401-0363-10L Analysis III
| Semester | Autumn Semester 2019 |
| Lecturers | F. Da Lio |
| Periodicity | yearly recurring course |
| Language of instruction | English |
Courses
| Number | Title | Hours | Lecturers | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| 401-0363-10 V | Analysis III Lectures in HG F 7 with video transmission in HG F 5. Starts in the second week of the semester. | 2 hrs |
| F. Da Lio | ||||||
| 401-0363-10 U | Analysis III Groups are selected in myStudies. Many of the exercise classes are offered in German. Zusätzlich wird das Study Center angeboten: Montag 16-18 ab der 3. Semesterwoche im ML H 41.1, wo die Möglichkeit des betreuten Lernens angeboten wird. Im Study Center können Studierende Vorlesungsstoff vor- oder nachbereiten und Übungen lösen. | 1 hrs | F. Da Lio |
Catalogue data
| Abstract | Introduction to partial differential equations. Differential equations which are important in applications are classified and solved. Elliptic, parabolic and hyperbolic differential equations are treated. The following mathematical tools are introduced: Laplace transforms, Fourier series, separation of variables, methods of characteristics. |
| Objective | Mathematical treatment of problems in science and engineering. To understand the properties of the different types of partial differential equations. |
| Content | Laplace Transforms: - Laplace Transform, Inverse Laplace Transform, Linearity, s-Shifting - Transforms of Derivatives and Integrals, ODEs - Unit Step Function, t-Shifting - Short Impulses, Dirac's Delta Function, Partial Fractions - Convolution, Integral Equations - Differentiation and Integration of Transforms Fourier Series, Integrals and Transforms: - Fourier Series - Functions of Any Period p=2L - Even and Odd Functions, Half-Range Expansions - Forced Oscillations - Approximation by Trigonometric Polynomials - Fourier Integral - Fourier Cosine and Sine Transform Partial Differential Equations: - Basic Concepts - Modeling: Vibrating String, Wave Equation - Solution by separation of variables; use of Fourier series - D'Alembert Solution of Wave Equation, Characteristics - Heat Equation: Solution by Fourier Series - Heat Equation: Solutions by Fourier Integrals and Transforms - Modeling Membrane: Two Dimensional Wave Equation - Laplacian in Polar Coordinates: Circular Membrane, Fourier-Bessel Series - Solution of PDEs by Laplace Transform |
| Lecture notes | Lecture notes by Prof. Dr. Alessandra Iozzi: https://polybox.ethz.ch/index.php/s/D3K0TayQXvfpCAA |
| Literature | E. Kreyszig, Advanced Engineering Mathematics, John Wiley & Sons, 10. Auflage, 2011 C. R. Wylie & L. Barrett, Advanced Engineering Mathematics, McGraw-Hill, 6th ed. S.J. Farlow, Partial Differential Equations for Scientists and Engineers, Dover Books on Mathematics, NY. G. Felder, Partielle Differenzialgleichungen für Ingenieurinnen und Ingenieure, hypertextuelle Notizen zur Vorlesung Analysis III im WS 2002/2003. Y. Pinchover, J. Rubinstein, An Introduction to Partial Differential Equations, Cambridge University Press, 2005 For reference/complement of the Analysis I/II courses: Christian Blatter: Ingenieur-Analysis https://people.math.ethz.ch/~blatter/dlp.html |
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 Materials Science 2017; Version 28.01.2020 (Examination Block 2) Bachelor's Degree Programme in Mechanical Engineering 2010; Version 24.02.2022 (Examination Block 1) Bachelor's Programme in Materials Science 2015; Version 22.08.2017 (Examination Block 2) |
| ECTS credits | 3 credits |
| Examiners | F. Da Lio |
| Type | session examination |
| Language of examination | English |
| Repetition | The performance assessment is offered every session. Repetition possible without re-enrolling for the course unit. |
| Mode of examination | written 120 minutes |
| Written aids | 20 pages (=10 sheets) DIN A4 handwritten or typed personal summary. English <-> German dictionary. No further aids (in particular, no pocket calculator). |
| 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 | Web-page at metaphor |
| Additional links | Class Content |
| Only public learning materials are listed. | |
Groups
| 401-0363-10 U | Analysis III | ||||||
| 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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| G-09 |
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| G-10 |
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| G-11 |
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| G-12 |
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| G-13 |
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| G-14 |
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| G-15 |
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| G-16NOP | |||||||
| G-17NOP | |||||||
Restrictions
| There are no additional restrictions for the registration. |
Offered in
| Programme | Section | Type | |
|---|---|---|---|
| Mechanical Engineering Bachelor | Examination Block 1 | O |  |
| Materials Science Bachelor | Examination Block 2 | O | |