the syllabus changed from 2008 to 2009, so a few of the 2007/8 questions cover material that is outside the current syllabus.
2007 test and Answers to and comments on the 2007 test
2008 test (unamended) and Answers to and comments on the 2008 test
2009 test paper, and Answers and comments on the 2009 test
2010 test paper, and Answers and comments on 2010 test.

Exam

The 2012 exam will follow the same style as the 2009/10/11 papers below: i.e. duration 2 hours, approximately 9 questions, all questions to be attempted. (Note that Question 7 from 2009 is no longer on the syllabus).

Examination papers from previous years:

2007 exam and 2007 exam answers and comments
2008 exam and 2008 exam answers and comments)
2009 exam and 2009 exam answers
2010 exam and 2010 exam answers (scanned)
2011 exam and 2011 exam answers (scanned)
Older papers can be found in the College Library collection of past Maths exam papers , but answers to these are not online.

Advice on examples and revision

Additional examples and revision for the final exam. Here is:
a Table showing past exam questions suitable as extra examples and for exam revision, and
some advice on what you need to know and the possible types of question. (note that dates from 2008-09, so the material about Index Notation and Ordinary Differential Equations is no longer on the syllabus).

For further examples please consult the books mentioned in the module information sheet.

Questionnaire results

A summary of questionnaire results will appear here in due course.