Complements of mathematics

A.Y. 2017/2018
6
Max ECTS
64
Overall hours
SSD
MAT/01 MAT/02 MAT/03 MAT/04 MAT/05 MAT/06 MAT/07 MAT/08 MAT/09
Language
Italian
Learning objectives
Undefined
Expected learning outcomes
Undefined
Course syllabus and organization

Single session

Responsible
Lesson period
First semester
Course syllabus
1.Introduction. General aims of numerical analysis. Definitions, sources and propagation of errors. Condition number of mathematical problems and algorithms. Computer representation of real numbers.
2.Rootfinding for nonlinear equations. The Bisection method. Newton's method. The Secant method. One-point iteration methods. Convergence analysis, order of convergence and error estimation.
3.Numerical solution of systems of linear equations. Error analysis and condition number of linear systems. A)Direct methods. Triangular systems. Gaussian elimination. LU factorization. Pivoting. Variants of Gaussian elimination. B)Iterative methods. Jacobi, Gauss-Seidel and SOR iterations. The methods of steepest descent. General framework for iteration methods. Splitting. Convergence analysis and error prediction.
4.Interpolation and approximation theory. Uniqueness of the interpolation polynomial. Lagrange's and Newton's divided differences interpolation methods, Hörner algorithm. Interpolation error analysis. Chebyshev interpolation. Linear and cubic spline interpolation functions. The discrete least squares approximation (data fitting).
5.Numerical integration. Newton-Cotes integration formulas. Quadrature errors and degree of precision of quadrature formulas. Composite formulas. Gaussian formulas.
6.Approximation of eigenvalues and eigenvectors. Eigenvalue location. The Power method.
7.Approximation of ODEs. One-step methods: Euler, Crank-Nicolson, Runge-Kutta 2 and 4. Consistency, convergence, zero-stability, absolute stability.
MAT/01 - MATHEMATICAL LOGIC - University credits: 0
MAT/02 - ALGEBRA - University credits: 0
MAT/03 - GEOMETRY - University credits: 0
MAT/04 - MATHEMATICS EDUCATION AND HISTORY OF MATHEMATICS - University credits: 0
MAT/05 - MATHEMATICAL ANALYSIS - University credits: 0
MAT/06 - PROBABILITY AND STATISTICS - University credits: 0
MAT/07 - MATHEMATICAL PHYSICS - University credits: 0
MAT/08 - NUMERICAL ANALYSIS - University credits: 0
MAT/09 - OPERATIONS RESEARCH - University credits: 0
Practicals: 48 hours
Lessons: 16 hours