27991 - Mathematical Analysis T-1

Learning outcomes

Knowledge of basic mathematical tools (limits, derivatives, integrals) for the qualitative analysis of functions and for applications.

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 theo rem, 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 theo rem; Lagrange's theo rem;  monotone functions and derivative; convexity;  Taylor polynomial.
Elementary functions; study of function.
Amplitude of a complex number,  complex roots, complex logarithms.
Indefinite integrals, integrals; mean value theo rem 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_1/programma/elenco_programmi. html

Readings/Bibliography

We propose the following texts:

1.    Carlo Ravaglia: Corso di Analisi Matematica 1,  Edizioni Dupress (2009)
 
2.    Carlo Ravaglia: Analisi Matematica I - Compiti d'esame, Edizioni Dupress (2003)   

For a description of the tools
and for the place where they are found see
http://www.ciram.unibo.it/~ravaglia/corsi/analisi_1/strumenti_didattici.html

Teaching methods

Lessons and exercises in classroom.

Assessment methods

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

For more details see
http://www.ciram.unibo. it/~ravaglia/corsi/comune/modalita11.htm .

See also
http://www.ciram.unibo.it/~ravaglia/corsi/analisi_1/calendario.html
for the dates of examinations.

Teaching tools

We propose the following didactic tools:

1.   Texts of examination exercises academic years  2009/10 and  2010/11.
2.    Examination exercises academic year 2010/11(texts and solutions).
3.    Partial examination exercises present  academic year  2011/12 after the assignation (texts and solutions).

4.    Examination exercises present academic year  2011/12,  after the assignation (texts and solutions)..
5.    Carlo Ravaglia: Exercises of Mathematical Analysis 1.
6.    Detailed contents with marks of importance of the topics. 
7.   Questions on theory and  immediate exercises. 

For a description of the tools
and for the place where they are found see
http://www.ciram.unibo.it/~ravaglia/corsi/analisi_1/strumenti_didattici.html

Links to further information

http://www.ciram.unibo.it/~ravaglia/corsi/analisi_1/analisi_1.html

Office hours

See the website of Carlo Ravaglia