401-0353-00L Analysis 3
| Semester | Autumn Semester 2019 |
| Lecturers | M. Iacobelli |
| Periodicity | yearly recurring course |
| Language of instruction | English |
Courses
| Number | Title | Hours | Lecturers | ||||||||||||||||||||||||||||
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| 401-0353-00 V | Analysis 3 | 2 hrs |
| M. Iacobelli | |||||||||||||||||||||||||||
| 401-0353-00 U | Analysis 3 Groups are selected in myStudies. Exercises start in the second week of the semester. Es wird auch mindestens eine Übungsgruppe auf Deutsch angeboten. | 2 hrs |
| M. Iacobelli |
Catalogue data
| Abstract | In this lecture we treat problems in applied analysis. The focus lies on the solution of quasilinear first order PDEs with the method of characteristics, and on the study of three fundamental types of partial differential equations of second order: the Laplace equation, the heat equation, and the wave equation. |
| Learning objective | The aim of this class is to provide students with a general overview of first and second order PDEs, and teach them how to solve some of these equations using characteristics and/or separation of variables. |
| Content | 1.) General introduction to PDEs and their classification (linear, quasilinear, semilinear, nonlinear / elliptic, parabolic, hyperbolic) 2.) Quasilinear first order PDEs - Solution with the method of characteristics - COnservation laws 3.) Hyperbolic PDEs - wave equation - d'Alembert formula in (1+1)-dimensions - method of separation of variables 4.) Parabolic PDEs - heat equation - maximum principle - method of separation of variables 5.) Elliptic PDEs - Laplace equation - maximum principle - method of separation of variables - variational method |
| Literature | Y. Pinchover, J. Rubinstein, "An Introduction to Partial Differential Equations", Cambridge University Press (12. Mai 2005) |
| Prerequisites / Notice | Prerequisites: Analysis I and II, Fourier series (Complex Analysis) |
Performance assessment
| Performance assessment information (valid until the course unit is held again) | |
Performance assessment as a semester course | |
| In examination block for | Bachelor's Degree Programme in Computational Science and Engineering 2016; Version 27.03.2018 (Examination Block G1) Bachelor's Degree Programme in Computational Science and Engineering 2018; Version 13.12.2022 (Examination Block G1) Bachelor's Degree Programme in Electrical Engineering and Information Technology 2016; Version 31.10.2017 (Examination Block 1) Bachelor's Degree Programme in Electrical Engineering and Information Technology 2017; Version 07.04.2022 (Examination Block 1) Bachelor's Degree Programme in Interdisciplinary Sciences 2010; Version 27.03.2018 (Examination Block) Bachelor's Programme in Computational Science and Engineering 2012; Version 13.12.2016 (Examination Block G1) Bachelor's Programme in Electrical Engineering and Information Technology 2012; Version 24.02.2016 (Examination Block 1) |
| ECTS credits | 4 credits |
| Examiners | M. Iacobelli |
| Type | session examination |
| Language of examination | German |
| Repetition | The performance assessment is offered every session. Repetition possible without re-enrolling for the course unit. |
| Mode of examination | written 180 minutes |
| Additional information on mode of examination | Die Prüfung wird auf Deutsch und Englisch angeboten. The exam will be offered in German and in English. |
| Written aids | -Standard Dictionary -Textbook (Pinchover) either original book, or printed (total or partial) version -Summary of the lectures. At most 4 Pages long (DIN A4 - either 2 sheets two-sided, or 4 sheets one-sided) must be personal & handwritten. Photocopies of summaries, or computer typed summaries are NOT accepted. NOT allowed during exam: -Exercises and solutions from this course (not allowed even as part of the summary). Random checks will be made on the day of the exam. |
| If the course unit is part of an examination block, the credits are allocated for the successful completion of the whole block. This information can be updated until the beginning of the semester; information on the examination timetable is binding. | |
Learning materials
| Main link | Link to website of the course |
| Only public learning materials are listed. | |
Groups
| 401-0353-00 U | Analysis 3 | ||||||
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| Groups | G-01 |
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| G-02 |
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| G-03 |
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| G-04 |
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| G-05 |
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| G-06 |
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| G-07 |
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| G-08 |
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Restrictions
| There are no additional restrictions for the registration. |
