M. Giaquinta, G. Modica, Note di Metodi Matematici per Ingegneria Informatica, Edizione 2007, Pitagora editrice, Bologna.
G.Modica, L. Poggiolini, Note di calcolo delle Probabilità, seconda edizione, 2013, Pitagora editrice, Bologna.
Learning Objectives
Be fluent with the proposed techniques and mathematical models
Prerequisites
Geometry, Linear Algebra, Mathematical Analysis
Teaching Methods
Frontal teaching
Type of Assessment
Three written exams during the course or Final Oral Exxamination
Course program
Selfadjoint operators on finite dimensional Euclidean and Hermitian spaces. Jordan's, polar and SVD decompositions of matrices. Least squares.
Moore-Penrose pseudoinverse. Tikhonov regularization.
Complex power series, holomorphic functions. Goursat's theorem. Singularities and residues. Computation of integrals and sums using the residues.
Banach's fixed point theorem. Powers of a matrix.
System of linear ODEs and the exponential matrix. Putzer method.
Probability measures. Bayes's formula, random variables. Independence.
Weak and strong law of large numbers. Monte Carlo method. Central limit theorem. Bernoulli's and Poisson's processes. Regular stochastic matrices.
Discrete time Markov chains with finite states. Characteristic parameters.
Continuous time Markov chains with finite states. Uniformization method.