Introduction to Computational Science

Computational Science, i.e. the mathematical modeling and numerical simulation of real world problems in natural and social sciences, engineering, finance, biology, and medicine, is of paramount importance for our modern knowledge and technology driven society. In fact, nowadays, computational science is indispensable in science and industry. Within this course, we will introduce basic and central concepts and techniques of mathematical modeling and numerical simulation and we will show how they can be used to model and simulate model problems and realistic problems. Topics will include condition numbers, numerical solution of linear systems, numerical solution of dynamic problems, and classical interpolation and approximation. Each of the presented numerical methods will be mathematically analyzed, implemented, and tested along an illustrative problem. Thus, the course will not only introduce methods and tools in Computational Science, but it will also create a direct bridge between theory and application.

REFERENCES

• Numerical Analysis in Modern Scientific Computing: An Introduction (Springer, Texts in Applied Mathematics) by Andreas Hohmann, Peter Deuflhard