Course 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
EXAM NOTES
Online session 1. Tuesday May 9th.
notes
video
Online session 1. Thursday May 18th.
notes
video
My full revision timetable is below (and it includes the timetable for ME10305 Maths 2). Please note that, at other times, I may be off-campus or engaged in final year project duties. Of course I am emailable.
You will see that I have some online sessions and some in-person sessions. So do make sure that
you are well prepared before seeing me; by this I mean that you need to make sure that
all the necessary bits of paper are immediately to hand - those behind you in the queue
won't be as patient as I am if you're searching for that bit of paper which you knew for sure
was hiding in that folder or was it that bag or back in your room on the table.....
Exam questions will be similar in style to those available online. Please note that solutions of Laplace's equation in squares and circles will not be on the exam paper even though these aspects of Separation of Variables and Fourier Series were in the videos. The solution of Laplace's equation in sectors of a circle could be on the paper.
Some definitions will be given on the paper. These include the appropriate Fourier Series
and Fourier Transform. They will also include the convolution theorem and the symmetry theorem should they be needed.
Transforms of derivatives and the shift theorems will not be stated on the paper but you will need to know how to
derive them.
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| Wed 3rd May | 10:15 to 11:15 | ME10305 | Problems class | Online |
| Thu 4th May | 12:15 to 13:15 | ME20021 | Problems class | 4E 3.40 |
| Thu 4th May | 13:15 to 14:15 | ME10305 | Office hour | 4E 2.54 |
| Fri 5th May | 11:15 to 13:15 | ME10305 | Problems class | 4E 3.40 |
| Tue 9th May | 9:15 to 10:15 | ME10305 | Problems class | Online |
| Tue 9th May | 10:15 to 11:15 | ME20021 | Problems class | Online |
| Fri 12th May | 10:15 to 12:15 | ME10305 | Office hour | 4E 2.54 |
| Fri 12th May | 10:15 to 12:15 | ME20021 | Office hour | 4E 2.54 |
| Thu 18th May | 9:15 to 10:15 | ME10305 | Problems class | Online |
| Thu 18th May | 10:15 to 11:15 | ME20021 | Problems class | Online |
| Mon 22nd May | 12:15 to 14:15 | ME10305 | Office hour | 4E 2.54 |
| Thu 25th May | 10:15 to 11:15 | ME20021 | Problems class | Online |
| Fri 26th May | 11:15 to 14:15 | ME20021 | Office hour | 4E 2.54 |
TYPESET notes
covering both Fourier Series and Fourier Transforms may be found
here .
If you have ordered one then you should have a physical copy of this.
Important:
There will be a lot of integration by parts. Please refresh your knowledge on this
by going to my ME10304 Mathematics 1 website and checking out the 4th Integration video
or the corresponding slides:
here .
Maths 1 and Maths 2 from year 1.
If you need to check out any of those topics, then here
they are:
ME10304 Maths 1 and
ME10305 Maths 2.
Syllabus:
My part of
the syllabus for this semester includes the use of
(i) Fourier Series and
(ii) Fourier Transforms, to
solve the three most common partial differential equations, namely,
Fourier's equation, Laplace's equation and the
wave equation.
Lecture plan:
1.
Video 1 (42.42)
Slides 1
Introduction to Separation of Variables for PDEs
2.
Video 2 (23.36)
Slides 2
Further examples. Full problems with half-range Fourier Series
2b.
Video 2b (22.43)
Slides 2b
Further examples. As video 2 but using the wave equation and many graphs!
3.
Video 3a (32.16)
Video 3b (20.29)
Slides 3
Fourier Cosine Series and Quarter-range Sine series (in video 3a). Solutions in finite domains (in video 3b).
4.
Video 4 (41.37)
Slides 4
PDEs in polar coordinates
5.
Video 5 (34.20)
Slides 5
Introduction to Fourier Transforms. 1. Definition and examples of transforms. Symmetries. Physical meaning.
6.
Video 6 (30.10)
Slides 6
Introduction to Fourier Transforms. 2. The two Shift theorems. Symmetry theorem. Convolution theorem. An ODE example.
7.
Video 7a (30.10)
Video 7b (27.10)
Slides 7
Application to PDEs 1. Fourier's equation and Laplace's equation.
8.
Video 8 (47.28)
Slides 8
Application to PDEs 2. FST and FCT. Introduction and example solutions.
Weekly plan (Updated January 4th 2023)
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|---|---|
| Mon 6th February DNJ | Tue 7th February DNJ |
| Mon 13th February DNJ | Tue 14th February DNJ |
| Mon 20th February DNJ | Tue 21st February DASR |
| Mon 27th February DNJ | Tue 28th February DASR |
| Mon 6th March DNJ | Tue 7th March DASR |
| Mon 13th March DNJ | Tue 14th March DASR |
| Mon 20th March DNJ | Tue 21st March DASR |
| Mon 27th March DNJ | Tue 28th March DASR |
| Mon 3rd April Easter | Tue 4th April Easter |
| Mon 10th April Easter | Tue 11th April Easter |
| Mon 17th April DNJ | Tue 18th April DASR |
| Mon 24th April DNJ | Tue 25th April DASR |
| Mon 1st May No lecture (P/H) | Tue 2nd May No lecture |
| Mon 8th May Revision week | Tue 9th May Revision week |
Problem Sheets:
Sheet 1 (fundamental solutions):
( problem sheet )
( solutions )
Sheet 2 (full problems I):
( problem sheet )
( solutions )
Sheet 3 (full problems II):
( problem sheet )
( solutions )
Sheet 4 (full problems III Polar coordinates):
( problem sheet )
( solutions )
Sheet 5: (Fourier Transforms - Introductory bits):
( problem sheet )
( solutions )
Sheet 6: (Fourier Transforms, Fourier Sine and Cosine Transforms)
( problem sheet )
( solutions )
Helpful Handouts
Four Figures (Laplace in a square
domain )
Hyperbolic functions
( hyperbolics.pdf )
Some comments on the ODEs which arise in the separation of variables:
( comments )
The various types of Fourier Series (non exhaustive, believe it or not):
( handout )
An example of each of the Fourier Series showing convergence:
( handout )
Definition of the Fourier Transform and some of its properties:
( defns )
Introductory lecture on FTs:
handout
slides
The Fourier Sine and Cosine Transforms handout:
( handout )
Here are some notes on Fourier himself, his life, work and death:
( notes )
Integration by Parts. Check out last year's notes
at
notes
and the problem and solutions sheets which are retrievable from the
Maths 1 webpage.
Past papers.
These may be found
here. Or else my two questions
are given below:
16/17
Outline solutions
Informal feedback document
Formal feedback document
There is a scanned version of the exam formula book
here.
(This is the new 2019/2020 version).
The University will be supplying calculators for the Modelling Techniques 2 exam.
17/18
Outline solutions
Formal feedback document
18/19
Outline solutions
Formal feedback document
19/20
Outline solutions
Formal feedback document
20/21
Outline solutions
Informal feedback document
21/22
Outline solutions
22/23
Outline solutions
Currently (i.e. May 2023)
the designated species is the Casio FX-991EX.
Further information may be found
here.