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MATHEMATICAL ANALYSIS 3

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

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.

AIMS AND LEARNING OUTCOMES

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

Exam Board

ADA ARUFFO (President)

GIOVANNI ALBERTI

GIANFRANCO BOTTARO

LESSONS

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.

LESSONS START

The class will start according to the academic calendar.

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

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

FURTHER INFORMATION

Attendance is recommended.


Prerequisite: Mathematical Analysis I and 2, Linear Algebra and Analitic Geometry, the first semester of Geometry.