81853 - Mathematical Analysis 1A (A-L)

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 teachers 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. Pitagora

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

The examination consists of a preliminary written test and a written theory one before a colloquium.

The written test consists of some exercises related to the arguments of the course, it lasts two and a half hours. In order to sustain the written test the student must register at least four days before the test through AlmaEsami. The maximum grade is 15. The student is admitted to the written-colloquial subsequent step, that it will be hold in a different day, if the realized score is grater or equal to 8.

The written test remains valid for the written-colloquial subsequent examination only in the same period. Namely only in January-February if the written exam has been held in January or February, or alternatively on June-July, if the written exam has been held in June-July, or alternatively on September, if the written exam has been held in September. 

The time for the written test before the colloquium is 45' and it takes place for all the admitted candidates at the beginning of the day in which is scheduled the session. The maximum score is 8. After it, there will be a colloquium only if the sum between the score in the first written exam is at least 15. Both the evaluations mainly concern 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. The maximum score at the colloquium is 12.

How to determine the final grade: in case the score at the colloquium were les or equal to 3, then the candidate the exam has to be repeated because it is not sufficient, even if the sum of the three grades were grater or equal to 18.

In case the colloquium were graded more or equal to 4, the the final grade is obtained by the sum of the three grades. Here below some examples:

(8,7,3), then the student is rejected; (8,7,4), the student is promoted with 19.

(10,7,3), rejected; (15,8,3), rejected; (15,8,4), grade 26; (8,7,12), grade 27. (15, 0, 12), grade 27.

 

 

Links to further information

https://www.unibo.it/sitoweb/fausto.ferrari

Office hours

See the website of Fausto Ferrari