CODE 29032 ACADEMIC YEAR 2018/2019 CREDITS 7 cfu anno 1 MATEMATICA 9011 (LM-40) - GENOVA 7 cfu anno 2 MATEMATICA 9011 (LM-40) - GENOVA 7 cfu anno 3 MATEMATICA 8760 (L-35) - GENOVA SCIENTIFIC DISCIPLINARY SECTOR MAT/05 LANGUAGE Italian TEACHING LOCATION GENOVA SEMESTER 1° Semester TEACHING MATERIALS AULAWEB OVERVIEW Some basic topics in Partial Differential Equations are covered. The lectures are delivered in Italian. AIMS AND CONTENT LEARNING OUTCOMES The aim of this course is to provide a first introduction to Partial Differential Equations Theory. AIMS AND LEARNING OUTCOMES To provide some basic contents in Mathematical Analysis (Partial Differential Equations Theory) that are considered important to get a well grounded knowledge in the basic branches of Mathematics for the students who want to get a master's degree in Applied Mathematics. Expected learning outcomes: The students will become acquainted with the concepts and proofs carried out in class and how they are used in practice to solve exercises; moreover they will know how to produce easy variants of demonstrations seen and construct examples on topics covered in this course. PREREQUISITES Mathematical Analysis I, 2 and 3, the first semester of Geometry, "IAS 1" TEACHING METHODS Both theory and exercises are presented by the teacher in the classroom on the blackboard. SYLLABUS/CONTENT Fundamental linear partial differential equations with constant coefficients: the transport equation, the equations of Laplace, Poisson, the heat and the wave equation. General properties of the solutions: mean value property, maximum principle, energy estimates and their consequences. Some general techniques to obtain explicit formulas for solutions: separation of variables, Green’s function, reflection method, Duhamel’s principle, spherical means, method of descent. First order quasilinear equations. Conservation laws. RECOMMENDED READING/BIBLIOGRAPHY Lawrence C. Evans, Partial Differential Equations, Graduate Studies in Math. Vol. 19, 1998, American Mathematical Society, Providence , Rhode Island. S. Salsa - Partial differential equations in action: from modelling to theory - Springer 2008 TEACHERS AND EXAM BOARD GIANFRANCO BOTTARO Ricevimento: At the end of lectures or by appointment. Exam Board GIANFRANCO BOTTARO (President) GIOVANNI ALBERTI FRANCESCA ASTENGO LESSONS LESSONS START The class will start according to the academic calendar. Class schedule DIFFERENTIAL EQUATIONS EXAMS EXAM DESCRIPTION Written and oral. Exam schedule Data appello Orario Luogo Degree type Note 22/01/2019 09:00 GENOVA Scritto 18/02/2019 09:00 GENOVA Scritto 28/06/2019 09:00 GENOVA Scritto 22/07/2019 09:00 GENOVA Scritto 12/09/2019 09:00 GENOVA Scritto
