OVERVIEW

The aim of the course is to consolidate the theoretical knowledge about Mathematical Analysis I and extend it to the study of functions of several variables.

LEARNING OUTCOMES

Introduction to mathematical analysis and differential calculus for scalar and vector functions of several real variables.

AIMS AND LEARNING OUTCOMES

The aim of the course is  providing students with the main notions of the differential calculus of functions of several variables and the introduction to the study of metric spaces. At the end of the course the student will have to know the definitions, to understand the main theorems, to solve and analyze problems of minimum / maximum of functions of several variables and to discuss existence and uniqueness of solutions of differential problems.

PREREQUISITES

Main theorems and definitions of the course Mathematical Analysis I.

Teaching methods

The course will be divided into two parts: theory and exercises. During the theoretical  lessons the definitions, the statements and the prooves of the theorems will be presented with many examples and exercises. During the other part of the course,  many examples and exercises will be studied and solved in order to  clarify the different aspects of the theory. During the academic year, two  guided exercises will be carried out.

SYLLABUS/CONTENT

Metric spaces; various types of convergence of sequences and series of functions, differential calculus of functions of several variables; Cauchy's problem for differential equations and systems.

RECOMMENDED READING/BIBLIOGRAPHY

 Nicola Fusco, Paolo Marcellini, Carlo Sbordone, Analisi matematica 2, Liguori

 Nicola Fusco, Paolo Marcellini, Carlo Sbordone, Lezioni di analisi matematica due, Zanichelli

 Marco Bramanti , Carlo D. Pagani, Sandro Salsa, Analisi matematica 2, Zanichelli

Exam Board

SIMONE DI MARINO (President)

FRANCESCA ASTENGO

MARCO BARONTI (President Substitute)

Teaching methods

The course will be divided into two parts: theory and exercises. During the theoretical  lessons the definitions, the statements and the prooves of the theorems will be presented with many examples and exercises. During the other part of the course,  many examples and exercises will be studied and solved in order to  clarify the different aspects of the theory. During the academic year, two  guided exercises will be carried out.

LESSONS START

Lessons start in September: 6 hours per week.

Exam description

Each exam session consists of a written test and an oral exam. In order to acces to the oral exam, the student will be required of an evaluation of at least 12/30.

Assessment methods

During the written test, the student will solve exercises mainly concerning sequences and series of functions, functions of several variables and differential problems. During the oral examination the student must highlight critical analysis,  skills and ability to apply the different  theorems to solve easy exercises. The demonstration of a theorem will not be a mnemonic exercise but a precise identification of the points, in which the various hypotheses are applied.

Exam schedule