- Docente: Giovanni Dore
- Credits: 9
- SSD: MAT/05
- Language: Italian
- Moduli: Giovanni Dore (Modulo 1) Giovanni Cupini (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 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
Reminders 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, monotony, theorems of Rolle, Cauchy, Lagrange, Taylor formula.
Readings/Bibliography
Notes of the teacher will be available on Insegnamenti Online.
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 an oral one.
The written test consists of five exercises related to the arguments of the course. In order to sustain the written test the student must register at least five days before the test through AlmaEsami.
The written test remains valid for the oral exam in the same examination period.
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.
Office hours
See the website of Giovanni Dore
See the website of Giovanni Cupini