- Docente: Giovanni Cupini
- Credits: 6
- SSD: MAT/05
- Language: Italian
- Teaching Mode: Traditional lectures
- Campus: Bologna
- Corso: First cycle degree programme (L) in Mathematics (cod. 6061)
-
from Feb 18, 2025 to May 30, 2025
Learning outcomes
At the end of the course, the student has completed the basic knowledge of Mathematical Analysis. In particular, in relation to the real functions of a real variable, he has completed his knowledge of differential calculus and knows about integral calculus; has knowledge of numerical series. The student knows how to apply this knowledge to the solution of simple practical problems posed by the pure and applied sciences.
Course contents
Local extrema.
Convex functions. Convexity criterion. Graphing functions of one real variable.
Riemann integral for functions of one real variable. Fundamental theorems of integral calculus. Antiderivatives. Application of integral calculus: first order linear differential equations.
Improper integrals. Numerical series.
Readings/Bibliography
Some teaching material will be uploaded on the web site "Virtuale" [https://virtuale.unibo.it/]
To study in depth the topics of the course, students can consult the following books.
Theory:
E. Lanconelli, Lezioni di Analisi Matematica 1, ed. Pitagora
G.C. Barozzi, G. Dore, E. Obrecht: Elementi di Analisi Matematica, vol. 1, Zanichelli.
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
Teaching methods
Lessons and exercises in the classroom.
Assessment methods
The examination consists of a preliminary written test and an oral one.
The written test consists of five exercises related to the arguments of the course in 2 hours and 30'. In order to participate to the written test the student must register at least four days before the test through AlmaEsami [https://almaesami.unibo.it/]. The written test is passed with a minimum score of 15 out of 30.
The written test remains valid for the oral exam in the same examination period.
The test about the theory 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 them.
Office hours
See the website of Giovanni Cupini