Exercise Session Announcements - Analysis 3
- 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 during the exercise session through this link.
- Exercise sessions cover the material of the last lecture , whereas the exercise sheets come a week later. Numeration of the sheets correspond 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.
Exercise Session Documents - Analysis 3
| Lecture 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 |