Applied Mathematics

Educational Goals General objectives: To provide students with the basics related to the study of functional spaces that intervene in various fields. In particular, linear operators will be studied between Banach or Hilbert spaces and their spectrum will be analyzed. Finally, some non-linear Functional Analysis techniques will be presented, suitable for the study of differential problems. Specific objectives: Knowledge and understanding: at the end of the course the student will have acquired the basic notions and results related to the Functional Analysis and to its different applications to differential problems. Apply knowledge and understanding: at the end of the course the student will be able to solve simple problems that require the use of functional analysis techniques. Critical and judgmental skills: the student will have the bases to analyze the similarities and relationships between the topics covered and topics already seen in previous courses; will also acquire the tools that have historically led to the solution of classical problems. It will be able (at least in model cases) to recognize functional spaces suitable for solving analysis problems, for example differential problems with boundary conditions. Communication skills: ability to expose the contents in the oral part of the assessment and in any theoretical questions present in the written test. Learning skills: the acquired knowledge will allow the application of the techniques to advanced problems of Functional Analysis and to differential problems.