G12NAN -- Numerical Analysis

Lecture notes and other supporting materials from a module given by me for the Mathematics Department of Nottingham University in 2003 and other years. 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.

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General Information:

New! Commentary on the attempted solutions to the May 2003 Exam. Old! Commentary on the attempted solutions to the May 2002 Exam. Very old! Commentary on the attempted solutions to the May 2001 Exam.

This is a 10-credit level 2 module given in the Spring semester, and meant primarily for Honours mathematicians and computational chemists, though other qualified students are welcome to attend. You will be assumed to have a general familiarity with concepts of computing, limits and other mathematical skills, such as could be obtained from modules G1ACOM, G1ALIM and G1AMSK.

There will be two lectures per week, and a problem class in [mostly] alternate weeks. Assessment will be by a two-hour written examination. Coursework will be set, but it will not count for assessment.

Content:

Reading:

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:

• Numerical Analysis, Burden and Faires, ITP, 6th edition 1997, QA 297 BUR.
• Numerical Mathematics and Computing, Cheney and Kincaid, ITP, 3rd edition 1994, QA 297 CHE.
• Applied Numerical Analysis, Gerald and Wheatley, Addison-Wesley, 5th edition, 1994, QA 297 GER.
• Theory and Applications of Numerical Analysis, Phillips and Taylor, Academic Press, 2nd edition, 1996, QA 297 PHI.

Aims, objectives, transferable skills:

Aims: The module aims to provide students with: techniques for finding approximate numerical 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, such as finding roots of equations, quadrature, the numerical solution of ODEs and linear algebra.

Transferable skills: Numerical skills; insight into efficiency of algorithmic processes.

Lectures:

Tuesday lectures, odd numbers, are at 3pm in C4; Thursday lectures, even numbers, at 10am also in C4. The clickable links for the lecture topics will take you to the OHP slides for that lecture.

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. See the `availability' notice on my notice-board for better information.

Problem Classes:

These are also in C4, on Fridays at 2pm and the following Tuesdays at 10am; they interleave with those for G12LAG. You should normally attend the Friday class if your last name begins with A to K, or the Tuesday class if with L to Z. You may attend the `other' class if timetabling makes this necessary.

Coursework:

These too interleave with those for G12LAG,

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