81853 - Mathematical Analysis 1A (M-Z)

Learning outcomes

At the end of the course, the student possesses the basic knowledge of Mathematical Analysis, identifying it as a unique and creative central science. He/she has knowledge of the concepts of limit, continuity and differentiability for the real functions of a real variable. The student knows how to apply this knowledge to the solution of simple practical problems, posed by pure and applied sciences.

Course contents

Preliminary notions on functions.

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, monotonicity, theorems of Rolle, Cauchy, Lagrange, Taylor formula.

Readings/Bibliography

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

E. Giusti, Analisi Matematica 1, ed. Boringhieri

Textbooks about exercises: Notes and exercices will be prepared by the teacher and they will be available on Vitual Learning Environment [https://virtuale.unibo.it/]. Students can also consult:

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 an oral one.

The written test consists of the resolution of some exercises related to the arguments of the course. In order to pass the written test, the student must register at least five days before the test through AlmaEsami [https://almaesami.unibo.it/] .

The result obtained in the written test remains valid for the oral exam in the same examination period. In order to be able to access the oral exam, the student must obtain a score at least 18/30 in the written part.

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.

Teaching tools

Tutorship (if appointed).

Office hours

See the website of Andrea Bonfiglioli