Topics in Scientific Computing

Volledige vakbeschrijving

Scientific computing concerns the use of computers to analyze and solve problems arising in biology, chemistry and physics. This generally involves the construction of a mathematical model of the scientific problem, and solving the mathematical problem using computational algorithms. The purpose may be to improve the understanding of natural phenomena or to make predictions of behaviour under different conditions. A broad range of scientific problems can be tackled computationally, including simulation methods (for dynamic systems); transform methods (for processing data and images) and optimisation methods (for learning models from data and improving technological processes). This course will focus on well-established algorithms which will each be applied to a realistic scientific case study. The methods are frequency- domain Fourier/wavelet analysis (for signal processing and quantum physics), principle component analysis and clustering algorithms (for classification of images), integrators for ordinary differential equations (for simulation and control of spaceships), finite-difference solvers for partial differential equations (for investigating pattern formation), and combinatorial optimisation (for phylogenetic reconstruction). The course will be entirely based on the use of Matlab, a high-level scientific programming language and interactive environment for numerical computation, visualization, and programming. This course is complemented by MAT3005 Numerical Mathematics, in which students learn in more depth the basic algorithms of scientific computing.