Alessandra Iozzi: Katalogdaten im Herbstsemester 2021

NameFrau Prof. em. Dr. Alessandra Iozzi
Adresse
Dep. Mathematik
ETH Zürich, HG G 37.4
Rämistrasse 101
8092 Zürich
SWITZERLAND
Telefon+41 44 632 35 88
E-Mailalessandra.iozzi@math.ethz.ch
URLhttp://www.math.ethz.ch/~iozzi
DepartementMathematik
BeziehungTitularprofessorin im Ruhestand

NummerTitelECTSUmfangDozierende
401-0363-10LAnalysis III Information 3 KP2V + 1UA. Iozzi
KurzbeschreibungIntroduction 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.
LernzielMathematical treatment of problems in science and engineering. To understand the properties of the different types of partial differential equations.
InhaltLaplace 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
SkriptLecture notes by Prof. Dr. Alessandra Iozzi:
https://polybox.ethz.ch/index.php/s/D3K0TayQXvfpCAA
LiteraturE. 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
401-3225-00LIntroduction to Lie Groups Information 8 KP4GA. Iozzi
KurzbeschreibungTopological groups and Haar measure. Definition of Lie groups, examples of local fields and examples of discrete subgroups; basic properties; Lie subgroups. Lie algebras and relation with Lie groups: exponential map, adjoint representation. Semisimplicity, nilpotency, solvability, compactness: Killing form, Lie's and Engel's theorems. Definition of algebraic groups and relation with Lie groups.
LernzielThe goal is to have a broad though foundational knowledge of the theory of Lie groups and their associated Lie algebras with an emphasis on the algebraic and topological aspects of it.
LiteraturA. Knapp: "Lie groups beyond an Introduction" (Birkhaeuser)
A. Sagle & R. Walde: "Introduction to Lie groups and Lie algebras" (Academic Press, '73)
F. Warner: "Foundations of differentiable manifolds and Lie groups" (Springer)
H. Samelson: "Notes on Lie algebras" (Springer, '90)
S. Helgason: "Differential geometry, Lie groups and symmetric spaces" (Academic Press, '78)
A. Knapp: "Lie groups, Lie algebras and cohomology" (Princeton University Press)
Voraussetzungen / BesonderesTopology and basic notions of measure theory. A basic understanding of the concepts of manifold, tangent space and vector field is useful, but could also be achieved throughout the semester.

Course webpage: https://metaphor.ethz.ch/x/2018/hs/401-3225-00L/
401-5000-00LZurich Colloquium in Mathematics Information 0 KPR. Abgrall, M. Iacobelli, A. Bandeira, A. Iozzi, S. Mishra, R. Pandharipande, Uni-Dozierende
KurzbeschreibungThe 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.
Lernziel
401-5530-00LGeometry Seminar Information 0 KP1KM. Burger, M. Einsiedler, P. Feller, A. Iozzi, U. Lang, Uni-Dozierende
KurzbeschreibungResearch colloquium
Lernziel
401-5990-00LZurich Graduate Colloquium Information 0 KP1KA. Iozzi, weitere Referent/innen
KurzbeschreibungThe 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.
Lernziel
406-0353-AALAnalysis III
Belegung ist NUR erlaubt für MSc Studierende, die diese Lerneinheit als Auflagenfach verfügt haben.

Alle anderen Studierenden (u.a. auch Mobilitätsstudierende, Doktorierende) können diese Lerneinheit NICHT belegen.
4 KP9RA. Iozzi
KurzbeschreibungEinführung in die partiellen Differentialgleichungen. Klassifizieren und Lösen von in der Praxis wichtigen Differentialgleichungen. Es werden elliptische, parabolische und hyperbolische Differentialgleichungen behandelt. Folgende mathematischen Techniken werden vorgestellt: Laplacetransformation, Fourierreihen, Separation der Variablen, Methode der Charakteristiken.
LernzielMathematische Behandlung naturwissenschaftlicher Probleme lernen. Verstehen der Eigenschaften der verschiedenen Typen von partiellen Differentialgleichungen.
InhaltLaplace 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. 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)
Voraussetzungen / BesonderesWeitere Informationen unter:
http://www.math.ethz.ch/education/bachelor/lectures/hs2013/other/analysis3_itet