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Department of Mathematics and Applications
"Renato Caccioppoli"


Mathematical Physics

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Mathematical Physics

Credits

12

Prerequisites

Mathematical Analysis 1.

Scientific-disciplinary sector (SSD)

MAT/07 Mathematical Physics.

Examination method

Written exam (exercises and numerical problems, possibly multiple-choice) and/or oral exam.

Learning
objectives

The course aims to provide students with the mathematical structures needed for the mathematical-physics knowledge required for the study of Classical Mechanics and Special Relativity. The course also addresses the mathematical modelling of simple constrained mechanical systems, including through the qualitative study of their behaviour. (Mechanics of a point particle, of discrete systems of points and of the rigid body)

Syllabus

Vector calculus, tensor calculus and differential equations in Euclidean spaces. Classical kinematics of rigid systems. Geometry of masses. Constrained systems. Fundamental kinetic and dynamic quantities. Kinematics of deformable continuous systems. Cardinal equations of the Mechanics of systems. Elements of the dynamics of deformable continua. Lagrange equations for holonomic systems. Statics of systems and study of the stability of equilibrium. Elements of Special Relativity.

Expected learning
outcomes

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

  • know and understand the issues related to the mathematical modelling of mechanical systems with a finite number of degrees of freedom;
  • are able to apply the theoretical knowledge acquired to tackle applied problems concerning the modelling and analysis of the evolution of real-world material systems with a finite number of degrees of freedom;
  • 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

Skill in the study of the Mechanics of systems with a finite number of degrees of freedom. Clarity, correctness and completeness in the written and/or oral presentation of the topics of the course.