87970 - ADVANCED MATHEMATICAL METHODS FOR PHYSICS

Conoscenze e abilità da conseguire

At the end of the course the student will learn some of the mathematical tools necessary for the study of modern theoretical physics. In particular, he/she will acquire advanced analytical and geometrical methods that have a wide range of theoretical applications.

Contenuti

1. Manifolds, vectors, tensors, forms.

2. Tensor calculus.

3. Lie derivatives.

4. Differential forms and their applications.

5. Lie groups and their Lie algebras.

6. Metric and affine connection. Riemannian geometry.

Testi/Bibliografia

My lectures notes.

Metodi didattici

Lectures on the blackboard.

Modalità di verifica e valutazione dell'apprendimento

Oral exams, which include also the solution of exercises. The list of exercises is presented to the students in advance and all the exercises were resolved during the lectures and are described in the lecture notes. The student should show the understanding of the main notions of the course and the capacity to do calculations, proofs and reasonings. After the solutions of the problem two other topics of the course are discussed.

 

Studenti/sse con DSA o disabilità temporanee o permanenti: si raccomanda di contattare per tempo l’ufficio di Ateneo responsabile ( https://site.unibo.it/studenti-con-disabilita-e-dsa/it): sarà sua cura proporre agli/lle studenti/sse interessati/e eventuali adattamenti, che dovranno comunque essere sottoposti, con un anticipo di 15 giorni, all’approvazione del/della docente, che ne valuterà l'opportunità anche in relazione agli obiettivi formativi dell'insegnamento.

Strumenti a supporto della didattica

Lectures.

Orario di ricevimento

Consulta il sito web di Alexandr Kamenchtchik