Roberta Marziani
University of Siena - Dipartimento di Ingegneria dell'Informazione e Scienze Matematiche
Course Type
Type B
Calendar
8-17/4/2026
Room
Program
This course introduces the principles of mathematical modeling and their application to microscopic-scale systems in engineering and the physical sciences. It explores how real-world phenomena are represented through mathematical structures, emphasizing the interplay between modeling, analysis, and computation. At the microscopic level, models are formulated as ordinary differential equations describing the evolution of interacting elements. Applications include population dynamics, vehicular traffic flow, mechanical and electrical systems, and biological processes. Topics cover model derivation, classification of ODE problems, stability and bifurcation analysis, and introductory numerical and perturbation methods. The course develops the ability to design and analyze models that connect mathematical theory with practical applications.
