Advanced Mathematical Physics

Credits

Prerequisites

None.

Scientific-disciplinary sector (SSD)

MAT/07 Mathematical Physics.

Examination method

Oral exam.

Learning
objectives

Acquisition of methodologies and skills in Analytical Mechanics with reference to applications. The course also aims to provide the first notions concerning the derivation of the classical partial differential equations of Mathematical Physics and their applications.

Syllabus

Hamilton’s canonical equations. Lagrangian models. Cyclic or ignorable coordinates. Variational principles of Mechanics. Canonical transformations. Elements of the theory of first-order linear and nonlinear partial differential equations. The Hamilton-Jacobi equation and its integration: the case of separation of variables and applications. Classical equations of Mathematical Physics and applications. Introduction to Continuum Mechanics. The perfect fluid model. Integral balance laws and their local formulation.

Expected learning
outcomes

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

know and understand the general issues relating to the study of the evolution of systems;
are able to apply the methodologies acquired, with the aid of the most suitable tools, in order to describe the evolution of a given system consistently with phenomenological reality;
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 related to the course topics and to interpret the results correctly.

Learning outcomes
to be assessed

Ability to use the techniques provided during the course for the study of the evolution of systems; clarity, correctness and completeness in the oral presentation of the course topics.

Advanced Mathematical Physics