## Francesca Da Lio: Catalogue data in Spring Semester 2018 |

Name | Prof. Dr. Francesca Da Lio |

Address | Dep. Mathematik ETH Zürich, HG G 37.2 Rämistrasse 101 8092 Zürich SWITZERLAND |

Telephone | +41 44 632 86 96 |

Fax | +41 44 632 10 85 |

francesca.dalio@math.ethz.ch | |

URL | http://www.math.ethz.ch/~fdalio |

Department | Mathematics |

Relationship | Adjunct Professor |

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

401-3352-09L | An Introduction to Partial Differential Equations | 6 credits | 3V | C. Busch, F. Da Lio | |

Abstract | This course aims at being an introduction to first and second order partial differential equations (in short PDEs). We will present the so called method of characteristics to solve quasilinear PDEs and some basic properties of classical solutions to second order linear PDEs. | ||||

Objective | |||||

Content | A preliminary plan is the following - Laplace equation, fundamental solution, harmonic functions and main properties, maximum principle. Poisson equation. Green functions. Perron method for the solution of the Dirichlet problem. Regularity of solutions to the Poisson Equation. - Heat equation, fundamental solution, existence of solutions to the Cauchy problem and representation formulas, main properties, uniqueness by maximum principle, regularity. - The Method of characteristics for first order equations, linear and nonlinear, transport equation, Hamilton-Jacobi equation, scalar conservation laws. -Time permitting: Wave equation, existence of the solution, D'Alembert formula, solutions by spherical means, main properties, uniqueness by energy methods. | ||||

Lecture notes | The teacher provides the students with personal notes. | ||||

Literature | Bibliography - L.Evans Partial Differential Equations, AMS 2010 (2nd edition) - D. Gilbarg, N.S. Trudinger Elliptic Partial Differential Equations of Second Order, Springer, 1998. - E. Di Benedetto Partial Differential Equations, Birkauser, 2010 (2nd edition). - W. A. Strauss Partial Differential Equations. An Introduction, Wiley, 1992. -Q. Han, A Basic Course in Partial Differential Equations, Graduate Studies in Mathematics Volume: 120; 2011. | ||||

Prerequisites / Notice | Differential and integral calculus for functions of several variables; elementary theory of ordinary differential equations, basic facts of measure theory. | ||||

401-5350-00L | Analysis Seminar | 0 credits | 1K | M. Struwe, A. Carlotto, F. Da Lio, A. Figalli, N. Hungerbühler, T. Kappeler, T. Rivière, D. A. Salamon | |

Abstract | Research colloquium | ||||

Objective | |||||

Content | Research seminar in Analysis | ||||

406-0353-AAL | Analysis IIIEnrolment 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. | 4 credits | 9R | F. Da Lio | |

Abstract | 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. | ||||

Objective | |||||

Literature | Reference books and notes Main books: Giovanni Felder: "Partielle Differenzialgleichungen für Ingenieurinnen und Ingenieure" (Download PDF: http://www.math.ethz.ch/u/felder/Teaching/Partielle_Differenzialgleichungen ), Erwin Kreyszig: "Advanced Engineering Mathematics", John Wiley & Sons, just chapters 11, 16. Extra readings: Norbert Hungerbühler: "Einführung in die partiellen Differentialgleichungen", vdf Hochschulverlag AG an der ETH Zürich, Yehuda Pinchover, Jacob Rubinstein: "Partial Differential Equations", Cambridge University Press 2005. For reference/complement of the Analysis I/II courses: Christian Blatter: Ingenieur-Analysis (Download PDF) | ||||

Prerequisites / Notice | The precise content changes with the examiner. Candidates must therefore contact the examiner in person before studying the material. |