Numerical Methods
This course is an introduction to scientific numerical
computation. Students are introduced to the elementary
problems of numerical computation. Practical solution methods are
described and implemented. The emphasis is on practical methods
and the issues that arise from them.
Mathematical sophistication is not assumed and all the
necessary tools are introduced in lectures.
Motivation
There is very
little need for understanding when a numerical computation program
or package produces accurate answers with reliable error bounds in
a reasonable time. But what should be done if
- the answers are suspected of or known to be grossly in error,
- the program takes far too long, or in the extreme case
- the program simply fails and its execution is stopped?
Well-engineered numerical software does as much as can be done
in these situations. Numerical software is used in almost all
areas of science and engineering and many other areas of computing
too. Some areas where numerical software is used but which might
not occur to you first-up include, computer graphics, image
processing and hardware design.
The numerical problems that will be addressed in the course
will come from among the following topics. Floating point numbers
and their representations, subtractive cancellation, machine
epsilon. Solution of non-linear equations by fixed point iteration
methods. Approximation of functions by polynomial and spline
functions. Methods of numerical integration, simple and composite
rules. Numerical solution of differential equations.
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