Unit lecturer: Dr D A S Rees Department of Mechanical Engineering. Room 4E 2.54.
E-mail Address: ensdasr@bath.ac.uk (formal) or D.A.S.Rees@bath.ac.uk (alias)
Notes, videos, problem sheets:
The full set of notes are here:
Semester 1
and the semester 2 notes will eventually be found here.
Schedule for semester 1.
My videos
Links to my lecture videos from 20/21 (and the associated slides).
Problem sheets and solutions.
The problems sheets are also at the back of the Course Notes document.
The solutions to be updated.
Ancilliary information:
Schedule
What are we doing when?
Resources
Some links to external support.
Miscellaneous
Mathematical links, some important, some useful, some frivolous.
Handouts
Some extra information that may be useful.
Ancilliary videos
Links to old videos from former parts of the curriculum. Useful to know and not examinable.
To be updated.
Other videos
Links to a few external videos that may be useful. Suggestions for others gratefully received.
Textbooks
Some advice on textbooks.
Examinations:
Past exam papers These cover the last five years. Includes outline solutions and general feedback.
Note that this year's syllabus doesn't correspond perfectly with that of the last five years.
University calculator
These are for when exams take place in the normal manner. They will be provided for the Maths exam.
SCHEDULE Return to the top
What am I doing and when?
Short answer.
Long answer.
The official detailed syllabus is
here.
This is a little incomplete.
SYLLABUS Return to the top The topics for this semester include
This unit is assessed 100% by examination only. There is no coursework element.
RESOURCES Return to the top
Main University webpage for students.
Mech Eng info for students (Moodle)
(You'll need to type your userid and password).
There is a
Maths and Stats Resource Centre at the
University of Bath. Called MASH, it operates drop-in sessions at various times.
In addition, there are further online
resources at the
Mathcentre
website.
MISCELLANEOUS Return to the top
Greek letters. Don't get your etas,
zetas and xis mixed up. Nor your phis and psis.
And meet your first discontinuous letter.
If you want hints on pronunciation depending on where you are in the world, then
this is the place.
SI prefixes and strange units of measurement.
Table of integrals.
History of the trigonometric functions.
Information on the hyperbola including where the name came from.
Why I am smug, what I don't expect in class, and I'm not sure that I believe this.
If it ever seems like this in a lecture, then you need to give me a good kicking!
Maths teaching in the past. Dodgy examples of exam/coursework submissions.
L'Hôpital's rule - the musical. (This isn't NSFW but....turn down the volume first!)
This is why your maths must be correct.
PROBLEM SHEETS AND SOLUTIONS Return to the top
Electronic copies of all the problem sheets and their solutions will eventually appear here. You'll be emailed whenever anything gets added. You are not expected to hand in your completed work.
Complex numbers:
Sheet 1 (2 pages)
[Available]
Solutions
[Available]
Differentiation:
Sheet 2 (2 pages)
[Available]
Solutions
[Available]
Differentiation:
Sheet 3 (1 page)
[Available]
Solutions
[Available]
Integration:
Sheet 4 (1 page)
[Available]
Solutions
[Available]
Integration:
Sheet 5 (2 pages)
[Available]
Solutions
[Available]
Series:
Sheet 6 (1 page)
[Available]
Solutions
[Available]
Series:
Sheet 7 (2 pages)
[Available]
Solutions
[Available]
ODEs:
Sheet 8 (2 pages)
[Available]
Solutions
[Available]
ODEs:
Sheet 9 (2 pages)
[Available]
Solutions
ODEs (extra, optional):
Sheet 9b (3 pages)
[Available]
Solutions
Laplace Transforms (preparatory:
Sheet 10pre (1 page)
Laplace Transforms:
Sheet 10 (2 pages)
[Available]
Solutions
Laplace Transforms:
Sheet 11 (2 pages)
[Available]
Solutions
[Not yet available]
COURSE NOTES Return to the top
These are meant to assist in your understanding of the various topics in the syllabus. If there is anything you didn't understand in the lectures, look it up here, and you won't be hindered by the remnants of a Welsh accent. Alternatively, you may wish to check out what I am about to do in the next lecture. Most of the examples presented in these printed notes are different from the ones given in the lectures so these may also be of some use.
The full set of Semester 1 notes is here.
But if you wish to go to the first page of the different sections, then these are the links:
0. Introductory material
1. Complex numbers
2. Differentiation
3. Integration
4. Series
5. ODEs
6. Laplace Transforms
Problem Sheets
HANDOUTS Return to the top
Checklist
for hyperbolic functions.
Proof of the
H=hxxhyy-(hxy)2 test. (Semester 2 and for interest only - not examinable).
MY VIDEOS
Return to the top
SEMESTER 1
Complex numbers: (2 videos).
Video (42.15)
Slides L1: Definition, arithmetic, complex exponentials, de Moivre.
Video (23.21)
Slides L2: Roots of complex numbers. Relation with hyperbolic functions.
Differentiation: (3 videos).
Video (14.22)
Slides L3: Introduction, limit definition, notation.
Video (39.19)
Slides L4: Product, chain and quotient rules.
Video (19.04)
Slides L5: Critical points.
Integration: (4 videos, but 3 lectures).
Video (19.00)
Slides L6a: Introductory bits and pieces.
Video (32.53)
Slides L6b: Integration by substitution.
Video (27.39)
Slides L7: Integration by partial fractions.
Video (36.07)
Slides L8: Integration by parts.
Series: (4 videos, but 3 lectures).
Video (64.14)
Slides L9: Binomial series.
Video (27.38)
Slides L10: Taylor's series.
Video (38.52)
Slides L11a: d'Alembert's convergence test.
Video (26.17)
Slides L11b: l'Hôpital's rule.
Ordinary Differential Equations (5 lectures)
Video (42.39)
Slides L12: Classification, reduction to first order form.
Video (41.40)
Slides L13: Separation of Variables, First Order linear.
Video (42.52)
Slides L14: Homogeneous linear constant-coefficient ODEs.
Video (30.29)
Slides L15: Inhomogeneous linear constant-coefficient ODEs I.
Video (20.02)
Slides L16: Inhomogeneous linear constant-coefficient ODEs II .
Laplace Transforms (4 lectures)
Video (39.25)
Slides L17: Introduction, LTs of some functions, some ODE solutions.
Video (43:59)
Slides L18: Unit impulse, integrals, ODE solutions with impulsive forcing.
Video (33:41)
Slides L19: Unit step function, s-shift and t-shift theorems.
Video (25:00)
Slides L20: Convolution: definition and theorem. Solution of systems of ODEs.
SEMESTER 2
In the process of being compiled and updated
ANCILLIARY VIDEOS Return to the top
In the process of being compiled
Curve sketching: (4 videos).
Video (27.43)
Slides 1: Polynomials, moduli, exponentials, hyperbolics.
Video (36.49)
Slides 2: Symmetries, envelopes, square roots and ratios of polynomials.
Video (4.12)
Scan: Extra ratios of polynomials case.
Video (11:21)
Scan: Extra examples of square roots of functions.
Surfaces: (1 video).
Video (40.49)
Slides 5: Surfaces, critical points and classification
Integration: (2 videos).
Video (43.34)
Slides 5: Applications I.
Video (27.30)
Slides 6: Applications II.
Vectors: (2 videos).
Video (34.07)
Slides 3: Areas, points and lines.
Video (27.13)
Slides 4: Points and planes. Some generalities.
Solutions of Laplace's equation in rectangular domains (1 lecture)
Video 3b (20.29)
Slides 3 (from page 13)
OTHER VIDEOS Return to the top
Solving a cubic which often needs complex numbers.
Tartaglia, del Ferro, Cardano, Ferrari et al.(36 minutes)
Multiplication and division of complex numbers. (7:01)
Roots of complex numbers despite the title of the video! (16:05)
Euler's identity as expounded by a viola-playing friend of mine. (5:19)
Taylor's series. The initial motivation is
a little different from mine. (12:42)
Integration (partial fractions). Not so keen on the last example. (50:05)
Integration (polar coordinates). Integrating the Gaussian, but
please please please don't expect me
to do it this way! (4:46)
Newton-Raphson. There are many interesting things in this video.
Probably it is better to watch this after knowing what the method is. (26:05)
Introduction to partial differentiation S2 (18:21)
PAST EXAM PAPERS Return to the top
Past papers are usually obtained from the library webpages, but the last five years' worth correspond to a
slightly differently-organised syllabus with a slightly different content and a different exam schedule.
The following links
also include my outline solutions (rather than full solutions) and my post-exam general feedback to the class.
2018/19
S1 paper
outline solutions
feedback
S2 paper
Outline solutions
Formal/Informal feedback document
2019/20
S1 paper
outline solutions
feedback
S2 paper
Outline solutions (full)
Outline solutions (short)
Formal/Informal feedback document
2020/21
S1 paper
outline solutions
feedback
S2 paper
Outline solutions
Informal feedback document
Formal feedback document
2021/22
S1 paper
outline solutions
feedback
S2 paper
Outline solutions
Informal feedback document
2022/23
S1 paper
outline solutions
feedback
S2 paper
Outline solutions
Informal feedback document
Note also that COVID affected some of these exams quite strongly.
18/19 and before: Both the S1 and S2 papers were in-person, on-campus, invigilated and two hours. Also for S1 in 19/20.
19/20: The S2 paper was open-book and online with three
weeks in which to return the scanned scripts for marking.
20/21: Both the S1 and S2 papers were open-book and online but now of 24 hours duration,
which included the scanning and uploading of the scripts.
21/22: The S1 paper was a two-hour open-book and online examination
with a maximum of 2 hours and 30 minutes to scan and upload the completed scripts.
Since then (i.e. S2 in 21/22 and both S1 and S2 for 22/23) my exams have been
written under normal conditions, i.e. in-person on campus,
invigilated and over two hours.
The Mathematics exam for 23/24 will be a three-hour paper in the Summer.
At the time of typing (i.e. 24/9/2023) I am unaware of any intermediate
exam or test, whether compulsory or optional.
There is a scanned version of the here. (This is the most recent 2019/2020 version. It is provided for the Maths exam).
UNIVERSITY CALCULATOR Return to the top
The University will be supplying the calculators which will be used for the ME12002 Mathematics exam.
I do not know what happens with other units!
Currently (i.e. September 2023)
the designated species is the Casio FX-991EX.
Further information on functionality may be found
here.
I would advise that you should get used to how this works, and the purchase of one may be the better option.
Even if you own an FX-991EX, you will be using a university calculator in the exam.
Essentially anything with the words "Engineering Mathematics" in the title is likely to be sound. So Glyn James, Stroud, Kreyszig, Croft and Davidson, Kuldeep Singh are all excellent.
Beware of the word "Advanced", as in "Advanced Engineering Mathematics" because some of these are seriously advanced. So check the contents pages. In fact, in book titles, the word "Elementary" doesn't always accord with the standard dictionary definition, and occasionally "An Introduction to..." requires you to have gained a PhD prior to even contemplating the merest possibility of looking inside the cover. So always check the index first. You've been warned.
HOWEVER, my advice is to check out some of these books in the Library prior to purchasing anything. Some people get on with Stroud but hate Croft, for example, whereas others feel precisely the opposite. Always check prices on amazon.co.uk.
You will generally find that textbooks have little to say about curve-sketching.
Last updated: 24th September 2023.
