CODE  25907 

ACADEMIC YEAR  2022/2023 
CREDITS 

SCIENTIFIC DISCIPLINARY SECTOR  MAT/05 
LANGUAGE  Italian 
TEACHING LOCATION 

SEMESTER  2° Semester 
TEACHING MATERIALS  AULAWEB 
The lectures are delivered in Italian.
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.
Introduction to Lebesgue's Integration Theory and to integration along curves and surfaces.
To continue the study of Classical Mathematical Analysis (curves, surfaces and 1differential 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.
Mathematical Analysis I and 2, Linear Algebra and Analitic Geometry, Geometry 1.
Both theory and exercises are presented by the teacher in the usual way. Moreover some tutorial exercitations will be carried out during the semester.
Notion of sigmaalgebra 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. Lusin theorem. Curves and surfaces; length and area; integration on curves and surfaces. Differential forms of degree 1; integration of 1differential forms on oriented curves; closed and exact 1differential forms.
W. Rudin  Real and Complex Analysis  McGrawHill 1970
Office hours: At the end of lectures or by appointment.
Office hours: Upon appointment.
ADA ARUFFO (President)
LAURA BURLANDO
TOMMASO BRUNO (President Substitute)
EMANUELA SASSO (President Substitute)
The class will start according to the academic calendar.
All class schedules are posted on the EasyAcademy portal.
Written and oral tests. Oral test, which students can access whatever the outcome of written test, has to be taken in the same exam session of written test.
If the University introduces again the obligation to perform even partially online exams (as happened in part of the academic years 201920, 202021 and 202122), the exam will consist only of oral test.
Students with DSA certification ("specific learning disabilities"), disability or other special educational needs are advised to contact the teacher at the beginning of the course to agree on teaching and examination methods that, in compliance with the teaching objectives, take account of individual learning arrangements and provide appropriate compensatory tools.
The written examination consists in some exercises about the topics covered in this course. In this test the ability to apply theoretical results in concrete situations is evaluated.
The test lasts two hours and it is possible to consult the notes and textbooks.
In the oral exam a discussion of the written examination is done; moreover some questions are asked on the course content and/or about the solution of some exercises about the topics covered in this course. In such way they are assessed the understanding, the knowledge of the concepts, and the skills in using them, acquired by the students.
Date  Time  Location  Type  Notes 

23/12/2022  10:00  GENOVA  Scritto  riservata agli studenti che hanno seguito nell'a.a.2021/22 e aa.aa. precedenti 
09/01/2023  09:00  GENOVA  Orale  riservata agli studenti che hanno seguito nell'a.a.2021/22 o aa.aa. precedenti 
13/01/2023  10:00  GENOVA  Scritto  riservato agli studenti iscritti a.a.2021/2022 e anni accademici precedenti 
27/01/2023  09:00  GENOVA  Orale  riservato agli studenti iscritti a.a.2021/2022 e anni accademici precedenti 
09/02/2023  10:00  GENOVA  Scritto  riservato agli studenti iscritti a.a.2021/2022 e anni accademici precedenti 
15/02/2023  09:00  GENOVA  Orale  riservato agli studenti iscritti a.a.2021/2022 e anni accademici precedenti 
16/06/2023  10:00  GENOVA  Scritto  
21/06/2023  09:00  GENOVA  Orale  
07/07/2023  10:00  GENOVA  Scritto  
12/07/2023  09:00  GENOVA  Orale  
14/09/2023  10:00  GENOVA  Scritto  
19/09/2023  09:00  GENOVA  Orale 
Attendance is recommended.
Students are suggested to enroll in AulaWeb, in order to be able to get further information by the teachers about the course.