## Mikaela Iacobelli: Catalogue data in Autumn Semester 2023 |

Name | Prof. Dr. Mikaela Iacobelli |

Field | Mathematics |

Address | Dep. Mathematik ETH Zürich, HG G 48.2 Rämistrasse 101 8092 Zürich SWITZERLAND |

Telephone | +41 44 632 50 68 |

mikaela.iacobelli@math.ethz.ch | |

URL | https://people.math.ethz.ch/~imikaela |

Department | Mathematics |

Relationship | Associate Professor |

Number | Title | ECTS | Hours | Lecturers | |
---|---|---|---|---|---|

401-0353-00L | Analysis 3 | 4 credits | 2V + 2U | M. Iacobelli | |

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. | ||||

Learning 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 | ||||

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

Prerequisites / Notice | Prerequisites: Analysis I and II, Fourier series (Complex Analysis) | ||||

401-2464-AAL | Analysis IV (Fourier Theory and Hilbert Spaces)Enrolment ONLY for MSc students with a decree declaring this course unit as an additional admission requirement. Any other students (e.g. incoming exchange students, doctoral students) CANNOT enrol for this course unit. | 6 credits | 13R | M. Iacobelli | |

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401-2465-AAL | Analysis III and IV (Measure Theory / Fourier Theory and Hilbert Spaces)Enrolment ONLY for MSc students with a decree declaring this course unit as an additional admission requirement. Any other students (e.g. incoming exchange students, doctoral students) CANNOT enrol for this course unit. | 12 credits | 26R | F. Da Lio, M. Iacobelli | |

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401-5000-00L | Zurich Colloquium in Mathematics | 0 credits | M. Iacobelli, A. Bandeira, S. Mishra, R. Pandharipande, T. Rivière, University lecturers | ||

Abstract | The lectures try to give an overview of "what is going on" in important areas of contemporary mathematics, to a wider non-specialised audience of mathematicians. | ||||

Learning objective | |||||

401-5350-00L | Analysis Seminar | 0 credits | 1K | F. Da Lio, A. Figalli, N. Hungerbühler, M. Iacobelli, T. Ilmanen, L. Kobel-Keller, S. Mayboroda, T. Rivière, J. Serra, University lecturers | |

Abstract | Research colloquium | ||||

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