Search result: Catalogue data in Autumn Semester 2017
|Computational Science and Engineering Bachelor|
|401-0353-00L||Analysis III||O||4 credits||2V + 1U||A. Figalli|
|Abstract||In this lecture we treat problems in applied analysis. The focus lies on the simplest cases of three fundamental types of partial differential equations of second order: the Laplace equation, the heat equation and the wave equation.|
|Content||1.) Klassifizierung von PDE's|
- linear, quasilinear, nicht-linear
- elliptisch, parabolisch, hyperbolisch
2.) Quasilineare PDE
- Methode der Charakteristiken (Beispiele)
3.) Elliptische PDE
- Bsp: Laplace-Gleichung
- Harmonische Funktionen, Maximumsprinzip, Mittelwerts-Formel.
- Methode der Variablenseparation.
4.) Parabolische PDE
- Bsp: Wärmeleitungsgleichung
- Bsp: Inverse Wärmeleitungsgleichung
- Methode der Variablenseparation
5.) Hyperbolische PDE
- Bsp: Wellengleichung
- Formel von d'Alembert in (1+1)-Dimensionen
- Methode der Variablenseparation
6.) Green'sche Funktionen
- Rechnen mit der Dirac-Deltafunktion
- Idee der Green'schen Funktionen (Beispiele)
7.) Ausblick auf numerische Methoden
- 5-Punkt-Diskretisierung des Laplace-Operators (Beispiele)
|Literature||Y. Pinchover, J. Rubinstein, "An Introduction to Partial Differential Equations", Cambridge University Press (12. Mai 2005)|
Erwin Kreyszig, "Advanced Engineering Mathematics", John Wiley & Sons, Kap. 8, 11, 16 (sehr gutes Buch, als Referenz zu benutzen)
Norbert Hungerbühler, "Einführung in die partiellen Differentialgleichungen", vdf Hochschulverlag AG an der ETH Zürich.
G. Felder:Partielle Differenzialgleichungen.
|Prerequisites / Notice||Prerequisites: Analysis I and II, Fourier series (Komplexe Analysis)|
|402-0811-00L||Programming Techniques for Scientific Simulations I||O||5 credits||4G||R. Käppeli|
|Abstract||This lecture provides an overview of programming techniques for scientific simulations. The focus is on advances C++ programming techniques and scientific software libraries. Based on an overview over the hardware components of PCs and supercomputer, optimization methods for scientific simulation codes are explained.|
|401-0663-00L||Numerical Methods for CSE||O||7 credits||4V + 2U||R. Alaifari|
|Abstract||The course gives an introduction into fundamental techniques and algorithms of numerical mathematics which play a central role in numerical simulations in science and technology. The course focuses on fundamental ideas and algorithmic aspects of numerical methods. The exercises involve actual implementation of numerical methods in C++.|
|Objective||* Knowledge of the fundamental algorithms in numerical mathematics|
* Knowledge of the essential terms in numerical mathematics and the
techniques used for the analysis of numerical algorithms
* Ability to choose the appropriate numerical method for concrete problems
* Ability to interpret numerical results
* Ability to implement numerical algorithms afficiently
|Content||1. Direct Methods for linear systems of equations|
2. Least Squares Techniques
3. Data Interpolation and Fitting
4. Filtering Algorithms
8. Approximation of Functions
9. Numerical Quadrature
10. Iterative Methods for non-linear systems of equations
11. Single Step Methods for ODEs
12. Stiff Integrators
|Lecture notes||Lecture materials (PDF documents and codes) will be made available to the participants through the course web page:|
|Literature||U. ASCHER AND C. GREIF, A First Course in Numerical Methods, SIAM, Philadelphia, 2011.|
A. QUARTERONI, R. SACCO, AND F. SALERI, Numerical mathematics, vol. 37 of Texts in Applied Mathematics, Springer, New York, 2000.
W. Dahmen, A. Reusken "Numerik für Ingenieure und Naturwissenschaftler", Springer 2006.
M. Hanke-Bourgeois "Grundlagen der Numerischen Mathematik und des wissenschaftlichen Rechnens", BG Teubner, 2002
P. Deuflhard and A. Hohmann, "Numerische Mathematik I", DeGruyter, 2002
|Prerequisites / Notice||The course will be accompanied by programming exercises in C++ relying on the template library EIGEN. Familiarity with C++, object oriented and generic programming is an advantage. Participants of the course are expected to learn C++ by themselves.|
|401-0603-00L||Stochastics (Probability and Statistics)||O||4 credits||2V + 1U||M. Schweizer|
|Abstract||This class covers the following concepts: random variables, probability, discrete and continuous distributions, joint and conditional probabilities and distributions, the law of large numbers, the central limit theorem, descriptive statistics, statistical inference, inference for normally distributed data, point estimation, and two-sample tests.|
|Objective||Knowledge of the basic principles of probability and statistics.|
|Content||Introduction to probability theory, some basic principles from mathematical statistics and basic methods for applied statistics.|
|Lecture notes||Lecture notes|
|252-0834-00L||Information Systems for Engineers||O||4 credits||2V + 1U||G. Fourny|
|Abstract||This course provides the basics of information systems from the perspective of the user. The main focus is on relational databases, including tabular data, the relational algebra, the SQL query language, schema design, normal forms, physical architecture, indices. The course also covers support for data cubes on top of relational databases.|
|Objective||After visiting this course, students should be capable to:|
1. Explain, in the big picture, how a relational database works and what it can do in their own words.
2. Explain the relational data model (tables, rows, attributes, primary keys, foreign keys), formally and informally, including the relational algebra operators (select, project, rename, all kinds of joins, division, cartesian product, union, intersection, etc).
3. Perform non-trivial reading SQL queries on existing relational databases, as well as insert new data, update and delete existing data.
4. Design a new relational schema to store data in accordance to the real world's constraints, such as relationship cardinality.
5. Adapt and improve an existing schema to make it more robust against anomalies, thanks to a very good theoretical knowledge of normal forms.
6. Understand how indices work (hash indices, B-trees), how they are implemented, and how to use them to make queries faster.
7. Access an existing relational database from a host language such as Java, using bridges such as JDBC.
8. Explain data independence.
9. Explain how a relational database is physically implemented.
10. Know and deal with the natural syntax for relational data, CSV.
11. Explain the data cube model including slicing and dicing.
12. Store data cubes in a relational database.
13. Map cube queries to SQL.
14. Slice and dice cubes in a UI.
|Content||Using a relational database|
1. Introduction (historical overview, data independence, data shapes)
2. The relational model (data models, tables, relational algebra, CSV syntax)
3. The query language SQL (DML 1 of 2, SQL shell, counterpart of selection, projection, grouping, ordering, renaming)
4. Schema definitions (DDL, data types, SQL)
5. Updates (DML 2 of 2, insertion, deletion, updates, SQL)
Taking a relational database to the next level
6. Best practices and normal forms (update/insert/delete anomalies, first, second, third, BC, fourth)
7. Physical architecture of a relational database (storage levels, tuple storage)
8. Indices and optimization (ISAM, B-tree, B+-tree, hash)
9. Communicating with a SQL database from a host language (Java, JDBC)
Analytics on top of a relational database
10. Analytics, data warehousing, OLAP vs. OLTP, the data cube model (dimensions, algebra)
11. Storing and querying data cubes in a relational database (star schema, snowflake schema)
12. Data cube optimization (indices, bitmaps)
13. Limits of tables and cubes (decision points for when and when not to use them vs. trees, graphs)
14. Limits of scaling up a single machine and transition to Big Data (introduction to data denormalization on simple cases, "hacking" a relational database onto several machines and issues)
|Literature||- Lecture material (slides).|
- Book: "Database Systems: The Complete Book", H. Garcia-Molina, J.D. Ullman, J. Widom
(It is not required to buy the book, as the library has it)
|Prerequisites / Notice||For non-CS/DS students only, BSc and MSc|
Elementary knowledge of set theory and logics
Knowledge as well as basic experience with a programming language such as Pascal, C, C++, Java, Haskell, Python
|401-0647-00L||Introduction to Mathematical Optimization||O||5 credits||2V + 1U||D. Adjiashvili|
|Abstract||Introduction to basic techniques and problems in mathematical optimization, and their applications to a variety of problems in engineering.|
|Objective||The goal of the course is to obtain a good understanding of some of the most fundamental mathematical optimization techniques used to solve linear programs and basic combinatorial optimization problems. The students will also practice applying the learned models to problems in engineering.|
|Content||Topics covered in this course include:|
- Linear programming (simplex method, duality theory, shadow prices, ...).
- Basic combinatorial optimization problems (spanning trees, shortest paths, network flows, ...).
- Modelling with mathematical optimization: applications of mathematical programming in engineering.
|Literature||Information about relevant literature will be given in the lecture.|
|Prerequisites / Notice||This course is meant for students who did not already attend the course "Mathematical Optimization", which is a more advance lecture covering similar topics. Compared to "Mathematical Optimization", this course has a stronger focus on modeling and applications.|
| Block G3|
All course units within Block G3 are offered in the spring semester.
| Block G4|
Students that enrol for the second year in the CSE Bachelor Programme and whose first year examination did not involve the subject "Physics I" will instead take the "Physics I and II" (402-0043-00L and 402-0044-00L) courses with performance assessment as a yearly course.
|402-0043-00L||Physics I||W||4 credits||3V + 1U||T. Esslinger|
|Abstract||Introduction to the concepts and tools in physics with the help of demonstration experiments: mechanics of point-like and ridged bodies, periodic motion and mechanical waves.|
|Objective||The concepts and tools in physics, as well as the methods of an experimental science are taught. The student should learn to identify, communicate and solve physical problems in his/her own field of science.|
|Content||Mechanics (motion, Newton's laws, work and energy, conservation of momentum, rotation, gravitation, fluids)|
Periodic Motion and Waves (periodic motion, mechanical waves, acoustics).
|Lecture notes||The lecture follows the book "Physics" by Paul A. Tipler.|
|Literature||Paul A. Tipler and Gene P. Mosca, Physics (for Scientists and Engineers), W. H. Freeman and Company|
|Prerequisites / Notice||Prerequisites: Mathematics I & II|
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