81854 - ANALISI MATEMATICA 1B

Learning outcomes

At the end of the course, the student will acquire the basic knowledge of mathematical analysis as a central science, useful and creative. He should master the concepts of limit, continuity and differentiability for functions of a real variable, with particular reference to the use of the Taylor formula. The student will be able to apply this knowledge to the solution of simple practical problems, posed by the pure and applied sciences.

Course contents

Convex functions of one real variable.

Taylor formula.

Riemann integral for real functions of a real variable. Antiderivatives. Fundamental Theorem of Calculus. Improper integrals.

Series.

Metric spaces.

Sequences and series of functions.

Readings/Bibliography

Ermanno Lanconelli, Lezioni di Analisi Matematica 1, Ed. Pitagora;

Enrico Giusti, Analisi Matematica 1, Ed. Boringhieri;

Carlo Pagani e Sandro Salsa, Analisi Matematica 1, Zanichell

Walter Rudin, Principles of Mathematical Analysis, Mcgraw-Hill.

Teaching methods

Lectures and exercises in classroom.

Assessment methods

The examination consists of a preliminary written test and an oral one.
The written test consists of exercises related to the arguments of the course. In order to sustain the written test the student must register through AlmaEsami [https://almaesami.unibo.it/] .

The written test remains valid for the oral exam in the same examination period.

The oral test follows the written test; it mainly concerns the theoretical aspects of the course. The student must show to know the concepts explained during the course (in particular definitions, theorems and their proofs) and how to connect with each other.

Office hours

See the website of Alberto Parmeggiani

See the website of Bruno Franchi