# Search result: Catalogue data in Autumn Semester 2021

Computational Science and Engineering Bachelor | ||||||

Fields of Specialization | ||||||

Astrophysics | ||||||

Number | Title | Type | ECTS | Hours | Lecturers | |
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401-7851-00L | Theoretical Astrophysics (University of Zurich) No enrolment to this course at ETH Zurich. Book the corresponding module directly at UZH as an incoming student. UZH Module Code: AST512 Mind the enrolment deadlines at UZH: https://www.uzh.ch/cmsssl/en/studies/application/deadlines.html | W | 10 credits | 4V + 2U | University lecturers | |

Abstract | This 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. | |||||

Objective | ||||||

Content | This 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. | |||||

Literature | Course 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 | |||||

Prerequisites / Notice | This 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 | |||||

401-7855-00L | Computational Astrophysics (University of Zurich)No enrolment to this course at ETH Zurich. Book the corresponding module directly at UZH as an incoming student. UZH Module Code: AST245 Mind the enrolment deadlines at UZH: https://www.uzh.ch/cmsssl/en/studies/application/deadlines.html | W | 6 credits | 2V | L. M. Mayer | |

Abstract | ||||||

Objective | Acquire 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 | |||||

Content | 1. 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 | |||||

Literature | Galactic 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) | |||||

Prerequisites / Notice | Some knowledge of UNIX, scripting languages (see www.physik.uzh.ch/lectures/informatik/python/ as an example), some prior experience programming, knowledge of C, C++ beneficial | |||||

Physics of the Atmosphere | ||||||

Number | Title | Type | ECTS | Hours | Lecturers | |

701-0023-00L | Atmosphere | W | 3 credits | 2V | E. Fischer, T. Peter | |

Abstract | Basic principles of the atmosphere, physical structure and chemical composition, trace gases, atmospheric cycles, circulation, stability, radiation, condensation, clouds, oxidation capacity and ozone layer. | |||||

Objective | Understanding of basic physical and chemical processes in the atmosphere. Understanding of mechanisms of and interactions between: weather - climate, atmosphere - ocean - continents, troposhere - stratosphere. Understanding of environmentally relevant structures and processes on vastly differing scales. Basis for the modelling of complex interrelations in the atmospehre. | |||||

Content | Basic principles of the atmosphere, physical structure and chemical composition, trace gases, atmospheric cycles, circulation, stability, radiation, condensation, clouds, oxidation capacity and ozone layer. | |||||

Lecture notes | Written information will be supplied. | |||||

Literature | - 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. | |||||

Chemistry | ||||||

Number | Title | Type | ECTS | Hours | Lecturers | |

529-0004-01L | Classical Simulation of (Bio)Molecular Systems | W | 6 credits | 4G | P. H. Hünenberger, J. Dolenc, S. Riniker | |

Abstract | Molecular 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). | |||||

Objective | Introduction to classical (atomistic) computer simulation of (bio)molecular systems, development of skills to carry out and interpret these simulations. | |||||

Content | Molecular 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). | |||||

Lecture notes | The powerpoint slides of the lectures will be made available weekly on the website in pdf format (on the day preceding each lecture). | |||||

Literature | See: www.csms.ethz.ch/education/CSBMS | |||||

Prerequisites / Notice | Since 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: www.csms.ethz.ch/education/CSBMS | |||||

Fluid Dynamics | ||||||

Number | Title | Type | ECTS | Hours | Lecturers | |

151-0103-00L | Fluid Dynamics II | W | 3 credits | 2V + 1U | P. Jenny | |

Abstract | Two-dimensional irrotational (potential) flows: stream function and potential, singularity method, unsteady flow, aerodynamic concepts. Vorticity dynamics: vorticity and circulation, vorticity equation, vortex theorems of Helmholtz and Kelvin. Compressible flows: isentropic flow along stream tube, normal and oblique shocks, Laval nozzle, Prandtl-Meyer expansion, viscous effects. | |||||

Objective | Expand basic knowledge of fluid dynamics. Concepts, phenomena and quantitative description of irrotational (potential), rotational, and one-dimensional compressible flows. | |||||

Content | Two-dimensional irrotational (potential) flows: stream function and potential, complex notation, singularity method, unsteady flow, aerodynamic concepts. Vorticity dynamics: vorticity and circulation, vorticity equation, vortex theorems of Helmholtz and Kelvin. Compressible flows: isentropic flow along stream tube, normal and oblique shocks, Laval nozzle, Prandtl-Meyer expansion, viscous effects. | |||||

Lecture notes | Lecture notes are available (in German). (See also info on literature below.) | |||||

Literature | Relevant chapters (corresponding to lecture notes) from the textbook P.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") | |||||

Prerequisites / Notice | Analysis I/II, Knowledge of Fluid Dynamics I, thermodynamics of ideal gas | |||||

Systems and Control | ||||||

Number | Title | Type | ECTS | Hours | Lecturers | |

227-0103-00L | Control Systems | W | 6 credits | 2V + 2U | F. Dörfler | |

Abstract | Study 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. | |||||

Objective | Study 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. | |||||

Content | Process 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. | |||||

Literature | K. 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. | |||||

Prerequisites / Notice | Prerequisites: Signal and Systems Theory II. MATLAB is used for system analysis and simulation. | |||||

227-0045-00L | Signals and Systems I | W | 4 credits | 2V + 2U | H. Bölcskei | |

Abstract | Signal theory and systems theory (continuous-time and discrete-time): Signal analysis in the time and frequency domains, signal spaces, Hilbert spaces, generalized functions, linear time-invariant systems, sampling theorems, discrete-time signals and systems, digital filter structures, Discrete Fourier Transform (DFT), finite-dimensional signals and systems, Fast Fourier Transform (FFT). | |||||

Objective | Introduction to mathematical signal processing and system theory. | |||||

Content | Signal theory and systems theory (continuous-time and discrete-time): Signal analysis in the time and frequency domains, signal spaces, Hilbert spaces, generalized functions, linear time-invariant systems, sampling theorems, discrete-time signals and systems, digital filter structures, Discrete Fourier Transform (DFT), finite-dimensional signals and systems, Fast Fourier Transform (FFT). | |||||

Lecture notes | Lecture notes, problem set with solutions. | |||||

Robotics Only one of the two course units 263-5902-00L Computer Vision resp. 227-0447-00L Image Analysis and Computer Vision may be recognised for credits. More precisely, it is also not allowed to have recognised one course unit for the Bachelor's and the other course unit for the Master's degree. The same restriction applied to the two course units 263-5210-00L Probabilistic Artificial Intelligence resp. 252-0535-00L Advanced Machine Learning | ||||||

Number | Title | Type | ECTS | Hours | Lecturers | |

151-0601-00L | Theory of Robotics and Mechatronics | W | 4 credits | 3G | P. Korba, S. Stoeter | |

Abstract | This 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. | |||||

Objective | Robotics 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. | |||||

Content | 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. | |||||

Lecture notes | available. | |||||

227-0447-00L | Image Analysis and Computer Vision | W | 6 credits | 3V + 1U | L. Van Gool, E. Konukoglu, F. Yu | |

Abstract | Light 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. | |||||

Objective | Overview of the most important concepts of image formation, perception and analysis, and Computer Vision. Gaining own experience through practical computer and programming exercises. | |||||

Content | This 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. | |||||

Lecture notes | Course material Script, computer demonstrations, exercises and problem solutions | |||||

Prerequisites / Notice | Prerequisites: Basic concepts of mathematical analysis and linear algebra. The computer exercises are based on Python and Linux. The course language is English. | |||||

252-0535-00L | Advanced Machine Learning | W | 10 credits | 3V + 2U + 4A | J. M. Buhmann, C. Cotrini Jimenez | |

Abstract | Machine 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. | |||||

Objective | Students 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. | |||||

Content | The 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 | |||||

Lecture notes | No lecture notes, but slides will be made available on the course webpage. | |||||

Literature | C. 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. | |||||

Prerequisites / Notice | The 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. | |||||

263-3210-00L | Deep Learning Number of participants limited to 320. | W | 8 credits | 3V + 2U + 2A | F. Perez Cruz, A. Lucchi | |

Abstract | Deep learning is an area within machine learning that deals with algorithms and models that automatically induce multi-level data representations. | |||||

Objective | In 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. | |||||

Prerequisites / Notice | This 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 https://ml2.inf.ethz.ch/courses/aml/ Computational Intelligence Lab http://da.inf.ethz.ch/teaching/2019/CIL/ Introduction to Machine Learning https://las.inf.ethz.ch/teaching/introml-S19 Statistical Learning Theory http://ml2.inf.ethz.ch/courses/slt/ Computational Statistics https://stat.ethz.ch/lectures/ss19/comp-stats.php Probabilistic Artificial Intelligence https://las.inf.ethz.ch/teaching/pai-f18 | |||||

151-0563-01L | Dynamic Programming and Optimal Control | W | 4 credits | 2V + 1U | R. D'Andrea | |

Abstract | Introduction to Dynamic Programming and Optimal Control. | |||||

Objective | Covers the fundamental concepts of Dynamic Programming & Optimal Control. | |||||

Content | Dynamic Programming Algorithm; Deterministic Systems and Shortest Path Problems; Infinite Horizon Problems, Bellman Equation; Deterministic Continuous-Time Optimal Control. | |||||

Literature | Dynamic Programming and Optimal Control by Dimitri P. Bertsekas, Vol. I, 3rd edition, 2005, 558 pages, hardcover. | |||||

Prerequisites / Notice | Requirements: Knowledge of advanced calculus, introductory probability theory, and matrix-vector algebra. | |||||

151-0851-00L | Robot Dynamics | W | 4 credits | 2V + 2U | M. Hutter, R. Siegwart | |

Abstract | We 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. | |||||

Objective | The 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. | |||||

Content | The 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. | |||||

Prerequisites / Notice | The contents of the following ETH Bachelor lectures or equivalent are assumed to be known: Mechanics and Dynamics, Control, Basics in Fluid Dynamics. | |||||

Robotics (continued) Only one of the two course units 263-5902-00L Computer Vision resp. 227-0447-00L Image Analysis and Computer Vision may be recognised for credits. More precisely, it is also not allowed to have recognised one course unit for the Bachelor's and the other course unit for the Master's degree. The same restriction applied to the two course units 263-5210-00L Probabilistic Artificial Intelligence resp. 252-0535-00L Advanced Machine Learning For the category assignment take contact with the Study Administration (www.math.ethz.ch/studiensekretariat). | ||||||

Number | Title | Type | ECTS | Hours | Lecturers | |

263-5902-00L | Computer Vision | W | 8 credits | 3V + 1U + 3A | M. Pollefeys, S. Tang, F. Yu | |

Abstract | The 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. | |||||

Objective | The 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. | |||||

Content | Camera 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 | |||||

Prerequisites / Notice | It is recommended that students have taken the Visual Computing lecture or a similar course introducing basic image processing concepts before taking this course. | |||||

263-5210-00L | Probabilistic Artificial Intelligence | W | 8 credits | 3V + 2U + 2A | A. Krause | |

Abstract | This 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. | |||||

Objective | How 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. | |||||

Content | Topics 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 | |||||

Prerequisites / Notice | Solid basic knowledge in statistics, algorithms and programming. The material covered in the course "Introduction to Machine Learning" is considered as a prerequisite. | |||||

Physics | ||||||

Number | Title | Type | ECTS | Hours | Lecturers | |

402-0809-00L | Introduction to Computational Physics | W | 8 credits | 2V + 2U | A. Adelmann | |

Abstract | This course offers an introduction to computer simulation methods for physics problems and their implementation on PCs and super computers. The covered topics include classical equations of motion, partial differential equations (wave equation, diffusion equation, Maxwell's equations), Monte Carlo simulations, percolation, phase transitions, and N-Body problems. | |||||

Objective | Students learn to apply the following methods: Random number generators, Determination of percolation critical exponents, numerical solution of problems from classical mechanics and electrodynamics, canonical Monte-Carlo simulations to numerically analyze magnetic systems. Students also learn how to implement their own numerical frameworks in Julia and how to use existing libraries to solve physical problems. In addition, students learn to distinguish between different numerical methods to apply them to solve a given physical problem. | |||||

Content | Introduction to computer simulation methods for physics problems. Models from classical mechanics, electrodynamics and statistical mechanics as well as some interdisciplinary applications are used to introduce modern programming methods for numerical simulations using Julia. Furthermore, an overview of existing software libraries for numerical simulations is presented. | |||||

Lecture notes | Lecture notes and slides are available online and will be distributed if desired. | |||||

Literature | Literature recommendations and references are included in the lecture notes. | |||||

Prerequisites / Notice | Lecture and exercise lessons in english, exams in German or in English | |||||

Computational Finance | ||||||

Number | Title | Type | ECTS | Hours | Lecturers | |

401-3913-01L | Mathematical Foundations for Finance | W | 4 credits | 3V + 2U | B. Acciaio | |

Abstract | First introduction to main modelling ideas and mathematical tools from mathematical finance | |||||

Objective | This 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. | |||||

Content | Topics 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 | |||||

Lecture notes | Lecture notes will be sold at the beginning of the course. | |||||

Literature | Lecture notes will be sold at the beginning of the course. Additional (background) references are given there. | |||||

Prerequisites / Notice | Prerequisites: 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. | |||||

401-4657-00L | Numerical Analysis of Stochastic Ordinary Differential Equations Alternative course title: "Computational Methods for Quantitative Finance: Monte Carlo and Sampling Methods" | W | 6 credits | 3V + 1U | A. Stein | |

Abstract | Course 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. | |||||

Objective | The 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. | |||||

Content | Generation 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 | |||||

Lecture notes | There will be English, typed lecture notes for registered participants in the course. | |||||

Literature | P. 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. | |||||

Prerequisites / Notice | Prerequisites: 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 | ||||||

Number | Title | Type | ECTS | Hours | Lecturers | |

227-2037-00L | Physical Modelling and Simulation | W | 6 credits | 4G | J. Smajic | |

Abstract | This 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. | |||||

Objective | Basic 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. | |||||

Content | The 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. | |||||

Geophysics Recommended combinations: Subject 1 + Subject 2 Subject 1 + Subject 3 Subject 2 + Subject 3 Subject 3 + Subject 4 Subject 5 + Subject 6 + Subject 8 Subject 4 + Subject 5 Subject 7 + Subject 8 | ||||||

Geophysics: Subject 1 | ||||||

Number | Title | Type | ECTS | Hours | Lecturers | |

651-4007-00L | Continuum Mechanics | W | 3 credits | 2V | T. Gerya | |

Abstract | In 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. | |||||

Objective | The 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. | |||||

Content | A 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). | |||||

Lecture notes | Script and Exam questions are available by request tgerya@ethz.ch | |||||

Literature | Taras Gerya Introduction to Numerical Geodynamic Modelling. Second Edition. Cambridge University Press, 2019 |

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