| CODE | 25907 |
|---|---|
| ACADEMIC YEAR | 2017/2018 |
| CREDITS | 7 credits during the 2nd year of 8760 Mathematics (L-35) GENOVA |
| SCIENTIFIC DISCIPLINARY SECTOR | MAT/05 |
| LANGUAGE | Italian |
| TEACHING LOCATION | GENOVA (Mathematics) |
| SEMESTER | 2° Semester |
| TEACHING MATERIALS | AULAWEB |
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.
Introduction to Lebesgue's Integration Theory and to integration along curves and surfaces.
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.
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.
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.
W. Rudin - Real and Complex Analysis - McGraw-Hill 1970
Office hours: At the end of lectures or by appointment.
Office hours: By appointment
ADA ARUFFO (President)
GIOVANNI ALBERTI
GIANFRANCO BOTTARO
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.
The class will start according to the academic calendar.
Written and oral tests.
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.
| Date | Time | Location | Type | Notes |
|---|---|---|---|---|
| 18/01/2018 | 10:00 | GENOVA | Scritto | |
| 19/01/2018 | 09:00 | GENOVA | Orale | |
| 09/02/2018 | 10:00 | GENOVA | Scritto | |
| 12/02/2018 | 09:00 | GENOVA | Orale | |
| 25/06/2018 | 10:00 | GENOVA | Scritto | |
| 26/06/2018 | 14:00 | GENOVA | Orale | |
| 24/07/2018 | 10:00 | GENOVA | Scritto | |
| 26/07/2018 | 09:00 | GENOVA | Orale | |
| 13/09/2018 | 10:00 | GENOVA | Scritto | |
| 14/09/2018 | 09:00 | GENOVA | Orale |
Attendance is recommended.
Prerequisite: Mathematical Analysis I and 2, Linear Algebra and Analitic Geometry, the first semester of Geometry.