00709 - Mathematical Methods Of Physics (M-Z)

Learning outcomes

At the end of the course the student acquires the mathematical notions and methods necessary for the understanding of the modern physics. First, the student studies the theory of holomorphic functions and is able to calculate the contour integrals in the complex plane. Then the student learns element of the topology, linear and normed spaces. Then the student studies the Hilbert spaces and their operators, which permits to use the mathematical formalism of quantum mechanics.

Course contents

1. Theory of functions of a complex variable

2. Topological spaces

3. Linear spaces and normed spaces

4. Hilbert spaces

5. Operators in the Hilbert spaces

Readings/Bibliography

Lecture notes by Fabio Ortolani (in italian)

Teaching methods

Lectures on the blackboard

Assessment methods

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 exercise(s) two other topics of the course are discussed. The final mark for the exam is given by taking into account the capacity to make calculations, to make logical reasoning, the knowledge of definitions and notions introduced during the course, the industriousness shown during the course, the capacity to think about topics which are close to those discussed in detail during the lectures.

Teaching tools

The course notes (lecture notes by F. Ortolani) will be made available on virtuale.unibo.it.

Office hours

See the website of Pierbiagio Pieri