Mikaela Iacobelli: Katalogdaten im Herbstsemester 2019

NameFrau Prof. Dr. Mikaela Iacobelli
LehrgebietMathematik
Adresse
Dep. Mathematik
ETH Zürich, HG G 48.2
Rämistrasse 101
8092 Zürich
SWITZERLAND
Telefon+41 44 632 50 68
E-Mailmikaela.iacobelli@math.ethz.ch
DepartementMathematik
BeziehungAusserordentliche Professorin

NummerTitelECTSUmfangDozierende
401-0353-00LAnalysis 3 Information 4 KP2V + 2UM. Iacobelli
KurzbeschreibungIn 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.
LernzielThe aim of this class is to provide students with a general overview of first and second order PDEs, and teach them how to solve some of these equations using characteristics and/or separation of variables.
Inhalt1.) General introduction to PDEs and their classification (linear, quasilinear, semilinear, nonlinear / elliptic, parabolic, hyperbolic)

2.) Quasilinear first order PDEs
- Solution with the method of characteristics
- COnservation laws

3.) Hyperbolic PDEs
- wave equation
- d'Alembert formula in (1+1)-dimensions
- method of separation of variables

4.) Parabolic PDEs
- heat equation
- maximum principle
- method of separation of variables

5.) Elliptic PDEs
- Laplace equation
- maximum principle
- method of separation of variables
- variational method
LiteraturY. Pinchover, J. Rubinstein, "An Introduction to Partial Differential Equations", Cambridge University Press (12. Mai 2005)
Voraussetzungen / BesonderesPrerequisites: Analysis I and II, Fourier series (Complex Analysis)
401-5350-00LAnalysis Seminar Information 0 KP1KM. Struwe, A. Carlotto, F. Da Lio, A. Figalli, N. Hungerbühler, M. Iacobelli, T. Ilmanen, Uni-Dozierende
KurzbeschreibungResearch colloquium
Lernziel