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## MATHEMATICAL ANALYSIS 2

CODE 72288 2021/2022 6 cfu during the 2nd year of 10800 INGEGNERIA MECCANICA - ENERGIA E PRODUZIONE (L-9) - SAVONA MAT/05 Italian SAVONA 1° Semester This unit is a module of: AULAWEB

## OVERVIEW

The main goal of this course is to present the basic topics in the mathematical analysis of functions of several variables. In particular, differential calculus in several variables, the theory of multiple and line integration is treated.

## AIMS AND CONTENT

### LEARNING OUTCOMES

The knowledge of the mathematical tools introduced and the skill of using them to solve problems eventually in a physical setting. The skill of  setting up a problem correctly and the development of intuitive and deductive skills in solving problems.

### AIMS AND LEARNING OUTCOMES

The knowledge of mathematical basic tools useful in Engineering as the level set, the partial derivatives, constrained and unconstrained optimization, multiple and line integration and the skill in using them. The skill of setting up and solving problems by using intuitive and deductive reasoning as well as recognizing and using the suitable mathematical tools in solving problems in a physical setting.

### TEACHING METHODS

The course consists of 36 hours of lectures and 24 hours of practices. In the lectures the topics of the syllabus are explained with definitions and theorems and some proofs which can be useful for the comprehension of the topics and to develop the logical and deductive skills. Every theoretical topic is explained with easy examples and some exercises. In the practices, many exercises are solved with the aim of going into the knowledge of theoretical topics treated in the lectures and preparing the student for the exam. Some guided practices will be held to help the student to valuate one's preparation. Several intermediate tests are provided

### SYLLABUS/CONTENT

Euclidean spaces. Toplology in R^n. Functions of several variables. Level sets. Continuity and differentiability. Directional and partial derivatives. Derivatives of higher order. Schwartz Theorem. Taylor approximation with Peano's and Lagrange's reminder. Quadratic forms. Unconstrained optimization. Necessary first order condition and sufficient second order condition. Least squares method. Implicit function theorem. Change of coordinates. Constrained optimization. System of nonlinear differential equations. Cauchy problem. Existence and uniqueness of the solution. Double and triple integrals. Normal domains in R^2. Integration formulas and theorem of change of variables.  Lines in R^n and line integral.

C. Canuto, A. Tabacco, "Analisi Matematica II", Springer, 2014.

M. Bramanti, C. Pagani, S. Salsa. “Analisi matematica 2”, Zanichelli, 2009.

S. Salsa, A. Squellati. “Esercizi di Analisi matematica 2”, Zanichelli 2011.

## TEACHERS AND EXAM BOARD

### Exam Board

CLAUDIO CARMELI (President)

ROBERTUS VAN DER PUTTEN

OTTAVIO CALIGARIS (President Substitute)

DANILO PERCIVALE (President Substitute)

## LESSONS

### LESSONS START

https://corsi.unige.it/10800/p/studenti-orario

### Class schedule

All class schedules are posted on the EasyAcademy portal.

## EXAMS

### EXAM DESCRIPTION

Final examination is structured as follows :

a preliminary test with multiple answers which will be held in the Campus in Savona by using Aulaweb. The students who pass the preliminary test, can take the examination which can be a written or an oral examination according to the choice of the student.It consists in two problems concernng the topics treted. The final evaluation holds in consideration both the test and the examination.

Two intermediate exhaminations will be held.

### ASSESSMENT METHODS

The aim of the exhamination is verifying the skills acquired by the student. The preliminary test and the problems proposed in the exhamination call for the choice and the application of suitable mathematical tools, besides their  solution needs the skill of constructing a logical connection applying theoretical topics treated.

### Exam schedule

Date Time Location Type Notes
18/02/2022 09:00 GENOVA Esame su appuntamento
13/06/2022 09:30 SAVONA Scritto
13/07/2022 09:30 SAVONA Scritto
15/09/2022 09:30 SAVONA Scritto
16/09/2022 09:00 GENOVA Esame su appuntamento

### FURTHER INFORMATION

The course assumes knowledge of the content of Mathematical Analysis 1 and Elements of Mathematics for Engineering