Suchergebnis: Katalogdaten im Herbstsemester 2021

Rechnergestützte Wissenschaften Bachelor Information
Vertiefungsgebiete
Astrophysik
NummerTitelTypECTSUmfangDozierende
401-7851-00LTheoretical Astrophysics (University of Zurich) Information
Der Kurs muss direkt an der UZH als incoming student belegt werden.
UZH Modulkürzel: AST512

Beachten Sie die Einschreibungstermine an der UZH:
Link
W10 KP4V + 2UUni-Dozierende
KurzbeschreibungThis course covers the foundations of astrophysical fluid dynamics, the Boltzmann equation, equilibrium systems and their stability, the structure of stars, astrophysical turbulence, accretion disks and their stability, the foundations of radiative transfer, collisionless systems, the structure and stability of dark matter halos and stellar galactic disks.
Lernziel
InhaltThis course covers the foundations of astrophysical fluid dynamics, the theory of collisions and the Boltzmann equation, the notion of equilibrium systems and their stability, the structure of stars, the theory of astrophysical turbulence, the theory of accretion disks and their stability, the foundations of astrophysical radiative transfer, the theory of collisionless system, the structure and stability of dark matter halos and stellar galactic disks.
LiteraturCourse Materials:
1- The Physics of Astrophysics, Volume 1: Radiation by Frank H. Shu
2- The Physics of Astrophysics, Volume 2: Gas Dynamics by Frank H. Shu
3- Foundations of radiation hydrodynamics, Dimitri Mihalas and Barbara Weibel-Mihalas
4- Radiative Processes in Astrophysics, George B. Rybicki and Alan P. Lightman
5- Galactic Dynamics, James Binney and Scott Tremaine
Voraussetzungen / BesonderesThis is a full black board ad chalk experience for students with a strong background in mathematics and physics.

Prerequisites:
Introduction to Astrophysics
Mathematical Methods for the Physicist
Quantum Mechanics
(All preferred but not obligatory)

Prior Knowledge:
Mechanics
Quantum Mechanics and atomic physics
Thermodynamics
Fluid Dynamics
Electrodynamics
401-7855-00LComputational Astrophysics (University of Zurich)
Der Kurs muss direkt an der UZH als incoming student belegt werden.
UZH Modulkürzel: AST245

Beachten Sie die Einschreibungstermine an der UZH:
Link
W6 KP2VL. M. Mayer
Kurzbeschreibung
LernzielAcquire knowledge of main methodologies for computer-based models of astrophysical systems,the physical equations behind them, and train such knowledge with simple examples of computer programmes
Inhalt1. Integration of ODE, Hamiltonians and Symplectic integration techniques, time adaptivity, time reversibility
2. Large-N gravity calculation, collisionless N-body systems and their simulation
3. Fast Fourier Transform and spectral methods in general
4. Eulerian Hydrodynamics: Upwinding, Riemann solvers, Limiters
5. Lagrangian Hydrodynamics: The SPH method
6. Resolution and instabilities in Hydrodynamics
7. Initial Conditions: Cosmological Simulations and Astrophysical Disks
8. Physical Approximations and Methods for Radiative Transfer in Astrophysics
LiteraturGalactic Dynamics (Binney & Tremaine, Princeton University Press),
Computer Simulation using Particles (Hockney & Eastwood CRC press),
Targeted journal reviews on computational methods for astrophysical fluids (SPH, AMR, moving mesh)
Voraussetzungen / BesonderesSome knowledge of UNIX, scripting languages (see Link as an example), some prior experience programming, knowledge of C, C++ beneficial
Atmosphärenphysik
NummerTitelTypECTSUmfangDozierende
701-0023-00LAtmosphäre Information W3 KP2VE. Fischer, T. Peter
KurzbeschreibungGrundlagen der Atmosphäre, physikalischer Aufbau und chemische Zusammensetzung, Spurengase, Kreisläufe in der Atmosphäre, Zirkulation, Stabilität, Strahlung, Kondensation, Wolken, Oxidationspotential und Ozonschicht.
LernzielVerständnis grundlegender physikalischer und chemischer Prozesse in der Atmosphäre. Kenntnis über die Mechanismen und Zusammenhänge von: Wetter - Klima, Atmosphäre - Ozeane - Kontinente, Troposphäre - Stratosphäre. Verständnis von umweltrelevanten Strukturen und Vorgängen in sehr unterschiedlichem Massstab. Grundlagen für eine modellmässige Darstellung komplexer Zusammenhänge in der Atmosphäre.
InhaltGrundlagen der Atmosphäre, physikalischer Aufbau und chemische Zusammensetzung, Spurengase, Kreisläufe in der Atmosphäre, Zirkulation, Stabilität, Strahlung, Kondensation, Wolken, Oxidationspotential und Ozonschicht.
SkriptSchriftliche Unterlagen werden abgegeben.
Literatur- John H. Seinfeld and Spyros N. Pandis, Atmospheric Chemistry and Physics: From Air Pollution to Climate Change, Wiley, New York, 1998.
- Gösta H. Liljequist, Allgemeine Meteorologie, Vieweg, Braunschweig, 1974.
Chemie
NummerTitelTypECTSUmfangDozierende
529-0004-01LClassical Simulation of (Bio)Molecular Systems Information W6 KP4GP. H. Hünenberger, J. Dolenc, S. Riniker
KurzbeschreibungMolecular models, classical force fields, configuration sampling, molecular dynamics simulation, boundary conditions, electrostatic interactions, analysis of trajectories, free-energy calculations, structure refinement, applications in chemistry and biology. Exercises: hands-on computer exercises for learning progressively how to perform an analyze classical simulations (using the package GROMOS).
LernzielIntroduction to classical (atomistic) computer simulation of (bio)molecular systems, development of skills to carry out and interpret these simulations.
InhaltMolecular models, classical force fields, configuration sampling, molecular dynamics simulation, boundary conditions, electrostatic interactions, analysis of trajectories, free-energy calculations, structure refinement, applications in chemistry and biology. Exercises: hands-on computer exercises for learning progressively how to perform an analyze classical simulations (using the package GROMOS).
SkriptThe powerpoint slides of the lectures will be made available weekly on the website in pdf format (on the day preceding each lecture).
LiteraturSee: Link
Voraussetzungen / BesonderesSince the exercises on the computer do convey and test essentially different skills than those being conveyed during the lectures and tested at the oral exam, the results of the exercises are taken into account when evaluating the results of the exam (learning component, possible bonus of up to 0.25 points on the exam mark).

For more information about the lecture: Link
Fluiddynamik
NummerTitelTypECTSUmfangDozierende
151-0103-00LFluiddynamik IIW3 KP2V + 1UP. Jenny
KurzbeschreibungEbene Potentialströmungen: Stromfunktion und Potential, Singularitätenmethode, instationäre Strömung, aerodynamische Begriffe.
Drehungsbehaftete Strömungen: Wirbelstärke und Zirkulation, Wirbeltransportgleichung, Wirbelsätze von Helmholtz und Kelvin.
Kompressible Strömungen: Stromfadentheorie, senkrechter und schiefer Verdichtungsstoss, Laval-Düse, Prandtl-Meyer-Expansion, Reibungseinfluss.
LernzielErweiterung der Grundlagen der Fluiddynamik.
Grundbegriffe, Phänomene und Gesetzmässigkeiten von drehungsfreien, drehungsbehafteten und eindimensionalen kompressiblen Strömungen vermitteln.
InhaltEbene Potentialströmungen: Stromfunktion und Potential, komplexe Darstellung, Singularitätenmethode, instationäre Strömung, aerodynamische Begriffe.
Drehungsbehaftete Strömungen: Wirbelstärke und Zirkulation, Wirbeldynamik und Wirbeltransportgleichung, Wirbelsätze von Helmholtz und Kelvin.
Kompressible Strömungen: Stromfadentheorie, senkrechter und schiefer Verdichtungsstoss, Laval-Düse, Prandtl-Meyer-Expansion, Reibungseinfluss.
Skriptja
(Siehe auch untenstehende Information betreffend der Literatur.)
LiteraturP.K. Kundu, I.M. Cohen, D.R. Dowling: Fluid Mechanics, Academic Press, 5th ed., 2011 (includes a free copy of the DVD "Multimedia Fluid Mechanics")

P.K. Kundu, I.M. Cohen, D.R. Dowling: Fluid Mechanics, Academic Press, 6th ed., 2015 (does NOT include a free copy of the DVD "Multimedia Fluid Mechanics")
Voraussetzungen / BesonderesAnalysis I/II, Fluiddynamik I, Grundbegriffe der Thermodynamik (Thermodynamik I).

Für die Formulierung der Grundlagen der Fluiddynamik werden unabdingbar Begriffe und Ergebnisse aus der Mathematik benötigt. Erfahrungsgemäss haben einige Studierende damit Schwierigkeiten.
Es wird daher dringend empfohlen, insbesondere den Stoff über
- elementare Funktionen (wie sin, cos, tan, exp, deren Umkehrfunktionen, Ableitungen und Integrale) sowie über
- Vektoranalysis (Gradient, Divergenz, Rotation, Linienintegral ("Arbeit"), Integralsätze von Gauss und von Stokes, Potentialfelder als Lösungen der Laplace-Gleichung) zu wiederholen. Ferner wird der Umgang mit
- komplexen Zahlen und Funktionen (siehe Anhang des Skripts Analysis I/II Teil C und Zusammenfassung im Anhang C des Skripts Fluiddynamik) benötigt.

Literatur z.B.: U. Stammbach: Analysis I/II, Skript Teile A, B und C.
Systems and Control
NummerTitelTypECTSUmfangDozierende
227-0103-00LRegelsysteme Information W6 KP2V + 2UF. Dörfler
KurzbeschreibungStudy of concepts and methods for the mathematical description and analysis of dynamical systems. The concept of feedback. Design of control systems for single input - single output and multivariable systems.
LernzielStudy of concepts and methods for the mathematical description and analysis of dynamical systems. The concept of feedback. Design of control systems for single input - single output and multivariable systems.
InhaltProcess automation, concept of control. Modelling of dynamical systems - examples, state space description, linearisation, analytical/numerical solution. Laplace transform, system response for first and second order systems - effect of additional poles and zeros. Closed-loop control - idea of feedback. PID control, Ziegler - Nichols tuning. Stability, Routh-Hurwitz criterion, root locus, frequency response, Bode diagram, Bode gain/phase relationship, controller design via "loop shaping", Nyquist criterion. Feedforward compensation, cascade control. Multivariable systems (transfer matrix, state space representation), multi-loop control, problem of coupling, Relative Gain Array, decoupling, sensitivity to model uncertainty. State space representation (modal description, controllability, control canonical form, observer canonical form), state feedback, pole placement - choice of poles. Observer, observability, duality, separation principle. LQ Regulator, optimal state estimation.
LiteraturK. J. Aström & R. Murray. Feedback Systems: An Introduction for Scientists and Engineers. Princeton University Press, 2010.
R. C. Dorf and R. H. Bishop. Modern Control Systems. Prentice Hall, New Jersey, 2007.
G. F. Franklin, J. D. Powell, and A. Emami-Naeini. Feedback Control of Dynamic Systems. Addison-Wesley, 2010.
J. Lunze. Regelungstechnik 1. Springer, Berlin, 2014.
J. Lunze. Regelungstechnik 2. Springer, Berlin, 2014.
Voraussetzungen / BesonderesPrerequisites: Signal and Systems Theory II.

MATLAB is used for system analysis and simulation.
227-0045-00LSignal- und Systemtheorie IW4 KP2V + 2UH. Bölcskei
KurzbeschreibungSignaltheorie und Systemtheorie (zeitkontinuierlich und zeitdiskret): Signalanalyse im Zeit- und Frequenzbereich, Signalräume, Hilberträume, verallgemeinerte Funktionen, lineare zeitinvariante Systeme, Abtasttheoreme, zeitdiskrete Signale und Systeme, digitale Filterstrukturen, diskrete Fourier-Transformation (DFT), endlich-dimensionale Signale und Systeme, schnelle Fouriertransformation (FFT).
LernzielEinführung in die mathematische Signaltheorie und Systemtheorie.
InhaltSignaltheorie und Systemtheorie (zeitkontinuierlich und zeitdiskret): Signalanalyse im Zeit- und Frequenzbereich, Signalräume, Hilberträume, verallgemeinerte Funktionen, lineare zeitinvariante Systeme, Abtasttheoreme, zeitdiskrete Signale und Systeme, digitale Filterstrukturen, diskrete Fourier-Transformation (DFT), endlich-dimensionale Signale und Systeme, schnelle Fouriertransformation (FFT).
SkriptVorlesungsskriptum, Übungsskriptum mit Lösungen.
Robotik
Höchstens eine der beiden Lerneinheiten
263-5902-00L Computer Vision bzw.
227-0447-00L Image Analysis and Computer Vision
darf an das gesamte Studium (Bachelor und Master) angerechnet werden.
Höchstens eine der beiden Lerneinheiten
263-5210-00L Probabilistic Artificial Intelligence bzw.
252-0535-00L Advanced Machine Learning
darf an das gesamte Studium (Bachelor und Master) angerechnet werden.
NummerTitelTypECTSUmfangDozierende
151-0601-00LTheory of Robotics and Mechatronics Information W4 KP3GP. Korba, S. Stoeter
KurzbeschreibungThis course provides an introduction and covers the fundamentals of the field, including rigid motions, homogeneous transformations, forward and inverse kinematics of multiple degree of freedom manipulators, velocity kinematics, motion planning, trajectory generation, sensing, vision, and control.
LernzielRobotics is often viewed from three perspectives: perception (sensing), manipulation (affecting changes in the world), and cognition (intelligence). Robotic systems integrate aspects of all three of these areas. This course provides an introduction to the theory of robotics, and covers the fundamentals of the field, including rigid motions, homogeneous transformations, forward and inverse kinematics of multiple degree of freedom manipulators, velocity kinematics, motion planning, trajectory generation, sensing, vision, and control.
InhaltAn introduction to the theory of robotics, and covers the fundamentals of the field, including rigid motions, homogeneous transformations, forward and inverse kinematics of multiple degree of freedom manipulators, velocity kinematics, motion planning, trajectory generation, sensing, vision, and control.
Skriptavailable.
227-0447-00LImage Analysis and Computer Vision Information W6 KP3V + 1UL. Van Gool, E. Konukoglu, F. Yu
KurzbeschreibungLight and perception. Digital image formation. Image enhancement and feature extraction. Unitary transformations. Color and texture. Image segmentation. Motion extraction and tracking. 3D data extraction. Invariant features. Specific object recognition and object class recognition. Deep learning and Convolutional Neural Networks.
LernzielOverview of the most important concepts of image formation, perception and analysis, and Computer Vision. Gaining own experience through practical computer and programming exercises.
InhaltThis course aims at offering a self-contained account of computer vision and its underlying concepts, including the recent use of deep learning.
The first part starts with an overview of existing and emerging applications that need computer vision. It shows that the realm of image processing is no longer restricted to the factory floor, but is entering several fields of our daily life. First the interaction of light with matter is considered. The most important hardware components such as cameras and illumination sources are also discussed. The course then turns to image discretization, necessary to process images by computer.
The next part describes necessary pre-processing steps, that enhance image quality and/or detect specific features. Linear and non-linear filters are introduced for that purpose. The course will continue by analyzing procedures allowing to extract additional types of basic information from multiple images, with motion and 3D shape as two important examples. Finally, approaches for the recognition of specific objects as well as object classes will be discussed and analyzed. A major part at the end is devoted to deep learning and AI-based approaches to image analysis. Its main focus is on object recognition, but also other examples of image processing using deep neural nets are given.
SkriptCourse material Script, computer demonstrations, exercises and problem solutions
Voraussetzungen / BesonderesPrerequisites:
Basic concepts of mathematical analysis and linear algebra. The computer exercises are based on Python and Linux.
The course language is English.
252-0535-00LAdvanced Machine Learning Information W10 KP3V + 2U + 4AJ. M. Buhmann, C. Cotrini Jimenez
KurzbeschreibungMachine learning algorithms provide analytical methods to search data sets for characteristic patterns. Typical tasks include the classification of data, function fitting and clustering, with applications in image and speech analysis, bioinformatics and exploratory data analysis. This course is accompanied by practical machine learning projects.
LernzielStudents will be familiarized with advanced concepts and algorithms for supervised and unsupervised learning; reinforce the statistics knowledge which is indispensible to solve modeling problems under uncertainty. Key concepts are the generalization ability of algorithms and systematic approaches to modeling and regularization. Machine learning projects will provide an opportunity to test the machine learning algorithms on real world data.
InhaltThe theory of fundamental machine learning concepts is presented in the lecture, and illustrated with relevant applications. Students can deepen their understanding by solving both pen-and-paper and programming exercises, where they implement and apply famous algorithms to real-world data.

Topics covered in the lecture include:

Fundamentals:
What is data?
Bayesian Learning
Computational learning theory

Supervised learning:
Ensembles: Bagging and Boosting
Max Margin methods
Neural networks

Unsupservised learning:
Dimensionality reduction techniques
Clustering
Mixture Models
Non-parametric density estimation
Learning Dynamical Systems
SkriptNo lecture notes, but slides will be made available on the course webpage.
LiteraturC. Bishop. Pattern Recognition and Machine Learning. Springer 2007.

R. Duda, P. Hart, and D. Stork. Pattern Classification. John Wiley &
Sons, second edition, 2001.

T. Hastie, R. Tibshirani, and J. Friedman. The Elements of Statistical
Learning: Data Mining, Inference and Prediction. Springer, 2001.

L. Wasserman. All of Statistics: A Concise Course in Statistical
Inference. Springer, 2004.
Voraussetzungen / BesonderesThe course requires solid basic knowledge in analysis, statistics and numerical methods for CSE as well as practical programming experience for solving assignments.
Students should have followed at least "Introduction to Machine Learning" or an equivalent course offered by another institution.

PhD students are required to obtain a passing grade in the course (4.0 or higher based on project and exam) to gain credit points.
263-3210-00LDeep Learning Information Belegung eingeschränkt - Details anzeigen
Number of participants limited to 320.
W8 KP3V + 2U + 2AF. Perez Cruz, A. Lucchi
KurzbeschreibungDeep learning is an area within machine learning that deals with algorithms and models that automatically induce multi-level data representations.
LernzielIn recent years, deep learning and deep networks have significantly improved the state-of-the-art in many application domains such as computer vision, speech recognition, and natural language processing. This class will cover the mathematical foundations of deep learning and provide insights into model design, training, and validation. The main objective is a profound understanding of why these methods work and how. There will also be a rich set of hands-on tasks and practical projects to familiarize students with this emerging technology.
Voraussetzungen / BesonderesThis is an advanced level course that requires some basic background in machine learning. More importantly, students are expected to have a very solid mathematical foundation, including linear algebra, multivariate calculus, and probability. The course will make heavy use of mathematics and is not (!) meant to be an extended tutorial of how to train deep networks with tools like Torch or Tensorflow, although that may be a side benefit.

The participation in the course is subject to the following condition:
- Students must have taken the exam in Advanced Machine Learning (252-0535-00) or have acquired equivalent knowledge, see exhaustive list below:

Advanced Machine Learning
Link

Computational Intelligence Lab
Link

Introduction to Machine Learning
Link

Statistical Learning Theory
Link

Computational Statistics
Link

Probabilistic Artificial Intelligence
Link
151-0563-01LDynamic Programming and Optimal Control Information W4 KP2V + 1UR. D'Andrea
KurzbeschreibungIntroduction to Dynamic Programming and Optimal Control.
LernzielCovers the fundamental concepts of Dynamic Programming & Optimal Control.
InhaltDynamic Programming Algorithm; Deterministic Systems and Shortest Path Problems; Infinite Horizon Problems, Bellman Equation; Deterministic Continuous-Time Optimal Control.
LiteraturDynamic Programming and Optimal Control by Dimitri P. Bertsekas, Vol. I, 3rd edition, 2005, 558 pages, hardcover.
Voraussetzungen / BesonderesRequirements: Knowledge of advanced calculus, introductory probability theory, and matrix-vector algebra.
151-0851-00LRobot Dynamics Information Belegung eingeschränkt - Details anzeigen W4 KP2V + 2UM. Hutter, R. Siegwart
KurzbeschreibungWe will provide an overview on how to kinematically and dynamically model typical robotic systems such as robot arms, legged robots, rotary wing systems, or fixed wing.
LernzielThe primary objective of this course is that the student deepens an applied understanding of how to model the most common robotic systems. The student receives a solid background in kinematics, dynamics, and rotations of multi-body systems. On the basis of state of the art applications, he/she will learn all necessary tools to work in the field of design or control of robotic systems.
InhaltThe course consists of three parts: First, we will refresh and deepen the student's knowledge in kinematics, dynamics, and rotations of multi-body systems. In this context, the learning material will build upon the courses for mechanics and dynamics available at ETH, with the particular focus on their application to robotic systems. The goal is to foster the conceptual understanding of similarities and differences among the various types of robots. In the second part, we will apply the learned material to classical robotic arms as well as legged systems and discuss kinematic constraints and interaction forces. In the third part, focus is put on modeling fixed wing aircraft, along with related design and control concepts. In this context, we also touch aerodynamics and flight mechanics to an extent typically required in robotics. The last part finally covers different helicopter types, with a focus on quadrotors and the coaxial configuration which we see today in many UAV applications. Case studies on all main topics provide the link to real applications and to the state of the art in robotics.
Voraussetzungen / BesonderesThe contents of the following ETH Bachelor lectures or equivalent are assumed to be known: Mechanics and Dynamics, Control, Basics in Fluid Dynamics.
Robotik (fortgesetzt)
Höchstens eine der beiden Lerneinheiten
263-5902-00L Computer Vision bzw.
227-0447-00L Image Analysis and Computer Vision
darf an das gesamte Studium (Bachelor und Master) angerechnet werden.
Höchstens eine der beiden Lerneinheiten
263-5210-00L Probabilistic Artificial Intelligence bzw.
252-0535-00L Advanced Machine Learning
darf an das gesamte Studium (Bachelor und Master) angerechnet werden.
Für die Kategoriezuordnung wenden Sie sich an das Studiensekretariat (Link).
NummerTitelTypECTSUmfangDozierende
263-5902-00LComputer Vision Information W8 KP3V + 1U + 3AM. Pollefeys, S. Tang, F. Yu
KurzbeschreibungThe goal of this course is to provide students with a good understanding of computer vision and image analysis techniques. The main concepts and techniques will be studied in depth and practical algorithms and approaches will be discussed and explored through the exercises.
LernzielThe objectives of this course are:
1. To introduce the fundamental problems of computer vision.
2. To introduce the main concepts and techniques used to solve those.
3. To enable participants to implement solutions for reasonably complex problems.
4. To enable participants to make sense of the computer vision literature.
InhaltCamera models and calibration, invariant features, Multiple-view geometry, Model fitting, Stereo Matching, Segmentation, 2D Shape matching, Shape from Silhouettes, Optical flow, Structure from motion, Tracking, Object recognition, Object category recognition
Voraussetzungen / BesonderesIt is recommended that students have taken the Visual Computing lecture or a similar course introducing basic image processing concepts before taking this course.
263-5210-00LProbabilistic Artificial Intelligence Information Belegung eingeschränkt - Details anzeigen W8 KP3V + 2U + 2AA. Krause
KurzbeschreibungThis course introduces core modeling techniques and algorithms from machine learning, optimization and control for reasoning and decision making under uncertainty, and study applications in areas such as robotics.
LernzielHow can we build systems that perform well in uncertain environments? How can we develop systems that exhibit "intelligent" behavior, without prescribing explicit rules? How can we build systems that learn from experience in order to improve their performance? We will study core modeling techniques and algorithms from statistics, optimization, planning, and control and study applications in areas such as robotics. The course is designed for graduate students.
InhaltTopics covered:
- Probability
- Probabilistic inference (variational inference, MCMC)
- Bayesian learning (Gaussian processes, Bayesian deep learning)
- Probabilistic planning (MDPs, POMPDPs)
- Multi-armed bandits and Bayesian optimization
- Reinforcement learning
Voraussetzungen / BesonderesSolid basic knowledge in statistics, algorithms and programming.
The material covered in the course "Introduction to Machine Learning" is considered as a prerequisite.
Physik
NummerTitelTypECTSUmfangDozierende
402-0809-00LIntroduction to Computational PhysicsW8 KP2V + 2UA. Adelmann
KurzbeschreibungDiese Vorlesung bietet eine Einführung in Computersimulationsmethoden für physikalische Probleme und deren Implementierung auf PCs und Supercomputern. Die betrachteten Themen beinhalten: klassische Bewegungsgleichungen, partielle Differentialgleichungen (Wellengleichung, Diffussionsgleichung, Maxwell-Gleichungen), Monte-Carlo Simulationen, Perkolation, Phasenübergänge und N-Body Probleme.
LernzielStudenten lernen die folgenden Methoden anzuwenden: Prinzipien zur Erstellung von Zufallszahlen, Berechnung von kritischen Exponenten am Beispiel von Perkolation, Numerische Lösung von Problemen aus der klassichen Mechanik und Elektrodynamik, Kanonische Monte-Carlo Simulationen zur numerischen Betrachtung von magnetischen Systemen. Studenten lernen die Programmiersprachen Julia und Bibliotheken zur Lösung physikalischer Probleme kennen. Zusätzlich lernen Studenten verschiedene numerische Verfahren zu unterscheiden und gezielt zur Lösung eines gegebenen physikalischen Problems einzusetzen.
InhaltEinführung in die rechnergestützte Simulation physikalischer Probleme. Anhand einfacher Modelle aus der klassischen Mechanik, Elektrodynamik und statistischen Mechanik sowie interdisziplinären Anwendungen werden moderne Programmiermethoden für numerische Simulationen mittels Julia vermittelt. Daneben wird ein Überblick über vorhandene Softwarebibliotheken für numerische Simulationen geboten.
SkriptSkript und Folien sind online verfügbar und werden bei Bedarf verteilt.
LiteraturLiteraturempfehlungen und Referenzen sind im Skript enthalten.
Voraussetzungen / BesonderesVorlesung und Übung in Englisch, Prüfung wahlweise auf Deutsch oder Englisch
Computational Finance
NummerTitelTypECTSUmfangDozierende
401-3913-01LMathematical Foundations for Finance Information W4 KP3V + 2UB. Acciaio
KurzbeschreibungFirst introduction to main modelling ideas and mathematical tools from mathematical finance
LernzielThis course gives a first introduction to the main modelling ideas and mathematical tools from mathematical finance. It mainly aims at non-mathematicians who need an introduction to the main tools from stochastics used in mathematical finance. However, mathematicians who want to learn some basic modelling ideas and concepts for quantitative finance (before continuing with a more advanced course) may also find this of interest.. The main emphasis will be on ideas, but important results will be given with (sometimes partial) proofs.
InhaltTopics to be covered include

- financial market models in finite discrete time
- absence of arbitrage and martingale measures
- valuation and hedging in complete markets
- basics about Brownian motion
- stochastic integration
- stochastic calculus: Itô's formula, Girsanov transformation, Itô's representation theorem
- Black-Scholes formula
SkriptLecture notes will be sold at the beginning of the course.
LiteraturLecture notes will be sold at the beginning of the course. Additional (background) references are given there.
Voraussetzungen / BesonderesPrerequisites: Results and facts from probability theory as in the book "Probability Essentials" by J. Jacod and P. Protter will be used freely. Especially participants without a direct mathematics background are strongly advised to familiarise themselves with those tools before (or very quickly during) the course. (A possible alternative to the above English textbook are the (German) lecture notes for the standard course "Wahrscheinlichkeitstheorie".)

For those who are not sure about their background, we suggest to look at the exercises in Chapters 8, 9, 22-25, 28 of the Jacod/Protter book. If these pose problems, you will have a hard time during the course. So be prepared.
401-4657-00LNumerical Analysis of Stochastic Ordinary Differential Equations Belegung eingeschränkt - Details anzeigen
Alternative course title: "Computational Methods for Quantitative Finance: Monte Carlo and Sampling Methods"
W6 KP3V + 1UA. Stein
KurzbeschreibungCourse on numerical approximations of stochastic ordinary differential equations driven by Wiener processes. These equations have several applications, for example in financial option valuation. This course also contains an introduction to random number generation and Monte Carlo methods for random variables.
LernzielThe aim of this course is to enable the students to carry out simulations and their mathematical convergence analysis for stochastic models originating from applications such as mathematical finance. For this the course teaches a decent knowledge of the different numerical methods, their underlying ideas, convergence properties and implementation issues.
InhaltGeneration of random numbers
Monte Carlo methods for the numerical integration of random variables
Stochastic processes and Brownian motion
Stochastic ordinary differential equations (SODEs)
Numerical approximations of SODEs
Applications to computational finance: Option valuation
SkriptThere will be English, typed lecture notes for registered participants in the course.
LiteraturP. Glassermann:
Monte Carlo Methods in Financial Engineering.
Springer-Verlag, New York, 2004.

P. E. Kloeden and E. Platen:
Numerical Solution of Stochastic Differential Equations.
Springer-Verlag, Berlin, 1992.
Voraussetzungen / BesonderesPrerequisites:

Mandatory: Probability and measure theory,
basic numerical analysis and
basics of MATLAB/Python programming.

a) mandatory courses:
Elementary Probability,
Probability Theory I.

b) recommended courses:
Stochastic Processes.

Start of lectures: Wednesday September 22, 2021.
Electromagnetics
NummerTitelTypECTSUmfangDozierende
227-2037-00LPhysical Modelling and SimulationW6 KP4GJ. Smajic
KurzbeschreibungThis module consists of (a) an introduction to fundamental equations of electromagnetics, mechanics and heat transfer, (b) a detailed overview of numerical methods for field simulations, and (c) practical examples solved in form of small projects.
LernzielBasic knowledge of the fundamental equations and effects of electromagnetics, mechanics, and heat transfer. Knowledge of the main concepts of numerical methods for physical modelling and simulation. Ability (a) to develop own simple field simulation programs, (b) to select an appropriate field solver for a given problem, (c) to perform field simulations, (d) to evaluate the obtained results, and (e) to interactively improve the models until sufficiently accurate results are obtained.
InhaltThe module begins with an introduction to the fundamental equations and effects of electromagnetics, mechanics, and heat transfer. After the introduction follows a detailed overview of the available numerical methods for solving electromagnetic, thermal and mechanical boundary value problems. This part of the course contains a general introduction into numerical methods, differential and integral forms, linear equation systems, Finite Difference Method (FDM), Boundary Element Method (BEM), Method of Moments (MoM), Multiple Multipole Program (MMP) and Finite Element Method (FEM). The theoretical part of the course finishes with a presentation of multiphysics simulations through several practical examples of HF-engineering such as coupled electromagnetic-mechanical and electromagnetic-thermal analysis of MEMS.
In the second part of the course the students will work in small groups on practical simulation problems. For solving practical problems the students can develop and use own simulation programs or chose an appropriate commercial field solver for their specific problem. This practical simulation work of the students is supervised by the lecturers.
Geophysik
Empfohlene Kombinationen:
Fach 1 + Fach 2
Fach 1 + Fach 3
Fach 2 + Fach 3
Fach 3 + Fach 4
Fach 5 + Fach 6 + Fach 8
Fach 4 + Fach 5
Fach 7 + Fach 8
Geophysik: Fach 1
NummerTitelTypECTSUmfangDozierende
651-4007-00LContinuum MechanicsW3 KP2VT. Gerya
KurzbeschreibungIn this course, students learn crucial partial differential equations (conservation laws) that are applicable to any continuum including the Earth's mantle, core, atmosphere and ocean. The course will provide step-by-step introduction into the mathematical structure, physical meaning and analytical solutions of the equations. The course has a particular focus on solid Earth applications.
LernzielThe goal of this course is to learn and understand few principal partial differential equations (conservation laws) that are applicable for analysing and modelling of any continuum including the Earth's mantle, core, atmosphere and ocean. By the end of the course, students should be able to write, explain and analyse the equations and apply them for simple analytical cases. Numerical solving of these equations will be discussed in the Numerical Modelling I and II course running in parallel.
InhaltA provisional week-by-week schedule (subject to change) is as follows:


Weeks 1,2: The continuity equation
Theory: Definition of a geological media as a continuum. Field variables used for the representation of a continuum.Methods for definition of the field variables. Eulerian and Lagrangian reference frames. Continuity equation in Eulerian and Lagrangian forms. Derivation of Eulerian continuity equation from simple principles. Advective transport term. Incompressible continuity equation.
Exercise: Computing the divergence of velocity field.

Weeks 3,4: Density and gravity
Theory: Density of rocks and minerals. Thermal expansion and compressibility. Dependence of density on pressure and temperature. Equations of state. Poisson equation for gravitational potential and its derivation from simple principles.
Exercises: Computing density, thermal expansion and compressibility from an equation of state. Derivation of gravitational acceleration and its divergence from gravitational potential.

Weeks 5,6: Stress and strain
Theory: Deformation and stresses. Definition of stress, strain and strain-rate tensors. Deviatoric stresses. Mean stress as a dynamic (nonlithostatic) pressure. Stress and strain rate invariants.
Exercises: Analysing strain rate tensor for solid body rotation. Computing stress invariants

Weeks 7,8: The momentum equation
Theory: Momentum equation and its derivation from simple principles. Viscosity and Newtonian law of viscous friction. Navier-–Stokes equation for the motion of a viscous fluid. Stokes equation of slow laminar flow of highly viscous incompressible fluid and its application to geodynamics. Simplification of the Stokes equation in case of constant viscosity and its relation to the Poisson equation. Exercises: Deriving momentum equation. Computing velocity for magma flow in a channel.

Week 9: Viscous rheology of rocks
Theory: Solid-state creep of minerals and rocks as themajor mechanism of deformation of the Earth’s interior. Dislocation and diffusion creep mechanisms. Rheological equations for minerals and rocks. Effective viscosity and its dependence on temperature, pressure and strain rate. Formulation of the effective viscosity from empirical flow laws.
Exercise: Deriving viscous rheological equations for computing effective viscosities from empirical flow laws.

Weeks 10,11: The heat conservation equation
Theory: Fourier’s law of heat conduction. Heat conservation equation and its derivation. Radioactive, viscous and adiabatic heating and their relative importance. Heat conservation equation for the case of a constant thermal conductivity and its relation to the Poisson equation.
Exercises: Computing of heat fluxes. Deriving equation for steady state temperature profile in a magmatic channel.

Week 12,13: Elasticity and plasticity
Theory: Elastic rheology. Maxwell viscoelastic rheology. Plastic rheology. Plastic yielding criterion. Plastic flow potential. Plastic flow rule.
Exercise: compute viscoelastic stress evolution.

Week 14: Fluid flow in deforming porous media. Darcy equation for fluid percolation. Derivation of Darcy equation from Stokes equation for channel flow. Dependence of permeability on porosity and grain size. Coupled hydro-mechanical momentum and continuity equations for solid matrix and percolating fluid. Fluid and solid Lagrangian reference frames.


GRADING will be based on honeworks (1/3) and oral exam (2/3).
SkriptScript and Exam questions are available by request Link
LiteraturTaras Gerya Introduction to Numerical Geodynamic Modelling. Second Edition. Cambridge University Press, 2019
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