Lecture notes and other supporting materials from a module given by me for the Mathematics Department of Nottingham University in 2005-07. Supplied as is, with no warranty as to their continued correctness! Use as you see fit, but please achnowledge this site if you publish or publicise this material.
Module convenor: Dr A. N. Walker.
[See also the entry for this module in the Catalogue of Modules.] This is a 10-credit level 3 module given in the Spring semester, and meant primarily for engineers, though other qualified students are welcome to attend. You will be assumed to have a general familiarity with basic engineering mathematics and with the University's computing facilities. It was previously given as HGCMCE.
There will be two lectures and either a computing session or an examples class per week. Assessment will be by a two-hour written examination [80%] and two courseworks [10% each].
We start with the basic philosophy of numerical analysis [NA], and its central problem of how to obtain accurate results to numerical problems by controlling errors. Then there are five sections, each dealing with one of the main relevant problem areas: basic NA and some simple methods; quadrature [the fancy name for numerical integration] and curve-fitting; numerical linear algebra; differential equations and partial differential equations. The symbolic algebra system Maple will be introduced and used to supplement and illustrate the methods.
I am not lecturing directly from any particular set book. But there is a wide choice of good books; see section QA 297 in the Library. My advice is to look for a recent edition of one of the `glossy' student texts, and check that you are happy with the general style. Although there is a lot of variation in the order of presentation, in the amount of detail and the number of worked examples. almost all such texts cover the material of this module, and much else besides. Modern books also usually include computer-related material. You may want to check that such material covers Maple, though the conversion from Mathematica or Fortran or Basic is easy enough for experienced computer users.
The following are commended -- there are at least six copies of each in the George Green Library:
Aims: The module aims to provide students with: techniques for finding approximate numerical, and especially computational, solutions to mathematical problems for which exact analytic solutions are unavailable or inappropriate; an appreciation of the difficulties involved in finding reliable solutions; methods for estimating errors in solutions in order to judge how reliable those solutions are.
Objectives: Successful students will have gained insight into the above three areas of study and will have gained practical knowledge of how to apply the techniques and methods to specific problems. [See also the more detailed content, below.]
Transferable skills: Numerical and computational skills; insight into efficiency of algorithmic processes.
All lectures are in A6, Pharmacy, on Tuesdays at 2pm and Thursdays at 9am. The clickable links with the lecture topics will take you to the lecture notes for that lecture, in either PDF or PostScript format.
| Jan 30th | 1 | Introduction; need for NA. PS or PDF |
|---|---|---|
| Feb 1st | 2 | Errors. PS or PDF |
| Feb 6th | 3 | Non-linear equations and other simple NA PS or PDF |
| Feb 8th | 4 | -- ditto -- PS or PDF |
| Feb 13th | 5 | -- ditto -- PS or PDF |
| Feb 15th | 6 | -- ditto -- PS or PDF |
| Feb 20th | 7 | Quadrature PS or PDF |
| Feb 22nd | 8 | -- ditto -- PS or PDF |
| Feb 27th | 9 | -- ditto -- PS or PDF |
| Mar 1st | 10 | -- ditto -- PS or PDF |
| Mar 6th | 11 | Linear algebra PS or PDF |
| Mar 8th | 12 | -- ditto -- PS or PDF |
| Mar 13th | 13 | -- ditto -- PS or PDF |
| Mar 15th | 14 | Ordinary differential equations PS or PDF |
| Mar 20th | 15 | -- ditto -- PS or PDF |
| Mar 22nd | 16 | -- ditto -- PS or PDF |
| Apr 24th | 17 | -- ditto -- PS or PDF |
| Apr 26th | 18 | Partial differential equations PS or PDF |
| May 1st | 19 | -- ditto -- PS or PDF |
| May 3rd | 20 | -- ditto -- PS or PDF |
During the `revision week', I shall keep `office hours' at the lecture times for otherwise unscheduled consultations with students. You are, of course, welcome to see me at any other time, whether or not by appointment, but at random times you take pot luck as to whether I am available and in my office, C302 Maths and Physics building. See the `availability' notice on my notice-board for better information.
These are scheduled for Friday 11am, either in Pope A16 [computer room, for the Maple sessions] or Pope B13 [committee room, for the problem classes], alternate weeks.
| Feb 2nd | 1 | Maple | Introduction | |
|---|---|---|---|---|
| Feb 9th | 1 | Problem Class | Errors | questions and solutions |
| Feb 16th | 2 | Maple | Basic commands | |
| Feb 23rd | 2 | Problem Class | Equations | questions and solutions |
| Mar 2nd | 3 | Maple | Equations and integrals | |
| Mar 9th | 3 | Problem Class | Quadrature | questions and solutions |
| Mar 16th | 4 | Maple | Linear algebra | |
| Mar 23rd | 4 | Problem Class | ODEs | questions and solutions |
| Apr 27th | 5 | Maple | Differential equations | |
| May 4th | 5 | Problem Class | PDEs | questions [no solutions] |
| set | due in | |
|---|---|---|
| 1 | Feb 22nd | Mar 6th |
| 2 | Mar 20th | Apr 26th |
New! Here is the draft version of the 2006-07 exam together with solutions and feedback. The results seemed to be overall very satisfactory, with the coursework and exam being slightly but clearly better than last year or the year before, and with attendance at problem classes and the Maple workshops also better. Well done! [I don't have your individual marks, thanks to anonymous marking, and in any case they are not yet finalised, so don't ask! -- ANW]