In this course we will consider the problem how to use a computer to solve mathematical problems. Is there a method to solve systems of linear equations involving hundreds of variables? What is the fastest way to reach a root of a given function? How can one compute an approximate value for an integral? Is it possible to predict how accurate this value might be compared to the exact solution?
We will study methods, so-called algorithms, that at least partially solve these questions. The aim is to understand why they work and what limitations they have. In particular, we will derive statements concerning the numerical error involved in these computations.
Programming will be a substantial part of the course; so it is required that all participants have access to a computer on which they can install software. We will mainly focus on Matlab and Mathematica, but other languages can also be used.
A first reference for this course is the following book which is available for download from the UGA network.
- Quarteroni, Saleri, Gervasio. Scientific Computing with MATLAB and Octave (Springer 2014)
- MATH 3000 or MATH 3300 or MATH 3500 or MATH 3500H
- MATH 3100