CODE 29024 ACADEMIC YEAR 2016/2017 CREDITS 7 cfu anno 3 MATEMATICA 8760 (L-35) - SCIENTIFIC DISCIPLINARY SECTOR MAT/05 LANGUAGE Italiano TEACHING LOCATION SEMESTER 1° Semester TEACHING MATERIALS AULAWEB 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. LEARNING OUTCOMES (FURTHER INFO) 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 - Analisi reale e complessa - Bollati Boringhieri 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. Exam Board GIANFRANCO BOTTARO (President) ADA ARUFFO ERNESTO DE VITO GIANCARLO MAUCERI LESSONS LESSONS START September 26, 2016 Class schedule ELEMENTS OF ADVANCED ANALYSIS 1 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 22/06/2017 10:00 GENOVA Scritto 27/06/2017 10:00 GENOVA Orale 21/07/2017 10:00 GENOVA Scritto 25/07/2017 10:00 GENOVA Orale 12/09/2017 10:00 GENOVA Scritto 15/09/2017 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.
