81854 - ANALISI MATEMATICA 1B

Learning outcomes

At the end of the course, the student will deepen the basic knowledge of Mathematical Analysis, as a unique and creative science of fundamental importance. He/she will gain the knowledge of the concepts of integral and of generalized integral of real function of one real variable, and of a numerical series and sequences of functions. He/she will be able to study real functions of one real variable. In particular, the student will know how to apply this knowledge to the solution of simple practical problems, appearing in the pure and applied sciences.

Course contents

-Convex functions: main definitions and criteria of convexity.

-Study of the graph of a function of one real variable (further enriched by the knowledge of the related topics of the course of Mathematical Analysis 1A).

-Riemann integral of a real function of one real variable. The Fundamental Theorems of Integral Calculus. Primitive functions. Application of the integral calculus to the linear Ordinary Differential Equations of the first order. Generalized integrals.

-Numeric series: definitions, main theorems and convergence criteria.

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

-Metric spaces (a general outline). The n-dimensional real Euclidean space.

Readings/Bibliography

In order to deepen the study of the topics of the course, students can consult the following textbooks.

--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

**VERY IMPORTANT:

During the course, pdf sheets of exercises will be available on the IOL website "Insegnamenti OnLine" https://iol.unibo.it/

For the preparation for the written exam, it is of fundamental importance that the student has carried out all the exercises uploaded by the teacher on the IOL dedicated website.

Teaching methods

Lectures and exercises in the classroom.

Upload on the IOL website of sheets of exercises.

Assessment methods

The examination consists of a preliminary written test and of an oral examination.

The written test consists of some exercises related to the arguments of the course. In order to take the written/oral examinations, student must register at least five days before the exam through the website 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 exhibit his/her knowledge of the concepts given during the course (in particular definitions, theorems and their proofs), and he/she must show how to connect these concepts with each other.

Teaching tools

Upload on the IOL website

https://iol.unibo.it/

of several sheets of exercises, very important for the preparation to the written examination.

Office hours

See the website of Andrea Bonfiglioli

See the website of Annalisa Baldi