00013 - Mathematical Analysis

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