CODE 57069 ACADEMIC YEAR 2025/2026 CREDITS 9 cfu anno 1 INFORMATICA 11896 (L-31 R) - GENOVA SCIENTIFIC DISCIPLINARY SECTOR MAT/05 LANGUAGE Italian TEACHING LOCATION GENOVA SEMESTER 2° Semester PREREQUISITES Propedeuticità in uscita Questo insegnamento è propedeutico per gli insegnamenti: Computer Science 8759 (coorte 2025/2026) INFORMATION THEORY AND INFERENCE 80249 Computer Science 11896 (coorte 2025/2026) INFORMATION THEORY AND INFERENCE 80249 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 Learning the fundamental concepts of differential and integral calculus for functions of a single variable, to be able to carry out function analysis and the calculation of areas of plane figures, and to understand the main properties of elementary functions using a correct mathematical formalism. 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. RECOMMENDED READING/BIBLIOGRAPHY 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 FEDERICO BENVENUTO GIOVANNI ALBERTI Ricevimento: By appointment LESSONS LESSONS START According to the calendar approved by the Degree Program Board: https://corsi.unige.it/corsi/11896/studenti-orario 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 Guidelines for students with certified Specific Learning Disorders, disabilities, or other special educational needs are available at https://corsi.unige.it/corsi/11896/studenti-disabilita-dsa 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. FURTHER INFORMATION For further information, please refer to the course’s AulaWeb module or contact the instructor.