OVERVIEW

The basic topics in calculus of severable variables are covered: numerical and Fourier series, differential calculus, study of maxima and minima of functions of two real variables.

LEARNING OUTCOMES

The students will become acquainted with the most important topics regarding functions of several variables and how they are used in practice. The only proof that are presented are those which show fundamental principles, and are free of technicalities.
 

AIMS AND LEARNING OUTCOMES

The course want to give the elementar notions on the numerical and power series, and the basic knowdlege on the differential and  for real and vectorial functions.

At the end, students should be able to:  

-correctly calculate elementar and standard calculations concerning numerical and power series, partial and directional derivates,              -determine maxima e minima for functions of several variables, 

-find the Fourier series of periodic functions.

PREREQUISITES

Differential and Integral Calculus 1.

Teaching methods

Both theory and exercises are presented by classroom lessons held at the blackboard. The semester is 12 weeks long with four hours of theory and two hours of exercsces each week. Some tutorial exercitation will be carried out during the semester. 

Attendance is mandatory.

SYLLABUS/CONTENT

This course covers differential, integral and vector calculus for functions of more than one variable. Topics include:

• Sequences and series of functions.
• Fourier series.
• Functions of several variables, continuity, differentiability, derivative.
• Parametrization of curves.

RECOMMENDED READING/BIBLIOGRAPHY

Baronti, M., De Mari, F., van der Putten, R., Venturi, I., Calculus Problems,
ISBN 978-3-319-15428-2, Springer-Verlag

O. Caligaris - P. Oliva, Analisi Matematica I e II, ECIG
J.P. Cecconi - G. Stampacchia, Analisi Matematica I e II, Liguori
T. Zolezzi, Analisi matematica II, Dispense 
Libri di esercizi svolti:
J.P. Cecconi - L. Piccinini - G. Stampacchia, Esercizi di Analisi Matematica I e II, Liguori
M. Chicco - F. Ferro, Esercizi svolti di Analisi Matematica II, ECIG
S. Salsa - A. Squellati, Esercizi di Matematica - Calcolo infinitesimale, volume 2, Zanichelli

Exam Board

VERONICA UMANITA' (President)

Teaching methods

Both theory and exercises are presented by classroom lessons held at the blackboard. The semester is 12 weeks long with four hours of theory and two hours of exercsces each week. Some tutorial exercitation will be carried out during the semester. 

Attendance is mandatory.

LESSONS START

The class will start according to the accademic calendar.

Exam description

Written  test.

Assessment methods

The written examination consists in some exercises about the topics covered in this course. The duration of the test is two and half hours and it is possible to consult the notes and textbooks. 

Exam schedule