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

1.  Real numbers; least upper bound, greatest lower bound,
   monotone functions; powers; radicals; real equations; inequalities.
2.  Complex numbers.
3.  The Euclidean space R^N.
4.  Continuity; Weierstrass's theorem, Bolzano's theorem; limits.
5.  Asymptotic equivalents functions, asymptotic negligible functions, principle of
   substitution for the limits.
6. Series; principle of comparison; absolutely convergent series.
7. Power series.
8. Derivative; local bound and derivative, Rolle's theorem; Lagrange's theo rem; monotone functions and derivative; convexity; Taylor polynomial.
9. Elementary functions; study of function.
10. Amplitude of a complex number, complex roots.
11. Developments in series.
12. Indefinite integrals, integrals; mean value theorem for integrals; integration by substitution, integration by parts; integration of
    rational functions.
13. Improper integrals.
    
    
    
    

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://people.ciram.unibo.it/~ravaglia/ corsi/analisi_1/strumenti_didattici.html

Teaching methods

Lessons and exercises in classroom. For each topic is reserved a fixed number of hours. The total hours of lessons and exercises are exactly  90, according the planned program

Assessment methods

The exam is written and is divided into two parts:
1.Test of  exercises,
2.Test of theory.
The exercises test comprises a series of exercises of a task,  the same or in different versions for all students. It aims to assess the skills achieved in solving problems in the context of the issues addressed. It is not consented to the use of books, notes, calculators and computer media. Each exercise has a score, for a total of 33 points. Who holds a vote greater than or equal to 12.5 and less than 14.5, he is admitted to a recovery test of exercises, which, if positive carries the vote to 14.5. To be admitted to the test of theory it is necessary to have obtained in the exercises test, including through the recovery test, at least 14.5.The exercise test gives for the final grade  a score equal to the vote of the test exercises divided by 30 and multiplied by 26. The test exercises is valid only for  the appeal.

The theory test comprises the iterative written answer to some questions of theory and to some simple exercise, from an individual card with questions randomly chosen. It aims to test the knowledge of the  program. The theory test gives for the final grade a score from -26 to 9.

The final grade is the sum of points obtained in the  exercises test and of points obtained in the theory test.

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

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

Top of page

Teaching tools

We propose the following didactic tools:

1. Texts of examination exercises academic years 2013/14 and 2014/15.
2. Examination exercises academic year 2014/15 (texts and solutions).
3. Examination exercises present academic Year 2015/16, after the assignation (text and solutions).
4. Carlo Ravaglia: Corso di Analisi Matematica 1 - Esercizi.
5. Detailed contents with marks of importance of the topics.
6. Questions on theory and immediate exercises.

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

Links to further information

http://people.ciram.unibo.it/~ravaglia/serverdidattica.html

Office hours

See the website of Carlo Ravaglia