Francesca Da Lio: Catalogue data in Spring Semester 2021

Name Prof. Dr. Francesca Da Lio
Address
Dep. Mathematik
ETH Zürich, HG G 37.2
Rämistrasse 101
8092 Zürich
SWITZERLAND
Telephone+41 44 632 86 96
Fax+41 44 632 10 85
E-mailfrancesca.dalio@math.ethz.ch
URLhttp://www.math.ethz.ch/~fdalio
DepartmentMathematics
RelationshipAdjunct Professor

NumberTitleECTSHoursLecturers
401-2284-00LMeasure and Integration Information Restricted registration - show details 6 credits3V + 2UF. Da Lio
AbstractIntroduction 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
ObjectiveBasic acquaintance with the abstract theory of measure and integration
ContentIntroduction 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
Lecture notesNew lecture notes in English will be made available during the course.
Literature1. L. Evans and R.F. Gariepy " Measure theory and fine properties of functions"
2. Walter Rudin "Real and complex analysis"
3. R. Bartle The elements of Integration and Lebesgue Measure
4. The notes by Prof. Michael Struwe Springsemester 2013, https://people.math.ethz.ch/~struwe/Skripten/AnalysisIII-FS2013-12-9-13.pdf.
5. The notes by Prof. UrsLang Springsemester 2019. https://people.math.ethz.ch/~lang/mi.pdf
6. P. Cannarsa & T. D'Aprile: Lecture notes on Measure Theory and Functional Analysis: http://www.mat.uniroma2.it/~cannarsa/cam_0607.pdf
.
401-5350-00LAnalysis Seminar Information 0 credits1KA. Carlotto, F. Da Lio, A. Figalli, N. Hungerbühler, M. Iacobelli, L. Keller, T. Rivière, J. Serra, University lecturers
AbstractResearch colloquium
Objective
ContentResearch seminar in Analysis
406-0353-AALAnalysis III
Enrolment ONLY for MSc students with a decree declaring this course unit as an additional admission requirement.

Any other students (e.g. incoming exchange students, doctoral students) CANNOT enrol for this course unit.
4 credits9RF. Da Lio
AbstractThe 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.
Objective
LiteratureReference books and notes

Main books:

Giovanni Felder: "Partielle Differenzialgleichungen für Ingenieurinnen und Ingenieure" (Download PDF: http://www.math.ethz.ch/u/felder/Teaching/Partielle_Differenzialgleichungen ),
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)
Prerequisites / NoticeThe precise content changes with the examiner. Candidates must therefore contact the examiner in person before studying the material.
406-2284-AALMeasure and Integration
Enrolment ONLY for MSc students with a decree declaring this course unit as an additional admission requirement.

Any other students (e.g. incoming exchange students, doctoral students) CANNOT enrol for this course unit.
6 credits13RF. Da Lio
AbstractIntroduction 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
ObjectiveBasic acquaintance with the abstract theory of measure and integration
ContentIntroduction 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
Lecture notesno lecture notes
Literature1. P.R. Halmos, "Measure Theory", Springer
2. Extra material: Lecture Notes by Emmanuel Kowalski and Josef Teichmann from spring semester 2012, http://www.math.ethz.ch/~jteichma/measure-integral_120615.pdf
3. Extra material: P. Cannarsa & T. D'Aprile, "Lecture Notes on Measure Theory and Functional Analysis", http://www.mat.uniroma2.it/~cannarsa/cam_0607.pdf
Prerequisites / NoticeThe precise content changes with the examiner. Candidates must therefore contact the examiner in person before studying the material.