# Alessandra Iozzi: Catalogue data in Spring Semester 2016

Name | Prof. Dr. Alessandra Iozzi |

Address | Dep. Mathematik ETH Zürich, HG G 37.4 Rämistrasse 101 8092 Zürich SWITZERLAND |

Telephone | +41 44 632 35 88 |

alessandra.iozzi@math.ethz.ch | |

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

Department | Mathematics |

Relationship | Adjunct Professor |

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

401-0232-10L | Analysis II | 8 credits | 4V + 2U | A. Iozzi | |

Abstract | Introduction to differential calculus and integration in several variables. | ||||

Objective | |||||

Content | Integration in several variables. More on differential equations. Differential calculus of several variables: maxima and minima, implicit function theorem. Vector calculus: line and surface integrals, the theorems of Green, Gauss and Stokes. Applications. | ||||

Lecture notes | Christian Blatter: Ingenieur-Analysis (Kapitel 4-6) | ||||

401-5530-00L | Geometry Seminar | 0 credits | 1K | M. Burger, M. Einsiedler, A. Iozzi, U. Lang, V. Schroeder, A. Sisto | |

Abstract | Research colloquium | ||||

Objective | |||||

401-5990-00L | Zurich Graduate Colloquium | 0 credits | 1K | A. Iozzi, University lecturers | |

Abstract | The Graduate Colloquium is an informal seminar aimed at graduate students and postdocs whose purpose is to provide a forum for communicating one's interests and thoughts in mathematics. | ||||

Objective | |||||

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 | A. Iozzi | |

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 | |||||

Content | Topics of the course (not definitive program!) 1. Introduction; 1-D wave equation; separation of variables. [Kreyszig 11.1, 11.2, 11.3, Felder 1] 2. Use of Fourier series for 1-D wave equation; review of Fourier series. [Kreyszig 11.3, Felder 3] 3. Solution of 1-D heat equation by Fourier series. [Kreyszig 11.5, Felder 3,5] 4. Solution of 1-D heat equation by Fourier integrals and transforms. [Kreyszig 11.6, Felder 4] 5. 2-D wave equation for a rectangular membrane; double Fourier series. [Kreyszig 11.7, 11.8, Felder 4] 6. Solution of 3-D wave equation by Fourier transforms. [Felder 6] 7. Laplace's equation; Dirichlet problem in a rectangle. [Kreyszig 11.5] 8. Laplacian in polar coordinates; vibrations of a circular membrane. [Kreyszig 11.9, 11.10] 9. Laplace's equation in cylindrical and spherical coordinates; Dirichlet problem on a sphere. [Kreyszig 11.11] 10. Spherical harmonics; potential theory; signal processing. [Kreyszig 16] 11. Solving by Laplace transforms. [Kreyszig 11.12] 12. Green's function; distributions. [Felder 7,8] 13. D'Alembert's solution of 1-D wave equation; method of characteristics. [Kreyszig 11.4, Felder 9] | ||||

Lecture notes | A handwritten version of Prof. Ana Cannas' notes will be periodically uploaded at the following address: http://www.math.ethz.ch/~acannas/AnalysisIII_HS2011/ | ||||

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. |