Physics

VIERI MASTROPIETRO
ALESSIO NOTARI

PART I
General goals:
The goal of the course is the study and the comprehension of advanced mathematical techniques. The student will acquire the basic concepts of complex
analysis and functional analysis and she/he will be able to apply them to the study of problems in classical (electromagnetism and continuum media) and
quantum physics. The know-how that the student acquires attending this course is indispensable for the Physics courses of the third year.

Specific goals:
Introduction to the fundamental concepts of complex analysis, i) to provide the student with a deep knowledge and understanding of these concepts, and ii) to
allow him/her to successfully apply them in various physical contexts. In particular, the student must be able to use techniques of integration in the complex
domain in all the physical
contexts in which they have applications. In order to achieve these goals, and to help the student to develop the capability i) to communicate the acquired
knowledges, and
ii) to continue the studies autonomously, we plan to involve him (her), during the theoretical lectures and exercises, through general and specific questions
related to the
subject; or through the presentation in depth of some specific subject agreed with the teacher

PART II
General goals:
The goal of the course is the study and the comprehension of advanced mathematical techniques. The student will acquire the basic concepts of complex
analysis and functional analysis and she/he will be able to apply them to the study of problems in classical (electromagnetism and continuum media) and
quantum physics. The know-how that the student acquires attending this course is indispensable for the Physics courses of the third year.

Specific goals:
Introduction to the fundamental concepts of functional analysis, i) to provide the student with a deep knowledge and understanding of these concepts, and ii) to
allow him/her to successfully apply them in various physical contexts. In particular, the student must be able to use the Fourier series, the Fourier and Laplace
transforms, and the distributions in all the physical contexts in which they have applications; in addition the student must be able to work with Hilbert spaces and
with operators on functional spaces of physical interest. In order to achieve these goals, and to help the student to develop the capability i) to communicate the
acquired knowledges, and ii) to continue the studies autonomously, we plan to involve him (her), during the theoretical lectures and exercises, through general
and specific questions related to the subject; or through the presentation in depth of some specific subject agreed with the teacher