ME20021 MODELLING TECHNIQUES 2.

ME20021 MODELLING TECHNIQUES 2.

Last updated 02/05/2023.

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 (2022/2023)


   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.


  Revision sessions for ME10305 and ME20021 (DASR) 2022/2023  

  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)


WEEKLY PLAN FOR ME20021 2022/2023

  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
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  

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

UNIVERSITY CALCULATOR

The University will be supplying calculators for the Modelling Techniques 2 exam.
Currently (i.e. May 2023) the designated species is the Casio FX-991EX.
Further information may be found here.