CODE 25900 ACADEMIC YEAR 2024/2025 CREDITS 8 cfu anno 2 MATEMATICA 8760 (L-35) - GENOVA SCIENTIFIC DISCIPLINARY SECTOR MAT/05 LANGUAGE Italian TEACHING LOCATION GENOVA SEMESTER 1° Semester TEACHING MATERIALS AULAWEB OVERVIEW The aim of the course is to consolidate the theoretical knowledge about Mathematical Analysis I and to extend it to the study of functions of several variables and to the study of sequences and series of functions. AIMS AND CONTENT LEARNING OUTCOMES Introduction to the mathematical analysis and to the differential calculus of scalar-valued and vector-valued functions of multiple variables. AIMS AND LEARNING OUTCOMES The aim of the course is providing students with the main notions of function sequences and series and of the differential calculus of functions of several variables. At the end of the course the student will have to know the definitions, understand the main theorems, and be able to solve and analyze problems. PREREQUISITES Mathematical Analysis I, Linear algebra and analytic geometry TEACHING METHODS The course will be divided into two parts: theory and exercises. During the theoretical lessons the definitions, the statements and the proofs of the theorems will be presented, in addition to examples and exercises. During the other part of the course, many examples and exercises will be studied and solved in order to clarify the different aspects of the theory. SYLLABUS/CONTENT Sequences and series of functions, power series Differential calculus of functions of several variables The Cauchy problem for ordinary differential equations and systems RECOMMENDED READING/BIBLIOGRAPHY Paolo Marcellini, Carlo Sbordone - Esercitazioni di analisi matematica due, Zanichelli Nicola Fusco, Paolo Marcellini, Carlo Sbordone - Lezioni di analisi matematica due, Zanichelli Marco Bramanti, Carlo D. Pagani, Sandro Salsa - Analisi matematica 2, Zanichelli Terence Tao, Analysis II, Springer TEACHERS AND EXAM BOARD MARCO BARONTI Ricevimento: The teacher receives students on a day in the week at the office located at the degree course building. The day will be fixed on February 2025. The e - mail address is : marco.baronti@unige.it FILIPPO DE MARI CASARETO DAL VERME Ricevimento: Weekly office hours, typically 2-hours per week, will be communicated. Meetings upon E-mail requests will also be considered compatibly with the teacher's availability. Exam Board FILIPPO DE MARI CASARETO DAL VERME (President) MARCO BARONTI LESSONS LESSONS START The class will start according to the academic calendar. Class schedule The timetable for this course is available here: Portale EasyAcademy EXAMS EXAM DESCRIPTION The exam consists of a written test and of an oral test. The oral exam is not compulsory, and only the students who obtain at least 15 in the written test may participate to the oral exam. If a student decides not to take the oral exam, the final mark will be the minimum between the mark of the written test and 25. Students with DSA certification ("specific learning disabilities"), disability or other special educational needs, are advised to follow carefully the instructions available on Aulaweb at https://2023.aulaweb.unige.it/course/view.php?id=12490#section-3. In particular, in order to be granted the necessary arrangements, it is necessary to notify the teachers via E-mail at least 10 days before the exam. ASSESSMENT METHODS Both written and oral exams consist in problems on the topics of the course and in the exposition of some parts of the theory. The student needs to show the ability of critical thinking, the ability of applying the results of the theory to solve the problems, and the knowledge of the theory. Exam schedule Data appello Orario Luogo Degree type Note 08/01/2025 09:00 GENOVA Scritto 14/01/2025 09:00 GENOVA Orale 03/02/2025 09:00 GENOVA Scritto 06/02/2025 09:00 GENOVA Orale 13/06/2025 09:00 GENOVA Scritto 16/06/2025 09:00 GENOVA Orale 09/07/2025 09:00 GENOVA Scritto 15/07/2025 09:00 GENOVA Orale 10/09/2025 09:00 GENOVA Scritto 15/09/2025 09:00 GENOVA Orale Agenda 2030 - Sustainable Development Goals Quality education Gender equality