Found 14 relevant results in 1.99s where lecturer="Alessandra Iozzi"
In this lecture we treat problems in applied analysis. The focus lies on the solution of quasilinear first order PDEs with the method of characteristics, and on the study of three fundamental types of partial differential equations of second order: the Laplace equation, the heat equation, and the wave equation.
Introduction to partial differential equations. Differential equations which are important in applications are classified and solved. Elliptic, parabolic and hyperbolic differential equations are treated. The following mathematical tools are introduced: Laplace transforms, Fourier series, separation of variables, methods of characteristics.
The focus lies on the simplest cases of three fundamental types of partial differential equations of second order: the Laplace equation, the heat equation and the wave equation.
The focus lies on the simplest cases of three fundamental types of partial differential equations of second order: the Laplace equation, the heat equation and the wave equation.
Measure and Integration
Mass und Integral
Introduction to abstract measure and integration theory, including the following topics: Caratheodory extension theorem, Lebesgue measure, convergence theorems, L^p-spaces, Radon-Nikodym theorem, product measures and Fubini's theorem, measures on topological spaces
The students presented results in various directions which involved the use of bounded cohomology for discrete groups as prior to the theory developed by Burger and Monod in 2000.
No description available.
Mathematical Methods
Mathematische Methoden
Foundations of complex calculus in theory & applications and introduction to integral transforms covering some applications.
We give an introduction to the homological algebra approach to the continuousbounded cohomology theory for general locally compact groups and with coefficientsdeveloped by Burger and Monod in 2000. This involves, among others, heavy functional analytical techniques and the theory of amenable actions.
Topological groups and Haar measure. Definition of Lie groups, examples of local fields and examples of discrete subgroups; basic properties; Lie subgroups. Lie algebras and relation with Lie groups: exponential map, adjoint representation. Semisimplicity, nilpotency, solvability, compactness: Killing form, Lie's and Engel's theorems. Definition of algebraic groups and relation with Lie groups.
1) Definition, basic properties. Lie subgroups.2) Lie algebras and their relation with Lie groups: exponential map, adjoint representation.3) Semisimplicity, nilpotency, solvability, compactness: Killing form, Lie's theorem, Engel's theorem.4) Definition of algebraic groups and relation with Lie groups.5) Applications: Lie groups in the diffeomorphism group of a manifold, invariant volume.
* Generalities on symmetric spaces: locally and globally symmetric spaces, groups of isometries, examples* Symmetric spaces of non-compact type: flats and rank, roots and root spaces* Iwasawa decomposition, Weyl group, Cartan decomposition* Geometry at infinity
* Generalities on symmetric spaces: locally and globally symmetric spaces, groups of isometries, examples* Symmetric spaces of non-compact type: flats and rank, roots and root spaces* Iwasawa decomposition, Weyl group, Cartan decomposition* Geometry at infinity