## OVERVIEW

This introductory calculus course covers differentiation and integration of functions of one variable, with applications.

## AIMS AND CONTENT

LEARNING OUTCOMES

The basic objective of Calculus is to relate small-scale (differential) quantities to large-scale (integrated) quantities. This is accomplished by means of the Fundamental Theorem of Calculus. Students should demonstrate an understanding of the integral as a cumulative sum, of the derivative as a rate of change, and of the inverse relationship between integration and differentiation.

TEACHING METHODS

Both theory and exercises are presented by the teacher in the classroom on the blackboard. The semester is 12 weeks. Moreover a tutor is available for this course. Some tutorial exercitations will be carried out during the semester.

SYLLABUS/CONTENT

- Both theory and exercises are presented by the teacher in the classroom on the blackboard. The semester is 12 weeks. Moreover a tutor is available for this course. Some tutorial exercitations will be carried out during the semester. Definition of derivative as a limit and the rules of differentiation to differentiate functions.
- The graph of a function using asymptotes, critical points, and the derivative test for increasing/decreasing and concavity properties.
- Max/min problems and the use of differentiation to solve them
- Integrals by using the Fundamental Theorem of Calculus.
- Techniques of integration, such as substitution, inverse substitution, partial fractions and integration by parts.

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

**Office hours:** Friday 14-16

Exam Board

ERNESTO DE VITO (President)

VINCENZA DEL PRETE (President)

ADA ARUFFO

SANDRO BETTIN

FILIPPO DE MARI CASARETO DAL VERME

GIANCARLO MAUCERI

## LESSONS

TEACHING METHODS

Both theory and exercises are presented by the teacher in the classroom on the blackboard. The semester is 12 weeks. Moreover a tutor is available for this course. Some tutorial exercitations will be carried out during the semester.

LESSONS START

According to the accademic calendar

Class schedule

All class schedules are posted on the EasyAcademy portal.

## EXAMS

EXAM DESCRIPTION

Written and oral tests.

ASSESSMENT METHODS

The written examination consists in some exercises about the topics covered in this course. In the oral exam a discussion of the written examination is done; moreover some questions are asked on the course content.

Exam schedule

Date | Time | Location | Type | Notes |
---|---|---|---|---|

15/01/2018 | 09:00 | GENOVA | Scritto | |

11/06/2018 | 09:00 | GENOVA | Scritto | |

25/06/2018 | 09:00 | GENOVA | Scritto | |

23/07/2018 | 09:00 | GENOVA | Scritto | Aula 506 |

23/07/2018 | 09:00 | GENOVA | Scritto | |

17/09/2018 | 09:00 | GENOVA | Scritto | |

16/01/2019 | 09:00 | GENOVA | Scritto |