Objectif
Part of the Bachelor in economics and management, Numerical Methods I is typically taken in the second year of the studies. The lectures and lab sessions introduce economics majors to scientific computing and to numerical methods often used for the solution of mathematical problems encountered in Economics and Statistics. MATLAB is the software environment used for implementation and application.
Descriptif
Topics covered :
- Algorithmic, a brief review
The fundamentals. Elements of syntax and implementation in Matlab
- Floating point arithmetic's and error measures
Rounding, truncation errors. Underlying mechanism of numerical instability, problem condition and error propagation.
- Interpolation and extrapolation
Interpolation: Theoretical fundamentals (Lagrange), Neville, Newton, Hermite, Spline functions
Extrapolation
- Numerical integration and differentiation
Integration: Newton-Cotes, Euler-Maclaurin, Richardson extrapolation, Gauss quadrature, Monte Carlo integration
Differentiation : finite differences, conditioning problems, Cauchy.
- Root finding algorithms
Bisection, bracketing, linear interpolation, fixed point, secant, Newton, combined methods. Error analysis