81854 - ANALISI MATEMATICA 1B

Course Unit Page

Academic Year 2018/2019

Course contents

Convex functions. Convexity criterion. Graphing functions of one real variable.

Riemann integral for functions of one real variable. Fundamental theorems of integral calculus. Antiderivatives. Application of integral calculus: first order linear differential equations. 

Improper integrals. Numerical series.

Sequences and series of functions: pointwise and uniform convergence. Power series. Taylor series.

Metric spaces. The n-dimensional Euclidean real space.

Readings/Bibliography

To study in depth the topics of the course, students can consult the following books.

Theory:

E. Lanconelli, Lezioni di Analisi Matematica 1, ed. Pitagora

P. Marcellini - C. Sbordone: Analisi Matematica 1, ed. Liguori

 E. Giusti, Analisi Matematica 1, ed. Boringhieri

Exercises:

M. Bramanti, Esercitazioni di Analisi Matematica 1, ed. Esculapio

P. Marcellini - C. Sbordone: Esercitazioni di Matematica, volume 1, parte seconda, ed. Liguori

E. Giusti, Esercizi e complementi di Analisi Matematica, volume 1, ed. Boringhieri

During the course some teaching material will be uploaded on the web site "Insegnamenti online" https://iol.unibo.it/

 

Teaching methods

Lectures and exercises in the classroom.

Assessment methods

The examination consists of a preliminary written test and an oral one.
The written test consists of five exercises related to the arguments of the course. In order to sustain the written test the student must register at least five days before the test 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 Giovanni Cupini

See the website of Giovanni Dore