Academic Year 2015/2016
- Docente: Vania Sordoni
- Credits: 12
- SSD: MAT/05
- Language: Italian
- Moduli: Vania Sordoni (Modulo 1) Marco Mughetti (Modulo 2)
- Teaching Mode: Traditional lectures (Modulo 1) Traditional lectures (Modulo 2)
- Campus: Bologna
- Corso: First cycle degree programme (L) in Computer Science (cod. 8009)
Learning outcomes
At the end of the course, the student knows the basic tools of
mathematical analysis such as real numbers, limits, continuity,
derivatives and integrals.
Moreover, he can use this knowledges for studying different
disciplines.
Course contents
The number systems: N,Z,Q,R.
The induction principle.
Sequences and series of real numbers.
Differential calculus for functions of one real variable.
Exponential and logarithmic functions. Trigonometric funtion.
Limits. Continuity (local and global properties).
Derivatives, monotony, convexity. Local maxima and local
minima.
Infinite and infinitesimal asymptotics. Taylor's formula.
Integral calculus for function of one real variable: primitive and
integral, techniques of integration (by parts, by substitution),
integral of rational functions. Generalized integrals.
An introduction to differential calculus for function of many
variables. Continuity and derivatives for function of due real
variables.
Integral calculus for function of two real variables.
Readings/Bibliography
Bertsch, Dal Passo, Giacomelli - Analisi matematica
(McGraw-Hill)
Bramanti, Pagani, Salsa Matematica (Zanichelli)
Salsa, Squellati - Esercizi di Matematica I(Zanichelli)
Salsa, Squellati - Esercizi di Matematica II (Zanichelli)
Teaching methods
During the lessons, the teacher explains the main lines of the theory, gives a lot of examples and shows how to solve various exercises.
Assessment methods
The examination aims to verify the reaching of the following
didactical goals:
-knowledge of basic notions of mathematical analysis
-ability in using these notions in solving exercises and
problems
The exam consists of two parts, written and oral.
1) The first part consists of a set of exercises. Books, notes,
computers and calculators are not allowed during this test.
2) The second test is oral. Only those that have passed the first
part are allowed to pass the second part.
Teaching tools
Blackboard, video and pc.
Some useful didactic material can be found at:
http://www.dm.unibo.it/~sordoni/Web/did2.html
Links to further information
http://www.dm.unibo.it/~sordoni/
Office hours
See the website of Vania Sordoni
See the website of Marco Mughetti