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

**Telephone:** (01225) 386775 (Office)

**E-mail Address:** D.A.S.Rees@bath.ac.uk or ensdasr@bath.ac.uk

**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.

** Examinations:**

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.
** 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.

**PROBLEM SHEETS AND SOLUTIONS**

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

- Ordinary Differential Equations
- Matrices
- Laplace Transforms
- Numerical Mathematics (iteration schemes)
- Fourier Series
- Least Squares Fitting of Data

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 AND MISCELLANEOUS INFORMATION**

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 amazon.co.uk.

**
There is a scanned version of the
**
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.