Some basic topics in partial differential equations are covered.
The lectures are delivered in Italian.
The aim of this course is to provide a first introduction to the theory of partial differential equations.
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.
Mathematical Analysis I, 2 and 3, the first semester of Geometry, "IAS 1" (Functional analysis and L^p spaces)
Both theory and exercises are presented by the teacher in the classroom on the blackboard.
Fundamental linear partial differential equations with constant coefficients: the transport equation, the Laplace equation, Poisson, the heat and the wave equation. General properties of the solutions: mean value property, maximum principles, energy estimates and their consequences. Some general techniques to obtain explicit formulas for solutions: separation of variables, Green’s functions, reflection method, Perron's method, some potential theory, Duhamel’s principle, spherical means, method of descent. Conservation laws.
S. Salsa - Partial differential equations in action: from modelling to theory - Springer 2016
MATTEO SANTACESARIA (President)
GIOVANNI ALBERTI
FRANCESCA ASTENGO (President Substitute)
The class will start according to the academic calendar.
DIFFERENTIAL EQUATIONS
Written and oral.
