Key words
Numerical mathematics
Objectives
Having insight in the diverse errors that can appear when calculating using a computer and how these errors propagate themselves. How to avoid gross errors in designing calculus algorithms, interpretation of the accuracy of numerical solutions.
Analysis of the iterative calculating processes and drawing up structure diagrams of the algorithms to get more insight in some programming techniques.
Acquiring some math ematical techniques and ideas that are commonly in use, like curve-fitting.
Prerequisites
Knowledge of linear algebra, differential calculus and programming structures as mentioned in the first year.
Topics
- Introduction: Object of numerical mathematics, accuracy and errors.
- Linear algebra: general ideas, Gauss' and Doolittle's method , calculating determinants and inverse matrices, Jacobi's and Gauss-Seidel's iteration method, errors in solving linear systems.
- Non-linear equations: generalities, iterative methods for one equation, extension for systems.
- Interpolation: Problem proposition, finite differentials, interpolating polynomials, spleen-interpolation.
- Numerical integration: problem proposition, integration with Riemann-sums, method of indefinite coëfficiënts, Newton-Côtes' formula, trapezium and Simpson's rule, Romberg's method and similar.
- Curve-fitting (Smallest squares methods).
Teaching Methods
Lectures, exercises.
Materials used
Teacher's course.
Study guidance
Assessment
Written examination.
Study costs
€ 10
Lecturer(s)
Language
Dutch
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