CODE 25907 ACADEMIC YEAR 2016/2017 CREDITS 7 cfu anno 2 MATEMATICA 8760 (L-35) - SCIENTIFIC DISCIPLINARY SECTOR MAT/05 LANGUAGE Italiano TEACHING LOCATION SEMESTER 2° Semester TEACHING MATERIALS AULAWEB OVERVIEW Some basic topics in Mathematical Analysis are covered, with the aim to complete the ones already covered in the previous courses of Mathematical Analysis I and 2. The lectures are delivered in Italian. AIMS AND CONTENT LEARNING OUTCOMES Introduction to Lebesgue's Integration Theory and to integration along curves and surfaces. LEARNING OUTCOMES (FURTHER INFO) To continue the study of Classical Mathematical Analysis (implicit functions, curves, surfaces and 1-differential forms) and to introduce the study of Lebesgue's Integration Theory: these are fundamental instruments in Mathematical Analysis, essential to get a well grounded knowledge in the basic branches of Mathematics and for the understanding of simultaneous and next courses. 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 Both theory and exercises are presented by the teacher in the classroom on the blackboard. Moreover some tutorial exercitations will be carried out during the semester. SYLLABUS/CONTENT Implicit functions, Dini theorem, local invertibility. Notion of sigma-algebra and measure. Lebesgue integral and theorems of convergence under sign of integral. Riesz extension of Riemann integral for continuous functions with compact support. Lebesgue measurable sets and their measure. Fubini theorem. Integrability criteria. Integrals depending by a parameter. Curves and surfaces; length and area; integration on curves and surfaces. Differential forms of degree 1; integration of 1-differential forms on oriented curves; closed and exact 1-differential forms. RECOMMENDED READING/BIBLIOGRAPHY W. Rudin - Real and Complex Analysis - McGraw-Hill 1970 TEACHERS AND EXAM BOARD ADA ARUFFO Ricevimento: At the end of lectures or by appointment. GIOVANNI ALBERTI Exam Board ADA ARUFFO (President) GIOVANNI ALBERTI GIANFRANCO BOTTARO LESSONS LESSONS START February 27, 2016 Class schedule MATHEMATICAL ANALYSIS 3 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 14/06/2017 10:00 GENOVA Scritto 19/06/2017 09:00 GENOVA Orale 07/07/2017 10:00 GENOVA Scritto 10/07/2017 09:00 GENOVA Orale 14/09/2017 10:00 GENOVA Scritto 15/09/2017 09:00 GENOVA Orale FURTHER INFORMATION Attendance is recommended. Prerequisite: Mathematical Analysis I and 2, Linear Algebra and Analitic Geometry, the first semester of Geometry.
