Scientific Computing

Skills
At course completion, the student should be able to:

• Choose an appropriate numerical method for the solution of the problem or sub-problem. The numerical method is selected among the methods presented in the course and it should be chosen with respect to the requirements of the model.
• Evaluate the numerical method with respect to potential accuracy, computational efficiency, robustness and memory requirements.
• Understand and program the numerical method from scratch in Python/Numpy, and solve the problem using their own programs.
• Calculate the quality of the solution with respect to the accuracy obtained and the sensitivity to model parameter variations.
• Estimate whether the quality of the solution is adequate relative to the desired use of the model.
• Analyse the reasons of a possible total failure of a method applied to a concrete problem.

Competences
The student will be able to use the methods presented in the course to perform numerical analysis for concrete problems in science, choose and program computational methods to solve them, and quantitatively bound the errors of the results obtained.

The solutions will be programmed in Python/Numpy.

Knowledge

The student will know about

• ideas behind and motivation for fundamental numerical methods for the solution of: linear and nonlinear equations, linear and nonlinear optimization, eigenvalue problems, initial value problems for ordinary differential equations, partial differential equations and the fast Fourier transform.
• simple mathematical models from science and numerical analysis of them.
• methods for expressing mathematical models concisely as efficient, correct program code.