OVERVIEW

The basic topics in calculus of severable variables are covered: differential calculus,  integration theory in two variables,  systems of differential equations and Fourier series. 

AIMS AND CONTENT

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.
Applications to Machine Learning and Computer Science are emphazised. 

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 integral calculus 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 maximus e minima for functions of several variables, and calculate multiple integrals.

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. Moreover a tutor is available for the course, and 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:

• Improper integrals.
• Sequences and series of functions.
• Functions of several variables, continuity, differentiability, derivative.
• Multiple integrals, change of variables,
• Systems of differential equations
• Fourier series

RECOMMENDED READING/BIBLIOGRAPHY

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

TEACHERS AND EXAM BOARD

Exam Board

VERONICA UMANITA' (President)

SILVIA VILLA

LESSONS

LESSONS START

The class will start according to the accademic calendar.

Class schedule

CALCULUS 2

EXAMS

EXAM DESCRIPTION

Written and oral tests.

ASSESSMENT METHODS

The written examination consists in some exercises about the topics covered in this course. The duration of the test is two/three hours and it is possible to consult the notes and textbooks. The same procedures apply to each of the two partial tests.

In the oral exam a discussion of the written examination is done; moreover some questions are asked on the course content.

Public speaking ability is assessed.

Exam schedule

FURTHER INFORMATION

This teaching is planned for the curriculum: methodological.

Registration for exams is required.