Analysis III D-ITET

• First lesson: Monday, 26.09.2011
• First exercise class: Friday, 30.09.2011
  
• Testat conditions: 60% of each exercise sheet correctly solved.
• The course will be in English, but the students can agree with the single assistants about the language of the exercise  classes.
  
• Präsenz and Ferienpräsenz: see here

Lecture notes

A handwritten version of Prof. Ana Cannas' notes will be periodically uploaded at the following address:

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

Topics 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.
[Kreysig 11.4, Felder 9]

Reference 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 )