81853 - Mathematical Analysis 1A (M-Z)

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

Real numbers, upper and lower bound. Natural numbers, the principle of induction.

Elementary functions.

Limits of sequences. Elementary topology of R.

Limits and continuity of functions of one real variable.

Differential calculus for real functions of a real variable. Calculation rules, monotony, theorems of Rolle, Cauchy, Lagrange, Taylor formula.

Readings/Bibliography

Notes of the teacher will be available on Virtuale [https://virtuale.unibo.it/] .

To study in depth the topics of the course, students can consult:

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

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

E. Giusti, Analisi Matematica 1, ed. Boringhieri

Textbooks about exercises:

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

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

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

Teaching methods

Lectures and exercises in the classroom.

Assessment methods

In order to access the exam, at each stage, it is mandatory to register on the lists of exam sessions published on AlmaEsami [https://almaesami.unibo.it/almaesami/welcome.htm].

The exam is divided into a written test and an oral-written test, divided into two parts.

The written test concerns exercises, has a total duration of 2 hours and 30 minutes; it is accessed by registering on the lists, opened on AlmaEsami, by the teacher. The written test awards up to 15 points and is considered passed by totaling at least 8 points.
Students who do not pass the written test will have to repeat the exam.

Students who pass the written test are admitted to the next oral-written phase which will take place on a different day. The oral-written phase, mainly concerning theory, begins with the administration of a written test lasting 45 minutes with which 8 points are awarded. At the end of the test, if the sum of the written score and the score of the preparatory test for the oral is greater than or equal to 15, the candidate will be admitted to the oral exam that will take place on the same day in the form of an interview on the contents of the course that the candidate must normally carry out on the blackboard. Further clarifications may also be requested on the tests carried out before the oral exam by the candidate.
The oral exam awards up to 12 points.

Methods for determining the grade. If the oral score is less than or equal to 3, then, even if the sum of the written and pre-oral is greater than or equal to 18, the candidate will be failed.
If the oral evaluation is greater than or equal to 4, then the grade out of thirtieths will be the sum of the written score, with that of the pre-oral test plus the score of the oral exam.
Some examples: (8,7,3), then the student is failed; (8,7,4), promoted with 19, (10,7,3), failed; (15,8,3), failed; (15,8,4), passed with 26; (8,7,13), passed with 28. (15, 0, 13), passed with 28.

The attribution of the laude may occur, at the discretion of the teacher, when the sum of three scores, taking into account the admission constraints, is strictly greater than 30.
For example, the following triplets: (10,8,13), (15,5,12) could result in a 30 with honors.

The validity of the score of the written tests is limited only to the exam period (January-February or June-July or September) in which they were taken and are not valid for any subsequent exam periods.

During the test, the use of notes, books or computer tools of any kind is not permitted. In particular, the use of cell phones is not permitted.

Links to further information

https://www.dm.unibo.it/~dore/

Office hours

See the website of Giovanni Dore