Analysis 3 — Exercise Session Materials

Partial Differential Equations · ETH Zurich · Autumn Semester 2025

Notes on this Page

I was glad to assist in the teaching of Analysis 3 — Partial Differential Equations during the Fall Semester 2025 at ETH Zurich. From the feedback I received, the students performed very well in the exam. I am proud to have been part of your success and wish you all continued success in your studies. I will be keeping the documents here for an indefinite amount of time for further reference.
You can access the Kahoots used during the exercise sessions through this link.
Exercise sessions cover the material of the last lecture, whereas the exercise sheets come a week later. Numeration of the sheets corresponds to the numeration of the week (e.g. Exercise Sheet 2 covers materials up to Week 2). So, when working on the exercise sheets, please work with the corresponding notes.

Session Documents

Date	Topics / Notes	Links
Week 1 22.09.2025	• Introduction, Preliminary Considerations • Classification of PDEs & Examples • Conditions for Appropriate Solutions	Notes Lecture Website Textbook Understanding PDEs & Heat Equation
Week 2 29.09.2025	• First order equations • Quasilinear equations • Method of Characteristics & Examples	Notes Video: Example for Method of Characteristics
Week 3 06.10.2025	• Examples of the Characteristics Method • Existence and Uniqueness Theorem	Notes Old Lecture Website: HS21 Transversality Picard-Lindelöf Theorem Implicit Function Theorem Recap Kahoot W3
Week 4 13.10.2025	• Conservation laws and shock waves • Rankine-Hugoniot condition	Notes Code
Week 5 20.10.2025	• Shock waves: the Rankine-Hugoniot condition, and the entropy condition. • Classification of second order linear PDEs.	Simay's Notes
Week 6 27.10.2025	• The one-dimensional wave equation, canonical form and general solution. • The Cauchy problem and d'Alembert formula.	Notes d'Alembert: Further Reading & Graphic Example Recap Kahoot W6
Week 7 03.11.2025	• Domain of dependence. • The non-homogeneous one-dimensional wave equation. • Nonhomogeneous d'Alembert formula. • Separation of variables.	Notes Play-Around: 1D-Wave Equation
Week 8 10.11.2025	• Separation of variables for the heat and wave equation, homogeneous problems. • Dirichlet and Neumann boundary conditions.	Notes Recap Kahoot W8
Week 9 17.11.2025	• Separation of variables for non-homogeneous equations. • Resonance. • The energy method for the wave and heat equation, and uniqueness of solutions.	Notes Tacoma Bridge Incident Resonance and Vibrations in Engineering
Week 10 24.11.2025	• Elliptic equations. • The weak maximum principle. • The mean value principle. • The strong maximum principle.	Notes Derivation: Laplacian in Spherical Coordinates
Week 11 01.12.2025	• Applications of maximum principle (uniqueness). • The maximum principle for the heat equation. • Separation of variables for elliptic problems.	Notes Recap Kahoot W11
Week 12 08.12.2025	• Separation of variables in rectangles, Dirichlet and Neumann compatibility conditions. • The Laplace equation in circular domains.	Notes
Week 13 15.12.2025	• The Laplace equation in circular domains: annulus and sectors.	Notes Recap Kahoot W13

All documents on Polybox