Numerical Analysis (5cr)

Objectives

This numerical analysis course focuses on combining mathematical theory and numerical techniques in computational sciences and technology. It teaches numerical discretization, approximation and solution methods for solving mathematical problems. The course has a variable content. After completing the course, the student will master the principles of numerical analysis for an entity which can  cover, for example, methods for discretizing ordinary differential and partial differential equations, solving linear and nonlinear systems as well as integrating and approximating functions. MATLAB software on will be preferred on the course. Alternatively the student can also use Python. The literature will be specific per course implementation.

Content

Core content:Discretizing ordinary differential equationsSolving linear and nonlinear systemsInterpolating functionsFunction approximationsNumerical integrationError analysisComplementary content:Matlab and/or Python in problem solvingVisualizing solutionsSpecial content:Numerical methods for partial differential equations, e.g., finite difference and finite element methodsRunge-Kutta and Leap-Frog methods for solving initial value problemsMethods for fining roots, e.g.,  Newton-Raphson methodPolynomial, spline and wavelet approximationsInterpolation methods such as Runge's methodNumerical quadratures, for example, Newton-Cotes -method, trapezoid and Simpson's formulaLeast squares fitting methods