CODE 29024 ACADEMIC YEAR 2017/2018 CREDITS 7 cfu anno 3 MATEMATICA 8760 (L-35) - 7 cfu anno 1 MATEMATICA 9011 (LM-40) - SCIENTIFIC DISCIPLINARY SECTOR MAT/05 LANGUAGE Italian TEACHING LOCATION SEMESTER 1° Semester OVERVIEW Some basic topics in Mathematical Analysis are covered, with the aim to continue the study already initiated in the previous courses of Mathematical Analysis I, 2 and 3. The lectures are delivered in Italian. AIMS AND CONTENT LEARNING OUTCOMES Introduction of further concepts of Lebesgue's Integration Theory and some basic ones of Functional Analysis. AIMS AND LEARNING OUTCOMES To provide some fondamental contents in Mathematical Analysis (Functional Analysis and Measure Theory) that are considered important to get a well grounded knowledge in the basic branches of Mathematics and for the students who want to get a master's degree in Mathematics. Expected learning outcomes: The students will become acquainted with the concepts and proofs carried out in class and how they are used in practice to solve exercises; moreover they will know how to produce easy variants of demonstrations seen and construct examples on topics covered in this course. TEACHING METHODS During the semester some exercitations will carried out in class. Both theory and exercises are presented by the teacher in the classroom on the blackboard. Moreover some tutorial exercitations can be carried out during the semester, if some students will be interested. The teaching materials is available at the teacher's web page. SYLLABUS/CONTENT Normed and Banach spaces; continuous operators. Hahn Banach, uniform boundedness, open map and closed graph theorems; Hilbert spaces, Riesz and projection theorems, L^p spaces. Convergences of measurable functions..Radon-Nikodym theorem; duals of L^p and C_{infinity}; bounded variation and absolutely continuous functions. RECOMMENDED READING/BIBLIOGRAPHY H. Brezis - Analyse Fonctionnelle, Theorie et applications - Masson 1983. N. Dunford, J.T. Schwartz - Linear Operators. Part I: General Theory - Interscience 1957. W. Rudin - Real and Complex Analysis - McGraw-Hill 1970 A.E. Taylor, D.C. Lay - Introduction to Functional Analysis - Wiley and Sons 1980. TEACHERS AND EXAM BOARD GIANFRANCO BOTTARO Ricevimento: At the end of lectures or by appointment. LESSONS LESSONS START The class will start according to the academic calendar. Class schedule The timetable for this course is available here: Portale EasyAcademy EXAMS EXAM DESCRIPTION Written and oral tests. ASSESSMENT METHODS The written examination consists in some exercises about the topics covered in this course. In the oral exam a discussion of the written examination is done; moreover some questions are asked on the course content. Exam schedule Data appello Orario Luogo Degree type Note 26/01/2018 10:00 GENOVA Scritto 29/01/2018 10:00 GENOVA Orale 16/02/2018 10:00 GENOVA Scritto 19/02/2018 10:00 GENOVA Orale 22/06/2018 10:00 GENOVA Scritto 26/06/2018 10:00 GENOVA Orale 20/07/2018 10:00 GENOVA Scritto 23/07/2018 10:00 GENOVA Orale 14/09/2018 10:00 GENOVA Scritto 17/09/2018 10:00 GENOVA Orale FURTHER INFORMATION Attendance is recommended. Prerequisite: Mathematical Analysis I, 2 and 3, Linear Algebra and Analitic Geometry, the first semester of Geometry.
