# MATHEMATICAL ANALYSIS 2

8 credits during the 2nd year of 8766 Mathematical Statistics and Data Management (L-35) GENOVA

OVERVIEW

The basic topics in calculus of severable variables are covered. The course is split in two semesters. Physics and SMID students need to take the first part devoted to differential calculus, integration theory in two variables. The second semester is mandatory only for Physics students covering integration along curves and surfaces, Gauss and Stokes' theorems and their consequences, and an introduction to systems of differential equations and Fourier series.

## AIMS AND CONTENT

LEARNING OUTCOMES

Students will become acquinted 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 illustrate fundamental principles and are free of technicalities.

Applications to Physics and Probability are emphasised.

Teaching methods

Both theory and exercises are presented by the teacher in the classroom on the blackboard. The first semester consists of 12 weeks with four hours of theory and two hours of exercices each week. The second semester consists of 12 weeks with three hours of theory and two hours of exercises each week.

SYLLABUS/CONTENT

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

- Sequences and series of functions.
- Functions of several variables, continuity, differentiability, derivative.
- Parametrized curves, arc length, curvature, torsion.
- Vector fields, gradient, curl, divergence.
- Multiple integrals, change of variables, line integrals, surface integrals.
- Stokes' theorem in one, two, and three dimensions.

RECOMMENDED READING/BIBLIOGRAPHY

Serge Lang - Calculus of Several Variables, Third Edition, Undergraduate Texts in Mathematics, Springer, 1987.

## TEACHERS AND EXAM BOARD

**Ricevimento:** At the end of lectures or by appointment.

**Ricevimento:** At the end of lectures or by appointment.

Exam Board

FRANCESCA ASTENGO (President)

ENRICO CALCAGNO

ADA ARUFFO

## LESSONS

Teaching methods

Both theory and exercises are presented by the teacher in the classroom on the blackboard. The first semester consists of 12 weeks with four hours of theory and two hours of exercices each week. The second semester consists of 12 weeks with three hours of theory and two hours of exercises each week.

LESSONS START

The class will start according to the accademic calendar.

## EXAMS

Exam description

Written and oral exam

Assessment methods

The written examination consists in four/five exercises.

The oral exam is optional. If a student does not give it

- the final mark is the grade of the written exam if less or equal than 24
- the final mark is 24 if the grade of the written exam if greater than 24

## FURTHER INFORMATION

For any further informations, please send a message to devito@dima.unige.it