Evolution Processes in Mathematical Physics

Credits

Prerequisites

None.

Scientific-disciplinary sector (SSD)

MAT/07 Mathematical Physics.

Examination method

Oral exam.

Learning
objectives

To provide students with some advanced mathematical methods for the study of evolution processes governed by differential equations. To enable students to read and understand recent contributions to the scientific literature aimed at practical applications in various areas of the Applied Sciences, such as Economics, Engineering, Epidemiology and Biology.

Syllabus

Tools of qualitative analysis, such as Stability Theory, Bifurcation Theory and Optimal Control Methods, for the study of processes governed by finite- and infinite-dimensional differential equations, such as growth processes, diffusion processes and processes with delay.

Expected learning
outcomes

By the end of the course, students must demonstrate that they

understand and know the general issues relating to the study of the time evolution of systems in the Applied Sciences (Economics, Engineering, Biology);
are able to apply the theoretical knowledge acquired to identify and solve specific mathematical models of the Applied Sciences;
are able to communicate ideas and solutions clearly, rigorously and effectively to both specialist and non-specialist audiences;
are able to identify the most appropriate methods to analyse and solve a problem relating to the course topics and to interpret the results correctly.

Learning outcomes
to be assessed

Ability to study evolution processes in the Applied Sciences using advanced mathematical techniques, demonstrating clarity, correctness and completeness in the oral presentation of the course topics.

Evolution Processes in Mathematical Physics