Alessandro Sisto: Catalogue data in Autumn Semester 2018

Name Dr. Alessandro Sisto
URLhttp://www.math.ethz.ch/~alsisto
DepartmentMathematics
RelationshipAssistant Professor

NumberTitleECTSHoursLecturers
401-0243-00LAnalysis III Information 3 credits2V + 1UA. Sisto
AbstractWe will model and solve scientific problems with partial differential equations. Differential equations which are important in applications will be classified and solved. Elliptic, parabolic and hyperbolic differential equations will be treated. The following mathematical tools will be introduced: Laplace and Fourier transforms, Fourier series, separation of variables, methods of characteristics.
ObjectiveLearning to model scientific problems using partial differential equations and developing a good command of the mathematical methods that can be applied to them. Knowing the formulation of important problems in science and engineering with a view toward civil engineering (when possible). Understanding the properties of the different types of partial differential equations arising in science and in engineering.
ContentClassification of partial differential equations

Study of the Heat equation general diffusion/parabolic problems using the following tools:
* Separation of variables
* Fourier series
* Fourier transform
* Laplace transform

Study of the wave equation and general hyperbolic problems using similar tools and the method of characteristics.

Study of the Laplace equation and general elliptic problems using similar tools and generalizations of Fourier series.
Lecture notesLecture notes will be provided.
LiteratureThe course material is taken from the following sources:

Stanley J. Farlow - Partial Differential Equations for Scientists and Engineers

G. Felder: Partielle Differenzialgleichungen.
https://people.math.ethz.ch/~felder/PDG/
Prerequisites / NoticeAnalysis I and II. In particular, knowing how to solve ordinary differential equations is an important prerequisite.
401-5530-00LGeometry Seminar Information 0 credits1KM. Burger, M. Einsiedler, A. Iozzi, U. Lang, A. Sisto, University lecturers
AbstractResearch colloquium
Objective
406-2554-AALTopology
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 credits13RA. Sisto
AbstractTopological spaces, continuous maps, connectedness, compactness, separation axioms, metric spaces, quotient spaces, homotopy, fundamental group and covering spaces, van Kampen Theorem, surfaces and manifolds.
Objective
LiteratureKlaus Jänich: Topologie (Springer-Verlag)
http://www.springerlink.com/content/978-3-540-21393-2/fulltext/#section=592889&page=1
James Munkres: Topology (Prentice Hall)
William Massey: Algebraic Topology: an Introduction (Springer-Verlag)
Alan Hatcher: Algebraic Topology (Cambridge University Press)
http://www.math.cornell.edu/~hatcher/AT/ATpage.html
Prerequisites / NoticeThe precise content changes with the examiner. Candidates must therefore contact the examiner in person before studying the material.