Lecturer

Mikaela Iacobelli

Coordinator

Lauro Silini

Information

Informations in ETHZ Course Catalogue.

Written Exam

The Exam will take place Friday, 28 January 2022, from 3pm to 6pm.

• Students will be able to take the exam either in German or in English (and bring a dictionary if needed).
• Electronic devices (such as, but not limited to, smartphones, calculators, tablets, laptops, etc.) are NOT allowed to use during the exam.
• Students are allowed to bring the book (Pinchover-Rubinstein) to the exam, either the original book, or a printed (total or partial) version. They can use markers for the pages, underline/highlight important formulae/concepts, as long as they do not add written text to it (on the sides, over post-its etc.).
• Students are allowed to bring a summary of the lectures. Summaries can be at most 4 pages long on a DIN A4 paper size (297x210 mm) (that is, either 2 sheets of paper two-sided, or 4 sheets of paper one-sided). Summaries must be personal and handwritten. Photocopies of summaries, or computer typed summaries are NOT allowed. The only exception are summaries handwritten on a tablet, that are allowed to be printed as long as they remain personal and as long as the font size is comparable to a Summary handwritten directly on paper.
• Students are NOT allowed to bring the exercises and the solutions from this course to the exam (even as part of the summary).

Random checks of the above rules will be made on the day of the exam.

Time and Room

The lecture takes place in room HG G3 every Monday at 08-10 a.m.

Live Streaming is available for members of ETH. A video recording of the lecture is uploaded every Tuesday under password protection.

Content

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.

Schematic Syllabus

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

Literature

Y. Pinchover, J. Rubinstein, "An introduction to Partial Differential Equations", Cambridge University Press (12. Mai 2005).

Prerequisites

Analysis I and II, Fourier series (Complex Analysis).

Lecture Summaries

Here is a first version of the complete LECTURE NOTES.

Exercises

Every Monday after the lecture the corresponding exercise list will be uploaded. We encourage the students to attempt solving the exercises. The first session will be on Friday October 1st . Please do not forget to register to one of the following exercise groups via myStudies.

Exercise classes