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.

AIMS AND CONTENT

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 equations.

PREREQUISITES

Mathematical Analysis I, Linear algebra and analytic geometry

TEACHING METHODS

The course will be divided into two parts: theory and exercises. During the theoretical lessons the definitions, the statements and the proofs of the theorems will be presented, in addition to 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.

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

 Paolo Marcellini, Carlo Sbordone - Esercitazioni di analisi matematica due, Zanichelli

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

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

 Terence Tao, Analysis II, Springer

TEACHERS AND EXAM BOARD

Exam Board

GIOVANNI ALBERTI (President)

ADA ARUFFO

MARCO BARONTI (President Substitute)

LESSONS

LESSONS START

The class will start according to the academic calendar.

Class schedule

The timetable for this course is available here: Portale EasyAcademy

EXAMS

EXAM DESCRIPTION

The exam consist of a multiple choice test and of a written test. In order to access the written exam, the student needs to pass the multiple choice test.

ASSESSMENT METHODS

The questions of the multiple choice quiz will be simple exercises or theoretical questions. In. this way, we assess the knowledge of the basic theoretical notions (mainly definitions and statements) and the ability to apply them to solve simple problems.

The written exam consists of more elaborated problems on the topics of the course and of the exposition of some parts of the theory (like, for example, statements and proofs). In the written exam the student needs to show the ability of critical thinking, the ability of applying the results of the theory to solve the problems, and the knowledge of the theory.

Exam schedule