COMPUTATIONAL MATHEMATICS
- Overview
- Assessment methods
- Learning objectives
- Contents
- Full programme
- Bibliography
- Teaching methods
- Contacts/Info
Linear algebra, calculus, programming.
Written and oral exam.
The written exam has a 3 hours duration. It requires the definition and analysis by written hand of the proposed numerical methods followed by a Matlab implementation for checking the theoretical analysis.
The first part of the exam is on the approximation of zeros of functions and the second part on the solution of linear systems.
The oral examination could be optional according to the written exam.
Basic skills to define, analyse and implement numerical methods and to evaluate both stability and computational cost.
Representation of numbers on PC and operations floating point.
Introduction to Matlab, scripts and functions. Recursion and plot of functions. Representation of numbers on the computer and error analysis. Evaluation of a polynomial at a point. (about 10 hours)
Numerical methods for approximating zeros of real functions in one variable: bisection method, functional iteration with convergence and order of convergence, Newton’s method and variants. (about 23 hours)
Solution of linear systems: conditioning, triangular linear systems, Gaussian elimination with pivoting and LU factorization, definition and convergence of stationary iterative methods, the iterative methods of Jacobi and Gauss-Seidel. (about 23 hours)
Representation of numbers on PC and operations floating point.
Introduction to Matlab, scripts and functions. Recursion and plot of functions. Representation of numbers on the computer and error analysis. Evaluation of a polynomial at a point. (about 10 hours)
Numerical methods for approximating zeros of real functions in one variable: bisection method, functional iteration with convergence and order of convergence, Newton’s method and variants. (about 23 hours)
Solution of linear systems: conditioning, triangular linear systems, Gaussian elimination with pivoting and LU factorization, definition and convergence of stationary iterative methods, the iterative methods of Jacobi and Gauss-Seidel. (about 23 hours)
“Scientific Computing with Matlab and Octave”, di A. Quarteroni e F. Saleri, Springer.
Teaching in the computer laboratory
Meeting by appointment.