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Analysis 3
Last Updated: 2026-06-01 11:31:01
Abstract
In this lecture we treat problems in applied analysis. The focus lies on the solution of quasilinear first order PDEs with the method of characteristics, and on the study of three fundamental types of partial differential equations of second order: the Laplace equation, the heat equation, and the wave equation.
Objective
The aim of this class is to provide students with a general overview of first and second order PDEs, and teach them how to solve some of these equations using characteristics and/or separation of variables.
Content
1.) General introduction to PDEs and their classification (linear, quasilinear, semilinear, nonlinear / elliptic, parabolic, hyperbolic) 2.) Quasilinear first order PDEs - Solution with the method of characteristics - Conservation laws 3.) Hyperbolic PDEs - wave equation - d'Alembert formula in (1+1)-dimensions - method of separation of variables 4.) Parabolic PDEs - heat equation - maximum principle - method of separation of variables 5.) Elliptic PDEs - Laplace equation - maximum principle - method of separation of variables - variational method
Resources
Literature
Y. Pinchover, J. Rubinstein, "An Introduction to Partial Differential Equations", Cambridge University Press (12. Mai 2005)
Learning Materials (Links)
- Main link
- Information
General Information
- Language
- English
- Levels
- BSC
- Frequency
- Yearly recurring
Examination
- Type
- session examination
- Mode
- written 180 minutes
- Aids
- -Standard Dictionary-Textbook (Pinchover) either original book, or printed (total or partial) version-Summary of the lectures. At most 4 Pages long (DIN A4 - either 2 sheets two-sided, or 4 sheets one-sided) must be personal & handwritten. Photocopies of summaries, or computer typed summaries are NOT accepted.NOT allowed during exam:-Exercises and solutions from this course (not allowed even as part of the summary).Random checks will be made on the day of the exam.
Course Components
| Type | Title | Time & Place | Hours |
|---|---|---|---|
| lecture | Analysis 3 |
|
2 h weekly |
| exercise |
Analysis 3
Groups are selected in myStudies.
Exercises start in the second week of the semester.
Mo 8-10, Mo 12-14 oder Mo 14-16 gemäss Gruppeneinteilung.
Es wird auch mindestens eine Übungsgruppe auf Deutsch angeboten.
|
|
2 h weekly |