| Aims: |
- To introduce some methods for approximating a function by polynomials, splines and
rational functions.
- To introduce the concept of best approximation.
- To introduce Gaussian quadrature rules.
|
| Intended
Learning Outcomes: |
On successful completion of this module students will:
- Have acquired active knowledge and understanding of basic approximation theory
(including the formulation of some best approximation problems) and of an advanced
technique in numerical integration.
- Be able to approximate a function by a polynomial, piecewise polynomial or Padé
approximant.
|
| Pre-requisites: |
153, 157, 211 (ex-UMIST),
MT1202 Sequences and Series (ex-VUM)
This course is NOT available to students who
have taken MT2181 in previous years. |
| Dependent Courses: |
|
| Course Description: |
The first half of the course is concerned with approximation
theory. The aim is to approximate a complicated function by a much simpler function (such
as a polynomial), which is easier to evaluate, differentiate and integrate. In numerical
integration, the course builds on the ideas introduced in Module 157. A family of
integration rules, known as Gaussian quadrature rules, is introduced. |
| Teaching Mode: |
2 Lectures per week |
|
1 Tutorial per week |
| Private Study: |
5 hours per week |
| Recommended Texts: |
E, Suli and D
Mayers. An Introduction to Numerical Analysis. CUP, 2003. |
| Assessment Methods: |
Coursework: 20% |
|
Coursework Mode: Test in Week 7: Students will be asked to
write out their solutions to a small number of problems chosen from a set notified in
advance. |
|
Examination: 80% |
|
Examination is of 2 hours duration at the end of the First
Semester. |