Introduction to Scientific Computing

Abstract

This course offers an introduction to the basics of scientific computing and modelling with applications in biology and biomechanics. The covered topics include floating point arithmetic, error estimation, spatial and temporal discretization techniques, numerical integration methods, stability, numerical solution of differential equations, particle simulations, parallelization etc.

Objective

This course aims at providing basic knowledge required to address scientific questions using quantitative numerical methods and computing. Students learn to recognize potential pitfalls and limitations associated with discretization and approximative numerical methods, and to select appropriate solution techniques for a given numerical problem.

Content

Besides experiments and theory, numerical simulations have become the third pillar of natural sciences and engineering. This course introduces fundamental principles of numerical computing and modelling with applications in biology and biomechanics. The course includes hands-on practical programming exercises in which the students learn how to implement and perform various numerical simulations. Time permitting, the tentative list of topics is: • Floating-point arithmetic • Algorithmic complexity • Numerical root finding • Numerical quadrature & integration • Mass-spring systems • Time propagation & stability • Particle simulations, molecular dynamics • Error estimation • Uncertainty propagation • Cell & tissue models • Ordinary & partial differential equations • Finite difference method • Finite element method • Parallel computing & computer architecture

Resources