- Docente: Giovanni Cupini
- Credits: 7
- SSD: MAT/05
- Language: Italian
- Moduli: Giovanni Cupini (Modulo 1) Giovanni Dore (Modulo 2)
- Teaching Mode: Traditional lectures (Modulo 1) Traditional lectures (Modulo 2)
- Campus: Bologna
- Corso: First cycle degree programme (L) in Mathematics (cod. 8010)
Learning outcomes
At the end of the course, the student deepens the basic knowledge of mathematical analysis, identifying it as a unique and creative central science. He has knowledge of the concept of integral and generalized integral of real functions of a real variable and of a number series. It is able to study real functions of a real variable. In particular, the student knows how to apply this knowledge to the solution of simple practical problems, posed by 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.
Metric spaces. The n-dimensional Euclidean real space.
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
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
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
See the website of Giovanni Dore