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## MATHEMATICAL ANALYSIS II

CODE 60243 2022/2023 6 cfu during the 2nd year of 10375 INGEGNERIA CHIMICA E DI PROCESSO (L-9) - GENOVA MAT/05 GENOVA 1° Semester Prerequisites You can take the exam for this unit if you passed the following exam(s): Civil and Environmental Engineering 8715 (coorte 2021/2022) MATHEMATICAL ANALYSIS I 72290 GENERAL PHYSICS 56686 GEOMETRY 56721 CHEMICAL AND PROCESSES ENGINEERING 10375 (coorte 2021/2022) MATHEMATICAL ANALYSIS I 56594 Prerequisites (for future units) This unit is a prerequisite for: Civil and Environmental Engineering 8715 (coorte 2021/2022) HYDROLOGY & HYDRAULIC URBAN INFRASTRUCTURES 66097 STRUCTURAL ENGINEERING I 72543 GEOTECHNICS 99062 STRUCTURAL MECHANICS II 66285 URBAN PLANNING AND TRANSPORTATION ENGINEERING 84522 This unit is a module of: AULAWEB

## OVERVIEW

The module Mathematical Analysis II (code 60243) deals with some issues of Mathematical Analysis with the aim to complete the basic learning and introduce some theoretical tools used in engineering science. The main topics concern with the study of maximum and minimum constrained for functions of more real variables, the integration for functions of two and three variables, the theory of differential forms and the Fourier's series.

## AIMS AND CONTENT

### AIMS AND LEARNING OUTCOMES

This module aims to provide the student with the knowledge of the following mathematical conceps:

1) Maximum and minimum constrained for functions of more real variables

2) Integration on R^2 and R^3. Integration of differential forms. Gradient, divergence, curl and their properties.

3) Fourier series.

The main learning outcomes consist of technical skills about the following issues:

Calculation of maximum and minimum constrained of functions of more real variables. Evaluation of integrals on R^2 and R^3. Integration of differential forms. Calculus of gradient, divergence, curl. Fourier series expansions.

### TEACHING METHODS

Both theory and exercises are presented by the teacher in the usual way. Moreover some tutorial exercitations can be carried out during the semester.

### SYLLABUS/CONTENT

- maximum and minimum constrained for functions of more real variables
- integrals on R^2 and R^3
- curves and surfaces in R^3. Vector analysis: differential forms and path integrals, closed and exact differential forms, gradient, curl, divergence. Stokes Theorem.
- Fourier series.

G. Anichini, G. Conti, M. Spadini - Analisi matematica 2 - Pearson
O. Caligaris, P. Oliva - Analisi matematica 2 - E.C.I.G.
O. Caligaris, P. Oliva - Complementi di analisi matematica
W. Rudin - Real and Complex Analysis - McGraw-Hill 1970
N. Fusco, P. Marcellini, C. Sbordone - Lezioni di analisi matematica 2 - Zanichelli (2020)
M. Chicco, F. Ferro - Esercizi di Analisi matematica II - E.C.I.G.
M. Boella, Analisi matematica 2, Esercizi - Pearson

## TEACHERS AND EXAM BOARD

### Exam Board

PIERRE OLIVIER MARTINETTI (President)

LAURA BURLANDO

CRISTINA CAMPI

MAURIZIO CHICCO

MARC ALEXANDRE MUNSCH

SIMONE MURRO (President Substitute)

## LESSONS

### LESSONS START

The class will start according to the academic calendar.

### Class schedule

All class schedules are posted on the EasyAcademy portal.

## EXAMS

### EXAM DESCRIPTION

Written and oral tests. Oral test, which students can access only if the grade of written test is at least 10, 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 2019-20, 2020-21 and 2021-22), 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.

### ASSESSMENT METHODS

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.

In the written test 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.

### Exam schedule

Date Time Location Type Notes
21/12/2022 15:00 GENOVA Scritto
12/01/2023 09:00 GENOVA Orale
02/02/2023 10:00 GENOVA Scritto
07/02/2023 09:00 GENOVA Orale
08/06/2023 10:00 GENOVA Scritto
14/06/2023 09:00 GENOVA Orale
06/07/2023 14:30 GENOVA Scritto
14/07/2023 09:00 GENOVA Orale
04/09/2023 10:00 GENOVA Scritto
13/09/2023 09:00 GENOVA Orale

### FURTHER INFORMATION

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.