CODE 57069 2024/2025 9 cfu anno 1 INFORMATICA 8759 (L-31) - GENOVA MAT/05 Italian GENOVA 2° Semester Questo insegnamento è propedeutico per gli insegnamenti: Computer Science 8759 (coorte 2024/2025) BASIC OF INFORMATION AND INFERENCE 80249 AULAWEB

## 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

• C. Canuto, A. Tabacco, Mathematical Analysis 1, ISBN: 9788891931115
• 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

## TEACHERS AND EXAM BOARD

### Exam Board

GIOVANNI ALBERTI (President)

FEDERICO BENVENUTO (President)

## LESSONS

### Class schedule

The timetable for this course is available here: Portale EasyAcademy

## EXAMS

### EXAM DESCRIPTION

The exam consists of one written test, composed of two parts:

• A test made of multiple-choice questions, about the theory seen during the course and with simple exercises
• Written test with more complex problems.

The exam is passed if both parts are sufficient. The final mark is given by

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

### ASSESSMENT METHODS

• The first part of the exam allows us to verify 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.