Alessandra Iozzi: Catalogue data in Autumn Semester 2018 |
| Name | Prof. em. Dr. Alessandra Iozzi |
| Address | Dep. Mathematik ETH Zürich, HG G 50.1 Rämistrasse 101 8092 Zürich SWITZERLAND |
| Telephone | +41 44 633 81 48 |
| alessandra.iozzi@math.ethz.ch | |
| URL | http://www.math.ethz.ch/~iozzi |
| Department | Mathematics |
| Relationship | Retired Adjunct Professor |
| Number | Title | ECTS | Hours | Lecturers | |
|---|---|---|---|---|---|
| 401-0231-10L | Analysis 1 Studierende im BSc EEIT können alternativ auch 401-1261-07L Analysis I (für BSc Mathematik, BSc Physik und BSc IN (phys.-chem. Fachrichtung)) belegen und den zugehörigen Jahreskurs prüfen lassen. Studierende im BSc EEIT, welche 401-1261-07L/401-1262-07L Analysis I/II anstelle von 401-0231-10L/401-0232-10L Analysis 1/2 belegen möchten, wenden sich vor der Belegung an ihren Studiengang. | 8 credits | 4V + 3U | A. Iozzi | |
| Abstract | Calculus of one variable: Real and complex numbers, vectors, limits, sequences, series, power series, continuous maps, differentiation and integration in one variable, introduction to ordinary differential equations | ||||
| Learning objective | Einfuehrung in die Grundlagen der Analysis | ||||
| Lecture notes | Christian Blatter: Ingenieur-Analysis (Kapitel 1-3) Skript der Vorlesung (A. Iozzi) Konrad Koenigsberger, Analysis I. | ||||
| 401-0363-10L | Analysis III  | 3 credits | 2V + 1U | A. Iozzi | |
| Abstract | Introduction to partial differential equations. Differential equations which are important in applications are classified and solved. Elliptic, parabolic and hyperbolic differential equations are treated. The following mathematical tools are introduced: Laplace transforms, Fourier series, separation of variables, methods of characteristics. | ||||
| Learning objective | Mathematical treatment of problems in science and engineering. To understand the properties of the different types of partial differential equations. The first lecture is on Thursday, September 27 13-15 in HG F 7 and video transmitted into HG F 5. The reference web-page for exercise sheets, solutions and further info is https://metaphor.ethz.ch/x/2018/hs/401-0363-10L/ The web-page to enroll for an exercise class is https://echo.ethz.ch The coordinator is Stefano D'Alesio https://www.math.ethz.ch/the-department/people.html?u=dalesios Study Center D-MAVT: 16-18 every Monday from the 3rd week of the semester (first appointment: October the 1st) room HG E22 http://www.rauminfo.ethz.ch/Rauminfo/RauminfoPre.do?region=Z&areal=Z&gebaeude=HG&geschoss=E&raumNr=22 Study Center D-MATL: 15-17 every Wednesday from the 5th week of the semester (first appointment: October the 17th) room HCI J 574 Ferienpräsenz: Tuesday 15 January 2019, at 12:30-14:00, in room HG G 19.1. Monday 21 January 2019, at 12:30-14:00, in room HG G 19.2. Prüfungseinsicht: Tuesday 26 February 2019, at 17:00-18:30, in room HG 19.1. Monday 4 March 2019, at 18:15-19:45, in room HG 19.1. | ||||
| Content | Laplace Transforms: - Laplace Transform, Inverse Laplace Transform, Linearity, s-Shifting - Transforms of Derivatives and Integrals, ODEs - Unit Step Function, t-Shifting - Short Impulses, Dirac's Delta Function, Partial Fractions - Convolution, Integral Equations - Differentiation and Integration of Transforms Fourier Series, Integrals and Transforms: - Fourier Series - Functions of Any Period p=2L - Even and Odd Functions, Half-Range Expansions - Forced Oscillations - Approximation by Trigonometric Polynomials - Fourier Integral - Fourier Cosine and Sine Transform Partial Differential Equations: - Basic Concepts - Modeling: Vibrating String, Wave Equation - Solution by separation of variables; use of Fourier series - D'Alembert Solution of Wave Equation, Characteristics - Heat Equation: Solution by Fourier Series - Heat Equation: Solutions by Fourier Integrals and Transforms - Modeling Membrane: Two Dimensional Wave Equation - Laplacian in Polar Coordinates: Circular Membrane, Fourier-Bessel Series - Solution of PDEs by Laplace Transform | ||||
| Lecture notes | Lecture notes by Prof. Dr. Alessandra Iozzi: https://polybox.ethz.ch/index.php/s/D3K0TayQXvfpCAA | ||||
| Literature | E. Kreyszig, Advanced Engineering Mathematics, John Wiley & Sons, 10. Auflage, 2011 C. R. Wylie & L. Barrett, Advanced Engineering Mathematics, McGraw-Hill, 6th ed. S.J. Farlow, Partial Differential Equations for Scientists and Engineers, Dover Books on Mathematics, NY. G. Felder, Partielle Differenzialgleichungen für Ingenieurinnen und Ingenieure, hypertextuelle Notizen zur Vorlesung Analysis III im WS 2002/2003. Y. Pinchover, J. Rubinstein, An Introduction to Partial Differential Equations, Cambridge University Press, 2005 For reference/complement of the Analysis I/II courses: Christian Blatter: Ingenieur-Analysis https://people.math.ethz.ch/~blatter/dlp.html | ||||
| 401-4220-68L | Symmetric Spaces of Non-Compact Type  Number of participants limited to 10. | 4 credits | 2S | A. Iozzi | |
| Abstract | |||||
| Learning objective | |||||
| Content | 1) Root systems of symmetric spaces and the Weyl group 2) Action of the Weyl group 3) The geodesic boundary 4) SL(n,R)/SO(n,R) 5) Parabolic subgroups 6) Iwasawa decomposition 7) The Tits metric | ||||
| Prerequisites / Notice | If you are interested in the seminar, please send an e-mail to yannick.krifka@math.ethz.ch with your mathematical background before Tuesday, August 28th. Priority will be given to students as follows: 1) Students knowledgeable about Lie groups and symmetric spaces; 2) Students knowledgeable about symmetric spaces. A limited number of spots might be allocated to students who do not satisfy either of the above requirements, depending on availability and background. | ||||
| 401-5000-00L | Zurich Colloquium in Mathematics | 0 credits | A. Iozzi, S. Mishra, R. Pandharipande, 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 | |||||
| 401-5530-00L | Geometry Seminar | 0 credits | 1K | M. Burger, M. Einsiedler, A. Iozzi, U. Lang, A. Sisto, University lecturers | |
| Abstract | Research colloquium | ||||
| Learning 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. | ||||
| Learning objective | |||||
| 406-0353-AAL | Analysis III 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. | 4 credits | 9R | A. Iozzi | |
| Abstract | Introduction to partial differential equations. Differential equations which are important in applications are classified and solved. Elliptic, parabolic and hyperbolic differential equations are treated. The following mathematical tools are introduced: Laplace transforms, Fourier series, separation of variables, methods of characteristics. | ||||
| Learning objective | Mathematical treatment of problems in science and engineering. To understand the properties of the different types of partlial differentail equations. | ||||
| Content | Laplace Transforms: - Laplace Transform, Inverse Laplace Transform, Linearity, s-Shifting - Transforms of Derivatives and Integrals, ODEs - Unit Step Function, t-Shifting - Short Impulses, Dirac's Delta Function, Partial Fractions - Convolution, Integral Equations - Differentiation and Integration of Transforms Fourier Series, Integrals and Transforms: - Fourier Series - Functions of Any Period p=2L - Even and Odd Functions, Half-Range Expansions - Forced Oscillations - Approximation by Trigonometric Polynomials - Fourier Integral - Fourier Cosine and Sine Transform Partial Differential Equations: - Basic Concepts - Modeling: Vibrating String, Wave Equation - Solution by separation of variables; use of Fourier series - D'Alembert Solution of Wave Equation, Characteristics - Heat Equation: Solution by Fourier Series - Heat Equation: Solutions by Fourier Integrals and Transforms - Modeling Membrane: Two Dimensional Wave Equation - Laplacian in Polar Coordinates: Circular Membrane, Fourier-Bessel Series - Solution of PDEs by Laplace Transform | ||||
| Literature | E. Kreyszig, Advanced Engineering Mathematics, John Wiley & Sons, 10. Auflage, 2011 C. R. Wylie & L. Barrett, Advanced Engineering Mathematics, McGraw-Hill, 6th ed. Stanley J. Farlow, Partial Differential Equations for Scientists and Engineers, (Dover Books on Mathematics). G. Felder, Partielle Differenzialgleichungen für Ingenieurinnen und Ingenieure, hypertextuelle Notizen zur Vorlesung Analysis III im WS 2002/2003. Y. Pinchover, J. Rubinstein, An Introduction to Partial Differential Equations, Cambridge University Press, 2005 For reference/complement of the Analysis I/II courses: Christian Blatter: Ingenieur-Analysis (Download PDF) | ||||
| Prerequisites / Notice | Up-to-date information about this course can be found at: http://www.math.ethz.ch/education/bachelor/lectures/hs2013/other/analysis3_itet | ||||