Unit lecturer: Dr D A S Rees Department of Mechanical Engineering. Room 4E 2.54.

Telephone: (01225) 386775 (Office)
E-mail Address: or

QUICK LINKS     (Last updated 14/04/2021 14:00)
Notes, videos, problem sheets:
   Course notes You should already have a copy of these, but here are the originals should they be needed.
   My videos Links to my lecture videos (and the associated slides) will appear here gradually as the semester progresses.
   Problem sheets and solutions These will be unveiled gradually as the semester progresses.
Ancilliary information:
   Syllabus Increasingly detailed lists of what we will be doing.
   Resources Some links to external support.
   Greek letters and miscellaneous info.
   Handouts Some extra information that may be useful.
   Textbooks Some advice on textbooks.
   Past exam papers These cover the last five years. Includes outline solutions and general feedback.
   University calculator These are used when exams take place in the normal manner.
LOIL notes: Their usefulness is in the eye of the beholder but they are a record of what was discussed!
   Links for Zoom meetings on Moodle.    Direct link for the LOIL (Everything 2) on April 23rd at 14:15.
   Feb 3rd notes  Feb 3rd video ODEs 1
   Feb 5th notes  Feb 5th video ODEs 2
   Feb 10th notes  Feb 10th video ODEs 3
   Feb 12th notes  Feb 12th video ODEs 4
   Feb 17th notes  Feb 17th video ODEs 5 / Matrices 1
   Feb 19th notes  Feb 19th video ODEs 6 / Matrices 2
   Feb 24th notes  Feb 24th video Matrices 3
   Feb 26th notes  Feb 26th video Matrices 4
   Mar 3rd notes  Mar 3rd video Matrices 5
   Mar 5th notes  Sorry, there was a glitch with the recording.
   Mar 10th notes  Mar 10th video Laplace 1
   Mar 12th notes  Mar 12th video Laplace 2 LT of an integral 
   Mar 17th notes  Mar 17th video Laplace 3
   Mar 19th notes  Mar 19th video Laplace 4
   Mar 24th notes  Mar 24th video Numerical 1
   Mar 26th notes  Mar 26th video Numerical 2
   April 14th notes  April 14th video Fourier 1
   April 16th notes  April 16th video Fourier 2
   April 21st notes  April 21st video Everything 1

MY VIDEOS All to appear in due course.

Ordinary Differential Equations (5 lectures)
   Video (42.39) Slides 1: Classification, reduction to first order form. (29/01/2021)
   Video (41.40) Slides 2: Separation of Variables, First Order linear. (29/01/2021) (Corrected)
   Video (42.52) Slides 3: Homogeneous linear constant-coefficient ODEs (05/02/2021)
   Video (30.29) Slides 4: Inhomogeneous linear constant-coefficient ODEs I (05/02/2021)
   Video (20.02) Slides 5: Inhomogeneous linear constant-coefficient ODEs II (05/02/2021)
Matrices (5 lectures)
   Video (41.47) Slides 1: Matrices: definition, multiplication and the zoo (12/02/2021)
   Video1 (20.54)   Video2 (40.23) Slides 2: Matrices: Determinants and Cramer's rule (19/02/2021)
   Video1 (24.54)   Video2 (6.57) Slides 3: Matrices: Gaussian Elimination (19/02/2021)
   Video (47.38) Slides 4: Eigenvalues and eigenvectors 1 (26/02/2021)
   Video 2 (25.29) Slides 5: Eigenvalues and eigenvectors 2 (26/02/2021)
   Video 2b (9.39) Slide 5b: Eigenvalues and eigenvectors 2b Extra example. (26/02/2021)
Laplace Transforms (4 lectures)
   Video (39.25) Slides 1: Introduction, LTs of some functions, some ODE solutions. (02/03/2021)
   Video (43:59) Slides 2: Unit impulse, integrals, LT. ODE solutions with impulsive forcing. (03/03/2021)
   Video (33:41) Slides 3: Unit step function, s-shift and t-shift theorems. (10/03/2021)
   Video (25:00) Slides 4: Convolution: definition and theorem. Solution of systems of ODEs. (11/03/2021)
Numerical Maths (iteration schemes) (2 lectures)
   Video (39:00) Slides 1: Ad hoc iteration schemes for finding roots. (15/03/2021)
   Video (32:56) Slides 2: The Newton-Raphson scheme. (15/03/2021)
Least Squares (1 lecture) Joke
   Video (50:00) Slides: Lots of Least Squares stuff.
Fourier Series (3 lectures but 1 video)
   Video (50:01) Slides: Everything you need and more.


Howlers from the 2019/2020 S1 exams: Sheet 0 Answers 0 [Available]

ODEs: ODEs Sheet 1 [Available] Solutions [Available] on the separation of variables and first order linear equations.
ODEs: ODEs Sheet 2 [Available] Solutions [Available] on the solution of linear constant-coefficient equations.
ODEs: ODEs Sheet 2b [Available] Solutions [Available] (supplementary) on random, miscellaneous and difficult but hopefully interesting ODEs.

Fourier Series: Sheet [Available] Solutions [Available] on Fourier series and their role in solving ODEs with periodic forcing.

Laplace Transforms: Introductory Sheet [Available] Yes, do have a go at this one before we start the lectures on the topic!
Laplace Transforms: Sheet 1 [Available] Solutions [Available] on basic transforms and their application for solving ODEs, and on the unit impulse.
Laplace Transforms: Sheet 2 [Available] Solutions [Available] on the two shift theorems and the convolution theorem.

Matrices: Sheet 1 [Available] Solutions [Available] on products of matrices.
Matrices: Sheet 2 [Available] Solutions [Available] on determinants, Cramer's rule and Gaussian Elimination.
Matrices: Sheet 3 [Available] Solutions [Available] on eigenvalues, eigenvectors and the solution of systems of ODEs.

Least Squares: Sheet [Available] Solutions Ounces/grams data for Q2 [Available]

Numerical Mathematics: Sheet [Available] Solutions [Available]


The syllabus for this semester includes

1. What am I doing and when? Answer. (UPDATED 18/1/2021)
2. A more detailed account of the order in which subtopics appear. (UPDATED 19/1/2021)
3. The official detailed syllabus is here, but it is not accurate due to curriculum creep.

This unit is assessed 100% by examination only. There is no coursework element.


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.


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


Note on the solution of homogeneous systems of ODEs.
Handout on the speed of convergence of Fourier Series.
Handout for the matrix beauty parade.


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. 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


There is a scanned version of the exam formula book here. (This is the new 2019/2020 version).

PLEASE NOTE THE FOLLOWING. Due to syllabus changes over the years old Maths 1 papers will be useful for Fourier Series. Also we now solve ODEs with a Fourier Series forcing term on the right hand side.

15/16 paper   Outline solutions   Informal feedback document
16/17 paper   Outline solutions   Informal feedback document [Note: Fourier Series now replaces Probability.]
17/18 paper   Outline solutions   Formal/Informal feedback document [Note: No question on numerical integration due to strike action.]
18/19 paper   Outline solutions   Formal/Informal feedback document
19/20 paper   Outline solutions (full)   Outline solutions (short)   Formal/Informal feedback document


The University will be supplying calculators for the Mathematics exams.
Currently (i.e. September 2018) the designated species is the Casio FX-85ES.
Further information on functionality may be found here.