81854 - Mathematical Analysis 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 (including the notion of convexity), 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.

-Riemann integral of a real function of one real variable. The Fundamental Theorems of Integral Calculus. Primitive functions. Generalized integrals.

-Taylor formula.

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

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 UniBo website "VIRTUALE" (Virtual Learning Environment) https://virtuale.unibo.it/

For the preparation to the written examination, it is of a fundamental importance that the student carried out all the exercises uploaded by the teacher on the VIRTUALE dedicated website.

Teaching methods

Lectures and exercises in the classroom (and, if need be, according to the dispositions of UniBo, via mixed learning or distance-learning).

Uploads on the VIRTUALE website of several pdf's of exercises.

Assessment methods

he 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. September is a separated 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.

 

Students with learning disorders and\or temporary or permanent disabilities: please, contact the office responsible (https://site.unibo.it/studenti-con-disabilita-e-dsa/en/for-students) as soon as possible so that they can propose acceptable adjustments. The request for adaptation must be submitted in advance (15 days before the exam date) to the lecturer, who will assess the appropriateness of the adjustments, taking into account the teaching objectives.

Teaching tools

Tutorship (if appointed).

Office hours

See the website of Annalisa Baldi

See the website of Andrea Bonfiglioli