Found 21 relevant results in 1.50s where lecturer="Francesca Da Lio"
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Introduction to first and second-order PDE: transport, wave, Laplace, and heat equations. PDE methods: superposition, representation formulae, Duhamel, separation of variables, etc. Introduction to existence and regularity theories. Some example results for nonlinear PDE.
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.
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
Measure and Integration Theory, including: Caratheodory's Theorem, Lebesgue Measure, Radon Measure, Hausdorff Measure, Convergence Theorems, L^p Spaces, Radon-Nikodym Theorem, Product Measure and Fubini's Theorem
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Measure and integration theory, including: Caratheodory's theorem, Lebesgue measure, Radon measure, Hausdorff measure, convergence theorems, L^p spaces, Radon-Nikodym theorem, product measure and Fubini's theorem
This class covers the basic theory of Hilbert spaces, Fourier series and Fourier Transform, and its application to the study of classical linear PDEs.
No description available.
Mathematical Methods
Mathematische Methoden
Foundations of complex calculus in theory & applications and introduction to integral transforms covering some applications.
No description available.
Many problems in mathematics, physics, and engineering can be described as optimization problems: finding the best possible shape, path, or configuration among many alternatives. The Calculus of Variations is a branch of mathematics that studies such problems by analyzing quantities such as length, energy, or cost, and by understanding how they can be minimized or maximized.
We will start by showing some examples of the different applications of the theory. We will then describe the properties of viscosity solutions and explain the methods to get existence and uniqueness results. We shall finally consider in more detail the application of the theory to study ergodic and homogenization problems for fully nonlinear first and second order pde's.
In this course I introduce the notion of viscosity solution for second order fully nonlinear elliptic and parabolic PDEs. We present the techniques and methods to get uniqueness and existence results in the second order case. In particular we give the proof of two fundamental results: the Jensen's Maximum Principle and the so called Ishii's Lemma.
This course covers mathematical concepts and techniques necessary to model, solve and discuss scientific problems - notably through ordinary differential equations.
Mathematics I
Mathematik I: Analysis I und Lineare Algebra
This course covers mathematical concepts and techniques necessary to model, solve and discuss scientific problems - notably through ordinary differential equations.
Mathematics I covers mathematical concepts and techniques necessary to model, solve and discuss scientific problems - notably through ordinary differential equations.The main focus of Mathematics II is multivariable calculus.
Mathematics II
Mathematik II: Analysis II
Continuation of the topics of Mathematics I, with main focus on multivariable calculus.
Mathematics III: Partial Differential Equations
Mathematik III: Partielle Differentialgleichungen
Examples of partial differential equations. Linear partial differential equations. Separation of variables. Fourier series, Fourier transform, Laplace transform. Applications to solving commonly encountered linear partial differential equations (Laplace's Equation, Heat Equation, Wave Equation).
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
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