CODE 29032 ACADEMIC YEAR 2023/2024 CREDITS 6 cfu anno 2 MATEMATICA 9011 (LM-40) - GENOVA 6 cfu anno 1 MATEMATICA 9011 (LM-40) - GENOVA SCIENTIFIC DISCIPLINARY SECTOR MAT/05 TEACHING LOCATION GENOVA SEMESTER 1° Semester TEACHING MATERIALS AULAWEB OVERVIEW The course introduces the study of partial differential equations (PDE). Given the richness and the variety of physical, geometric and probabilistic phenomena that these equations can describe, there is no general theory that allows them to be studied and solved in a unified way. We therefore aim to analyze equations and methods that are the most important for applications. Large attention will be given to some specific linear PDEs of the first and second order (linear transport equation, Laplace and Poisson equations, heat equation, wave equation); hints of theory for some non-linear PDEs will also be provided. AIMS AND CONTENT LEARNING OUTCOMES The aim of this course is to provide a first introduction to the theory of partial differential equations. AIMS AND LEARNING OUTCOMES Learn to classify partial differential equations and identify the most appropriate resolution or analysis methods for each of the "classical" ones; know how to apply them to find formulas for representing solutions or to establish their qualitative properties. PREREQUISITES A basic knowledge of measure theory, Lebesgue spaces and ordinary differential equations is recommended. TEACHING METHODS Traditional teaching (theoretical lessons on the blackboard and exercises) SYLLABUS/CONTENT Linear transport equation, Laplace and Poisson equations, harmonic functions, Perron method, heat equation, wave equation, method of characteristics, conservation laws, other methods for representing solutions. RECOMMENDED READING/BIBLIOGRAPHY Evans, "Partial Differential Equations" Salsa, "Equazioni a derivate parziali" TEACHERS AND EXAM BOARD FLAVIANA IURLANO Ricevimento: By appointment Exam Board FLAVIANA IURLANO (President) SIMONE DI MARINO FILIPPO DE MARI CASARETO DAL VERME (President Substitute) ANDREA BRUNO CARBONARO (Substitute) MATTEO SANTACESARIA (Substitute) LESSONS LESSONS START Classes begin October 2, 2023 Class schedule The timetable for this course is available here: Portale EasyAcademy EXAMS EXAM DESCRIPTION Written and oral exam ASSESSMENT METHODS The written exam will verify: the ability to identify suitable methods to solve the proposed problems; the ability to apply the identified methods; the ability to argue and justify the steps taken. The oral exam will verify: demonstrative and argumentative skills; knowledge not positively assessed in the written exam. Exam schedule Data appello Orario Luogo Degree type Note 15/01/2024 10:00 GENOVA Scritto 06/02/2024 10:00 GENOVA Scritto 11/06/2024 10:00 GENOVA Scritto 15/07/2024 10:00 GENOVA Scritto