From 2 November 2020, the autumn semester 2020 will take place online. Exceptions: Courses that can only be carried out with on-site presence. Please note the information provided by the lecturers via e-mail.

Alessandra Iozzi: Catalogue data in Spring Semester 2016

Name Prof. Dr. Alessandra Iozzi
Address
Dep. Mathematik
ETH Zürich, HG G 37.4
Rämistrasse 101
8092 Zürich
SWITZERLAND
Telephone+41 44 632 35 88
E-mailalessandra.iozzi@math.ethz.ch
URLhttp://www.math.ethz.ch/~iozzi
DepartmentMathematics
RelationshipAdjunct Professor

NumberTitleECTSHoursLecturers
401-0232-10LAnalysis II8 credits4V + 2UA. Iozzi
AbstractIntroduction to differential calculus and integration in several variables.
Objective
ContentIntegration in several variables. More on differential equations. Differential calculus of several variables: maxima and minima, implicit function theorem. Vector calculus: line and surface integrals, the theorems of Green, Gauss and Stokes. Applications.
Lecture notesChristian Blatter: Ingenieur-Analysis (Kapitel 4-6)
401-5530-00LGeometry Seminar Information 0 credits1KM. Burger, M. Einsiedler, A. Iozzi, U. Lang, V. Schroeder, A. Sisto
AbstractResearch colloquium
Objective
401-5990-00LZurich Graduate Colloquium Information 0 credits1KA. Iozzi, University lecturers
AbstractThe Graduate Colloquium is an informal seminar aimed at graduate students and postdocs whose purpose is to provide a forum for communicating one's interests and thoughts in mathematics.
Objective
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 credits9RA. Iozzi
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
ContentTopics of the course (not definitive program!)

1. Introduction; 1-D wave equation; separation of variables.
[Kreyszig 11.1, 11.2, 11.3, Felder 1]
2. Use of Fourier series for 1-D wave equation; review of Fourier series.
[Kreyszig 11.3, Felder 3]
3. Solution of 1-D heat equation by Fourier series.
[Kreyszig 11.5, Felder 3,5]
4. Solution of 1-D heat equation by Fourier integrals and transforms.
[Kreyszig 11.6, Felder 4]
5. 2-D wave equation for a rectangular membrane; double Fourier series.
[Kreyszig 11.7, 11.8, Felder 4]
6. Solution of 3-D wave equation by Fourier transforms.
[Felder 6]
7. Laplace's equation; Dirichlet problem in a rectangle.
[Kreyszig 11.5]
8. Laplacian in polar coordinates; vibrations of a circular membrane.
[Kreyszig 11.9, 11.10]
9. Laplace's equation in cylindrical and spherical coordinates; Dirichlet problem on a sphere.
[Kreyszig 11.11]
10. Spherical harmonics; potential theory; signal processing.
[Kreyszig 16]
11. Solving by Laplace transforms.
[Kreyszig 11.12]
12. Green's function; distributions.
[Felder 7,8]
13. D'Alembert's solution of 1-D wave equation; method of characteristics.
[Kreyszig 11.4, Felder 9]
Lecture notesA handwritten version of Prof. Ana Cannas' notes will be periodically uploaded at the following address:

http://www.math.ethz.ch/~acannas/AnalysisIII_HS2011/
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.