FISICA MATEMATICA A - L

Knowledge and understanding: Students will learn some basic concepts of complex analysis, Laplace transforms, and rational mechanics. They will develop skills in computation, algebraic manipulation, and mathematical formalization of problems.

Applying knowledge and understanding: Students will be able to apply the techniques learned to the evaluation of integrals, the solution of integro-differential problems with delay, and the study of mechanical systems. Students will also learn to use qualitative physical intuition as a guide to the quantitative analytical study of problems.

Making judgements: The theoretical knowledge acquired will guide students in choosing the best solution techniques — for example, how to use residues to evaluate integrals, which transform rule to apply, and how to apply the tools of analysis to determine the equilibria and stability of dynamical systems.

Communication skills: Students will learn to use correct language to communicate clearly in a scientific context, not only within mathematics.

Learning skills: Students, particularly the more motivated ones, will be encouraged to gain a thorough understanding of specific topics.

Lectures on theoretical arguments and exercises will be given in class at the blackboard. Teaching may also be carried out on line, should the conditions require it.

The prerequisite established by the degree programme is Calculus I (Analisi Matematica I). Tools learned in the courses of Physics I, Linear Algebra and Geometry, and Calculus II (Analisi Matematica II) will also be used.

Complex numbers; holomorphic and meromorphic functions; integration with residues; Laplace transform and applications to differential equations; vector calculus and trigonometry; cinematic and dynamic of points, conservative forces, constraints; reference systems and fictitious forces; cinematic of rigid bodies and geometry of masses; dynamic of rigid bodies; stability and constraint forces; exercises on past written exams.

1. Notes
2. G. Barozzi, Matematica per l'ingegneria dell'informazione, Zanichelli, Bologna (2004)
3. P. Biscari, T. Ruggeri, G. Saccomandi, M. Vianello, Meccanica razionale, Springer (2016)
4. A. Muracchini, T. Ruggeri, Esercizi di Meccanica Razionale,