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406-0353-AAL  Analysis III

SemesterFrühjahrssemester 2016
DozierendeA. Iozzi
Periodizitätjedes Semester wiederkehrende Veranstaltung
LehrspracheEnglisch
KommentarBelegung 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.


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.
Lernziel
InhaltTopics 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]
SkriptA handwritten version of Prof. Ana Cannas' notes will be periodically uploaded at the following address:

http://www.math.ethz.ch/~acannas/AnalysisIII_HS2011/
LiteraturReference 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)
Voraussetzungen / BesonderesThe precise content changes with the examiner. Candidates must therefore contact the examiner in person before studying the material.