17909 - Mathematical Analysis L-A

Learning outcomes

The course intends the following aims
  ·        To stengthen the logical-deductive method, used in mathematics.

 ·         To strengthen and to systematize topics of elementary mathematics, for instance equations and inequalities.

 ·         To develop the classical topics of a course of Mathematical Analysis of first level: limits, derivatives, study of function, integrals.

Course contents

Real numbers; least upper bound, greatest lower bound,
monotone functions; powers; radicals; real equations; inequalities.
Complex numbers. 
The Euclidean space R^N.
Continuity;  Weierstrass's theorem, Bolzano' s theorem; limits.
Asymptotic equivalents functions, asymptotic negligible functions, principle of
substitution for the limits.
Series; principle of comparison; absolutely convergent series.
Derivative; local bound and derivative,  Rolle's theorem; Lagrange's theorem;  monotone functions and derivative; convexity;  Taylor polynomial.
Elementary functions; study of function.
Amplitude of a complex number,  complex roots.
Indefinite integrals, integrals; mean value theorem for integrals ;
integration by substitution, integration by parts; integration of
 rational functions.
Improper integrals.

For  detailed contents with marks of importance of the topics (in Italian)
see
http://www.ciram.unibo.it/~ravaglia/corsi/analisi_la/programma/elenco_programmi.html

Readings/Bibliography

We propose the following texts:

1.    Carlo Ravaglia: Corso di Analisi Matematica L-A, d.u.press (2006)
 
2.    Carlo Ravaglia: Analisi Matematica I - Compiti d'esame, Edizioni Nautilus (2003)   

For a description of the tools
and for the place where they are found see
http://www.ciram.unibo.it/~ravaglia/corsi/analisi_la/strumenti_didattici.html

Teaching methods

Lessons and exercises in classroom

Assessment methods

Partial examination exercises during the development of the course.
Written examination; oral examination.

For more details see
http://www.ciram.unibo.it/~ravaglia/corsi/comune/modalita06.htm .

See also
http://www.ciram.unibo.it/~ravaglia/corsi/analisi_la/calendario.html
for the dates of examinations.

Teaching tools

We propose the following didactic tools:

1.   Texts of examination exercises academic years  2005/06 and  2006/07.
2.    Examination exercises academic year 2006/07.
3.    Partial examination exercises present  academic year  2007/08.
4.    Examination exercises present academic year  2007/08.
5.    Carlo Ravaglia: Exercises of Mathematical Analysis L-A.
6.    Detailed contents with marks of importance of the topics.
  
For a description of the tools
and for the place where they are found see
http://www.ciram.unibo.it/~ravaglia/corsi/analisi_la/strumenti_didattici.html

Links to further information

http://www.ciram.unibo.it/~ravaglia/corsi/analisi_la

Office hours

See the website of Carlo Ravaglia