CODE 115527 ACADEMIC YEAR 2024/2025 CREDITS 6 cfu anno 1 INGEGNERIA NAVALE 8722 (L-9) - GENOVA SCIENTIFIC DISCIPLINARY SECTOR MAT/05 TEACHING LOCATION GENOVA SEMESTER 1° Semester PREREQUISITES Propedeuticità in uscita Questo insegnamento è propedeutico per gli insegnamenti: Naval Architecture and Marine Engineering 8722 (coorte 2024/2025) HYDRODYNAMICS 66282 Naval Architecture and Marine Engineering 8722 (coorte 2024/2025) STRUCTURAL MECHANICS AND HYDRODYNAMICS 66281 TEACHING MATERIALS AULAWEB OVERVIEW The aim of the course is to provide the basic elements of differential calculus for functions of one variable AIMS AND CONTENT LEARNING OUTCOMES The course provides some basic concepts of mathematical analysis and the first elements of differential calculus for functions of one variable AIMS AND LEARNING OUTCOMES The main expected learning outcomes are • to master the mathematical notation • the knowledge of the properties of the main elementary functions • the ability to follow the logical concatenation of arguments • to master simple demonstration techniques • the ability to solve exercises, discussing the reasonableness of the results Transversal skills: Literacy (basic level): Ability to communicate effectively in written and oral form, adaptation of one's communication to the context, use of sources and aids of various kind PREREQUISITES Numerical sets, equations and inequalities, analytical geometry, trigonometry TEACHING METHODS Lecture classes and exercise classes. For the transversal skills, a problem solving based approach will be used SYLLABUS/CONTENT Real numbers, the oriented real line. The Cartesian plane, graphs of elementary functions. Operations on functions and their graphical interpretation. Monotonicity. Composition and inversion. Powers, exponentials and logarithms. Supremum and infimunm. Numerical sequences: the basic notions and examples. Limits of functions. Infinitesimal and infinite functions. Continuous functions and their local and global properties. Derivatives and derivation rules. Derivatives of elementary functions. Sign of derivatives in the study of monotonicity and convexity. The classical theorems of Rolle, Cauchy, Lagrange and de l'Hôpital. Study of the graph of functions. Taylor expansions and theoir applications. RECOMMENDED READING/BIBLIOGRAPHY • C. Canuto, A. Tabacco, Analisi Matematica 1, 4a edizione, Springer-Verlag Italia, 2014, • M. Baronti, M., F. De Mari, R. van der Putten, I. Venturi, Calculus Problems, Springer International Publishing Switzerland, 2016 TEACHERS AND EXAM BOARD ANDREA BRUNO CARBONARO Ricevimento: By appointment, to be scheduled by e-mail CHIARA ROMANENGO Exam Board ANDREA BRUNO CARBONARO (President) MARCO BARONTI (President Substitute) SIMONE DI MARINO (President Substitute) CLAUDIO ESTATICO (President Substitute) EDOARDO MAININI (President Substitute) CHIARA ROMANENGO (President Substitute) LESSONS LESSONS START https://corsi.unige.it/en/corsi/8720/studenti-orario Class schedule The timetable for this course is available here: Portale EasyAcademy EXAMS EXAM DESCRIPTION The exam consists of • Multiple choice test • Written exam To enroll the exam you must register by the deadline on the website https://servizionline.unige.it/studenti/esami/prenotazione ASSESSMENT METHODS Multiple choice tests: It is aimed to verify the student's ability to manage mathematical notation and to carry out simple computations and simple deductive reasoning. It is necessary to be successful in the multiple choice test in order to access the written exam Written exam: This part includes open questions and exercises. It is aimed to verify the knowledge of the main tools of differential calculus. The written exam consists of exercises with several questions of different difficulty. The student must be able to solve the exercises correctly and to justify the necessary steps to obtain the final result, and to use the correct formalism. Exam schedule Data appello Orario Luogo Degree type Note 22/01/2025 08:00 GENOVA Scritto 07/02/2025 08:00 GENOVA Scritto 17/06/2025 08:00 GENOVA Scritto 16/07/2025 08:00 GENOVA Scritto 05/09/2025 08:00 GENOVA Scritto FURTHER INFORMATION Ask the professor for other information not included in the teaching schedule. Agenda 2030 - Sustainable Development Goals Quality education Gender equality