- Lecturer
- Alessio Figalli
- Coordinator
- Pengyu Le

Informations in ETHZ Course Catalogue

The lecture will take place at 8-10a.m. on Monday in HG E5. The first lecture will be on 25.09.

For the exercise classes, see the section Exercise classes.

There will be Q&A sessions during the semester, see the section Q&A session.

In this lecture we treat problems in applied analysis. The focus lies on the simplest cases of three fundamental types of partial differential equations of second order: the Laplace equation, the heat equation and the wave equation.

Analysis I and II, Fourier series(Komplexe Analysis)

- Y. Pinchover, J. Rubinstein, "An introduction to Partial Differential Equations", Cambridge University Press(12. Mai 2005).
- Zusätzliche Literatur:
- Erwin Kreyszig, "Advanced Engineering Mathematics", John Wiley & Sons, Kap. 8, 11, 16 (sehr gutes Buch, als Referenz zu benutzen).
- Norbert Hungerbühler, "Einführung in die partiellen Differentialgleichungen", vdf Hochschulverlag AG an der ETH Zürich.
- G. Felder: Partielle Differenzialgleichungen.

Time | Preview of the Lecture | Chapters of the Literature | Comments |
---|---|---|---|

18.12 | Course review | - | - |

Time | Summaries of the Lecture | Chapters of the Literature | Comments |
---|---|---|---|

25.9 | Classification of PDEs, examples, associated conditions to obtain a unique solution | 1.1, 1.2, 1.3, 1.4.1, 1.4.2(up to line 2 page 10), 1.5.1, 1.5.2(first half, Dirichlet condition and Newmann condition for the Heat equation) | - |

02.10 | First order equations, quasilinear equations, the method of characteristics, examples | 2.1, 2.2, 2.3(up to Example 2.2) | - |

09.10 | Examples of the characteristics method, the existence and uniqueness theorem | 2.3, 2.4, 2.5 | - |

16.10 | Conservation laws and shock waves, second-order linear equations in two independent variables: classification, canonical form of hyperbolic equations | 2.7(up to example 2.15), 3.1, 3.2, 3.3 | - |

23.10 | The one-dimensional wave equation: canonical form and general solution, the Cauchy problem and d'Alembert's formula, domain of dependence and region of influence | 4.1, 4.2, 4.3, 4.4 | - |

30.10 | The Cauchy problem for the nonhomogeneous wave equation, The method of separation of variables: Introduction, Heat equation: homogeneous boundary condition. | 4.5(up to example 4.12), 5.1, 5.2(up to page 103 (5.15)) | - |

06.11 | Heat equation: homogeneous boundary condition, separation of variables for the wave equation | 5.2, 5.3 | - |

13.11 | Separation of variables for nonhomogeneous equation; Sturm-Liouville problems: Nonhomogeneous equations, Nonhomogeneous boundary conditions | 5.4, 6.5 example (6.45), 6.6 example (6.46) | Errata: In (6.91) it should be 1/2mπ and not 1/mπ. |

20.11 | elliptic equations: introduction, basic properties of elliptic problems, the maximal principle, applications of the maximum principle | 7.1, 7.2, 7.3, 7.4 | - |

27.11 | elliptic equations: Green's identities, the maximum principle for the heat equation, seperation of variables for elliptic problems | 7.5, 7.6, 7.7 (up to page 190) | - |

04.12 | elliptic equations: seperation of variables for elliptic problems | 7.7.1 | - |

11.12 | elliptic equations: seperation of variables for elliptic problems, Poisson's formula | 7.7.2 (up to Remark 7.29),7.8 | - |

Students should be prepared and come to the session with concrete questions. The Präsenz offered by D-MATH assistant group 6 will also be helpful.

Time | Room | Content | Assistants |
---|---|---|---|

13-14 Tue, 24.10 | HG G 19.2 | Lectures 1-4 | Pengyu Le, Johannes Sager |

13-14 Mon, 30.10 | HG G 19.2 | Lectures 1-5 | Leonard Deuschle, Pengyu Le, Manuel Madlener |

13-14 Fri, 24.11 | HG G 19.2 | Lectures 1-8 | Timo Laaksonlaita, Pengyu Le |

The students could find the exercise box in the room HG F 28. Please hand in the exercise in the corresponding box of your assistant before the deadline showed below.

exercise sheet | due by | solutions |
---|---|---|

Exercise sheet 1 | Fri 06.10 | Solution 1 |

Exercise sheet 2 | Fri 13.10 | Solution 2 |

Exercise sheet 3 | Fri 20.10 | Solution 3 |

Exercise sheet 4 | Fri 27.10 | Solution 4 |

Exercise sheet 5 | Fri 03.11 | Solution 5 |

Exercise sheet 6 | Fri 10.11 | Solution 6 |

Exercise sheet 7 | Fri 17.11 | Solution 7 |

Exercise sheet 8(New version, updated on 20.11) | Fri 24.11 | Solution 8 |

Exercise sheet 9 | Fri 01.12 | Solution 9 |

Exercise sheet 10 | Fri 08.12 | Solution 10 |

Exercise sheet 11 | Fri 15.12 | Solution 11 |

Exercise sheet 12 | - | Solution 12 |

Exercise sheet 13 | - | Solution 13 |

The students can choose the preferred exercise class to attend.

Zeit | Raum | Tutor | Sprache |
---|---|---|---|

Fr 10-11 | CLA E 4 | Leonard Deuschle | de |

Fr 10-11 | HG E 33.3 | Marina Durrer | de |

Fr 10-11 | HG F 26.3 | Michelle Inauen | de |

Fr 10-11 | HG G 26.5 | Timo Laaksonlaita | de |

Fr 11-12 | CLA E 4 | Manuel Madlener | de |

Fr 11-12 | HG E 33.3 | Johannes Sager | de |

Fr 11-12 | HG F 26.3 | Fynn Von Kistowski | de |

Fr 11-12 | HG G 26.5 | Xiao Yang | de |