Francesca Da Lio: Katalogdaten im Frühjahrssemester 2018

NameFrau Prof. Dr. Francesca Da Lio
Dep. Mathematik
ETH Zürich, HG G 37.2
Rämistrasse 101
8092 Zürich
Telefon+41 44 632 86 96
Fax+41 44 632 10 85

401-3352-09LAn Introduction to Partial Differential Equations Information 6 KP3VC. Busch, F. Da Lio
KurzbeschreibungThis course aims at being an introduction to first and second order partial differential equations (in short PDEs).
We will present the so called method of characteristics to solve quasilinear PDEs and some basic properties of classical solutions to second order linear PDEs.
InhaltA preliminary plan is the following
- Laplace equation, fundamental solution, harmonic functions and main properties, maximum principle. Poisson equation. Green functions. Perron method for the solution of the Dirichlet problem. Regularity of solutions to the Poisson Equation.
- Heat equation, fundamental solution, existence of solutions to the Cauchy problem and representation formulas, main properties, uniqueness by maximum principle, regularity.
- The Method of characteristics for first order equations, linear and nonlinear, transport equation, Hamilton-Jacobi equation, scalar conservation laws.
-Time permitting: Wave equation, existence of the solution, D'Alembert formula, solutions by spherical means, main properties, uniqueness by energy methods.
SkriptThe teacher provides the students with personal notes.
- L.Evans Partial Differential Equations, AMS 2010 (2nd edition)
- D. Gilbarg, N.S. Trudinger Elliptic Partial Differential Equations of Second Order, Springer, 1998.
- E. Di Benedetto Partial Differential Equations, Birkauser, 2010 (2nd edition).
- W. A. Strauss Partial Differential Equations. An Introduction, Wiley, 1992.
-Q. Han, A Basic Course in Partial Differential Equations, Graduate Studies in Mathematics Volume: 120; 2011.
Voraussetzungen / BesonderesDifferential and integral calculus for functions of several variables; elementary theory of ordinary differential equations, basic facts of measure theory.
401-5350-00LAnalysis Seminar Information 0 KP1KM. Struwe, A. Carlotto, F. Da Lio, A. Figalli, N. Hungerbühler, T. Kappeler, T. Rivière, D. A. Salamon
InhaltResearch seminar in Analysis
406-0353-AALAnalysis III
Belegung ist NUR erlaubt für MSc Studierende, die diese Lerneinheit als Auflagenfach verfügt haben.

Alle anderen Studierenden (u.a. auch Mobilitätsstudierende, Doktorierende) können diese Lerneinheit NICHT belegen.
4 KP9RF. Da Lio
KurzbeschreibungThe 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.
LiteraturReference books and notes

Main books:

Giovanni Felder: "Partielle Differenzialgleichungen für Ingenieurinnen und Ingenieure" (Download PDF: ),
Erwin Kreyszig: "Advanced Engineering Mathematics", John Wiley & Sons, just chapters 11, 16.

Extra readings:

Norbert Hungerbühler: "Einführung in die partiellen Differentialgleichungen", vdf Hochschulverlag AG an der ETH Zürich,
Yehuda Pinchover, Jacob Rubinstein: "Partial Differential Equations", Cambridge University Press 2005.

For reference/complement of the Analysis I/II courses:

Christian Blatter: Ingenieur-Analysis (Download PDF)
Voraussetzungen / BesonderesThe precise content changes with the examiner. Candidates must therefore contact the examiner in person before studying the material.