# CALCULUS 1

iten
Code
57069
2020/2021
CREDITS
9 credits during the 1st year of 8759 Computer Science (L-31) GENOVA
SCIENTIFIC DISCIPLINARY SECTOR
MAT/05
LANGUAGE
Italian
TEACHING LOCATION
GENOVA (Computer Science)
semester
2° Semester
Teaching materials

## OVERVIEW

This introductory calculus course builds up on the mathematics learnt during the high school. The main topics of the course are differentiation and integration of functions of one variable.

## 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.

AIMS AND LEARNING OUTCOMES

At the end of this course the students are expected:

• to master the mathematical notation;
• to know the properties of the elementary functions and their graph;
• to be able to follow the mathematical arguments;
• and to solve simple exercises, and discuss the results obtained.

PREREQUISITES

Sets, equalities and inequalities, analytic geometry, trigonometry.

TEACHING METHODS

Both theory and exercises are presented by the teachers. Some tutorials will be carried out during the semester.

SYLLABUS/CONTENT

The real numbers - The real numbers, maxima, minima, supremum, infimum.

Functions - Elementary functions, composite function, inverse function.

Limits and continuity - Limits of functions. Continuity. Global properties of continuous functions. The intermediate value theorem and the extreme value theorem.

Differentiation - Derivative of a function. Tangent line. Derivative of the composite function and of the inverse function. The theorems of Rolle, Chauchy and Lagrange. De l’Hôpital's rule.

Integration - Riemann and Cauchy sums. Indefinite integral. Area of a planar region. Mean value theorem. Integral functions. The fundamental theorem of calculus. Calculating primitives.

Some notes and exercises are available.

Recommended books

• M. Oberguggenberger, A. Ostermann, Analysis for Computer Scientists: Foundations, Methods, and Algorithms, Springer-Verlag,
ISBN 978-0-85729-445-6
• M. Baronti, M., F. De Mari,  R. van der Putten, I. Venturi,  Calculus Problems, Springer-Verlag, ISBN: 978-3-319-15427-5
• G. Crasta- A. Malusa, Elementi di Analisi Matematica e Geometria con prerequisiti ed esercizi svolti, Edizione La Dotta, ISBN: 978-88-986482-5-2

## TEACHERS AND EXAM BOARD

Office hours: By appointment

Exam Board

GIOVANNI ALBERTI (President)

FEDERICO BENVENUTO

## LESSONS

TEACHING METHODS

Both theory and exercises are presented by the teachers. Some tutorials will be carried out during the semester.

LESSONS START

Class schedule

All class schedules are posted on the EasyAcademy portal.

## EXAMS

EXAM DESCRIPTION

The exam consists of two written tests:

• Test with multiple answers, consisting of questions on the theory and of simple exercises. In order to participate to the second part of the exam the students need to obtain at least 15 points.
• Written test with more complex problems. In order to pass this part the students need to obtain at least 18.

The final mark of the exam is given by

(first part)*1/3 + (second part)*2/3

rounded up to the nearest whole number.

ASSESSMENT METHODS

• The first part of the exam allows us to verify the knowledge of the students and the ability of the students to handle the mathematical notation and to make simple deductive reasonings.
• The second part allows us to verify the ability to solve simple calculations and the knowledge of the main tools related to differentiation and integration.

Exam schedule

Date Time Location Type Notes
11/01/2021 09:00 GENOVA Scritto
11/01/2021 10:00 GENOVA Scritto 10 gennaio 2022 aula 506
07/06/2021 10:00 GENOVA Scritto 10 gennaio 2022 aula 506
30/06/2021 10:00 GENOVA Scritto 10 gennaio 2022 aula 506
19/07/2021 10:00 GENOVA Scritto 10 gennaio 2022 aula 506
13/09/2021 10:00 GENOVA Scritto 10 gennaio 2022 aula 506
10/01/2022 10:00 GENOVA Scritto 10 gennaio 2022 aula 506