Module

Description

M1: Number representation and errors

Floating point representation of real numbers, rounding errors

M2: Systems of linear equations

Algorithms for the solution of systems of linear equations. Gauss method, Gauss – Seidel iterative method, pivot strategies

M3: Solution of non-linear equations

Numerical solution of equations and study of convergence properties. Bisection method, Secant method, Newton ’s method, other iterative methods, Aitken, Steffenson

M4: Function approximation

Polynomial interpolation of functions and approximation of functions by means of regression methods. Interpolation ( Newton ’s method, splines), Curve fitting (least squares method)

M5: Numerical integration

Numerical solution of definite integrals by means of function approximation. Trapezoidal rule, Simpson’s rule, Romberg integration, adaptive integration

M6: Numerical solution of differential equations

Numerical solution of differential equations by iterative methods. Euler’s method, Runge Kutta methods, implicit methods, stiffness and stability