Elements of Probability and Statistics. Ordinary differential equations: first order systems; Cauchy problems; boundary value problems; Sturm-Liouville problems. Elements of complex analysis, functional analysis and of Fourier analysis. Partial differential equations.
M.Bramanti, C.D. Pagani, S. Salsa, Matematica, Zanichelli, Bologna, 2004.
V.Comincioli, Problemi e Modelli Matematici nelle Scienze Applicate, Casa Editrice Ambrosiana, Milano, 1993.
V.Comincioli, Metodi Numerici e Statistici per le Scienze Applicate, Casa Editrice Ambrosiana, Milano, 1992.
G.C. Barozzi, Matematica per l'ingegneria dell'informazione, Zanichelli, 2001.
S.Salsa, Equazioni a derivate parziali, Springer, 2004
Learning Objectives
Aim of the course is to provide the students an approach to mathematical modeling. In particular the object of this course is to give them the ability of making use of both deterministic and statistic techniques necessary to formulate a model, analyze it, and compare the results with experimental data.
Prerequisites
Courses required: none
Courses recommended: none
Teaching Methods
Total number of hours for Lectures (hours): 48
Type of Assessment
Oral test, at least 8 exam sessions.
Course program
Partial differential equations. Cauchy Problems. Radioactive decay. Linear systems. Stability of the stationary solutions. Phase plane. Linearization. Chemical oscillations.
Elements of complex analysis: complex functions; holomorphic functions. Power series. Analytic Functions.
Elements of functional analysis: linear spaces, Banach spaces, Hilbert spaces. Linear operators.
Elements of Fourier analysis: series expansions. Periodic functions; generalized functions. Fourier transform.
Boundary value problems. Sturm-Liouville problems. First Scroendinger equation. Partial differential equations. Wave equation, heat equation, diffusion equation.
Elements of Probability and Statistics. Applications: Brownian diffusion; Markov chains; statistical mechanics laws.