Introduction to Numerical Algorithms

• explain and apply basic notions such as iteration and convergence
• discuss the effect of truncation and rounding errors
• critically compare alternative methods regarding efficiency and accuracy
• apply numerical algorithms to actual (simple) problems
• implement simple numerical algorithms in Python
• apply existing Python programs in the solution of a given problem
• perform sensitivity analysis of a simple problem
• estimate and in some cases derive estimates of the accuracy of the computed solution
• convey and discuss the topics of the course in a clear technical language
• develop computational methods in such that they are first tested and evaluated on selected test problems

Approximations and rounding errors. Numerical algorithms for solving systems of linear equations, interpolation, numerical integration, roots in functions, linear data fitting, and ordinary differential equations. Implementation and use of selected numerical algorithms in Python.

02002/02631/02632/02633/02525/01002/01004/01005/01006/01015/01016, Taylor’s formula, roots of polynomials, ordinary differential equations and linear algebra. These subjects are covered by 01005/01006 Mathematics 1 whos second semester has to be taken at least at the same semester. Elementary programming in Python.

Lectures and exercises in the databar.

The course gives a general introduction to numerical algorithms. It is a prerequisite for the following courses given by the scientific computing group at DTU Compute: 02526 – Mathematical Modeling, 02610 Optimization and Data Fitting, 02614 High Performance Computing, 02616 Large-Scale Modelling,02623 The Finite Element Method for Partial Differential Equations, 02624 – Inverse Problems and Imaging, 02686 – Scientific Computing for differential equations 1.