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Analysis III
Last Updated: 2026-02-05 15:36:28
Abstract
Introduction to partial differential equations. Differential equations which are important in applications are classified and solved. Elliptic, parabolic and hyperbolic differential equations are treated. The following mathematical tools are introduced: Laplace transforms, Fourier series, separation of variables, methods of characteristics.
Objective
Mathematical treatment of problems in science and engineering. To understand the properties of the different types of partial differential equations.
Content
Laplace Transforms: - Laplace Transform, Inverse Laplace Transform, Linearity, s-Shifting - Transforms of Derivatives and Integrals, ODEs - Unit Step Function, t-Shifting - Short Impulses, Dirac's Delta Function, Partial Fractions - Convolution, Integral Equations - Differentiation and Integration of Transforms Fourier Series, Integrals and Transforms: - Fourier Series - Functions of Any Period p=2L - Even and Odd Functions, Half-Range Expansions - Forced Oscillations - Approximation by Trigonometric Polynomials - Fourier Integral - Fourier Cosine and Sine Transform Partial Differential Equations: - Basic Concepts - Modeling: Vibrating String, Wave Equation - Solution by separation of variables; use of Fourier series - D'Alembert Solution of Wave Equation, Characteristics - Heat Equation: Solution by Fourier Series - Heat Equation: Solutions by Fourier Integrals and Transforms - Modeling Membrane: Two Dimensional Wave Equation - Laplacian in Polar Coordinates: Circular Membrane, Fourier-Bessel Series - Solution of PDEs by Laplace Transform
Resources
Lecture Notes
Lecture notes by Prof. Dr. Alessandra Iozzi:https://polybox.ethz.ch/index.php/s/D3K0TayQXvfpCAA
Literature
E. Kreyszig, Advanced Engineering Mathematics, John Wiley & Sons, 10. Auflage, 2011 C. R. Wylie & L. Barrett, Advanced Engineering Mathematics, McGraw-Hill, 6th ed. S.J. Farlow, Partial Differential Equations for Scientists and Engineers, Dover Books on Mathematics, NY. G. Felder, Partielle Differenzialgleichungen für Ingenieurinnen und Ingenieure, hypertextuelle Notizen zur Vorlesung Analysis III im WS 2002/2003. Y. Pinchover, J. Rubinstein, An Introduction to Partial Differential Equations, Cambridge University Press, 2005 For reference/complement of the Analysis I/II courses: Christian Blatter: Ingenieur-Analysis https://people.math.ethz.ch/~blatter/dlp.html
Learning Materials (Links)
- Main link
- Moodle course
General Information
- Language
- English
- Levels
- BSC
- Frequency
- Yearly recurring
Examination
- Type
- session examination
- Mode
- written 120 minutes
- Aids
- 20 pages (=10 sheets) DIN A4 handwritten or typed personal summary. English <-> German dictionary. No further aids (in particular, no pocket calculator).
Course Components
| Type | Title | Time & Place | Hours |
|---|---|---|---|
| lecture |
Analysis III
The lecturers will communicate the exact lesson times of ONLINE courses.
|
|
2 h weekly |
| exercise |
Analysis III
Groups are selected in myStudies.
Many of the exercise classes are offered in German.
Do 15-16 im ML F 38 für Studiengang Materialwissenschaft (zuvor Übungen Stochastik im selben Raum).
Diverse Termine am Donnerstagnachmiitag gemäss Gruppeneinteilung für Studiengang Maschineningenieurwissenschaften.
Zusätzlich wird das Study Center angeboten: Fr 18-20 ab der 3. Semesterwoche im HG D 1.1, wo die Möglichkeit des betreuten Lernens angeboten wird. Im Study Center können Studierende Vorlesungsstoff vor- oder nachbereiten und Übungen lösen.
The ONLINE exercise class "G-ON 01" takes place Thu 16:45-17:30 and "G-ON 02" takes place Thu 15:15-16:00.
|
|
1 h weekly |