401-0373-00L Mathematics III: Partial Differential Equations
| Semester | Autumn Semester 2019 |
| Lecturers | T. Ilmanen, C. Busch |
| Periodicity | yearly recurring course |
| Language of instruction | English |
Courses
| Number | Title | Hours | Lecturers | |||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 401-0373-00 V | Mathematics III: Partial Differential Equations | 2 hrs |
| T. Ilmanen, C. Busch | ||||||||||||
| 401-0373-00 U | Mathematics III: Partial Differential Equations Groups are selected in myStudies. Exercises Thu 9-10 (alternatively Thu 12-13) | 1 hrs |
| T. Ilmanen, C. Busch |
Catalogue data
| Abstract | Examples of partial differential equations. Linear partial differential equations. Separation of variables. Fourier series, Fourier transform, Laplace transform. Applications to solving commonly encountered linear partial differential equations (Laplace's Equation, Heat Equation, Wave Equation). |
| Objective | Classical tools to solve the most common linear partial differential equations. |
| Content | 1) Examples of partial differential equations - Classification of PDEs - Superposition principle 2) One-dimensional wave equation - D'Alembert's formula - Duhamel's principle 3) Fourier series - Representation of piecewise continuous functions via Fourier series - Examples and applications 4) Separation of variables - Solution of wave and heat equation - Homogeneous and inhomogeneous boundary conditions - Dirichlet and Neumann boundary conditions 5) Laplace equation - Solution of Laplace's equation on the rectangle, disk and annulus - Poisson formula - Mean value theorem and maximum principle 6) Fourier transform - Derivation and definition - Inverse Fourier transformation and inversion formula - Interpretation and properties of the Fourier transform - Solution of the heat equation 7) Laplace transform (if time allows) - Definition, motivation and properties - Inverse Laplace transform of rational functions - Application to ordinary differential equations |
| Lecture notes | See the course web site (linked under Lernmaterialien) |
| Literature | 1) S.J. Farlow, Partial Differential Equations for Scientists and Engineers, Dover Books on Mathematics, NY. 2) N. Hungerbühler, Einführung in partielle Differentialgleichungen für Ingenieure, Chemiker und Naturwissenschaftler, vdf Hochschulverlag, 1997. Additional books: 3) T. Westermann: Partielle Differentialgleichungen, Mathematik für Ingenieure mit Maple, Band 2, Springer-Lehrbuch, 1997 (chapters XIII,XIV,XV,XII) 4) E. Kreyszig, Advanced Engineering Mathematics, John Wiley & Sons (chapters 1,2,11,12,6) For additional sources, see the course web site (linked under Lernmaterialien) |
| Prerequisites / Notice | Required background: 1) Multivariate functions: partial derivatives, differentiability, Jacobian matrix, Jacobian determinant 2) Multiple integrals: Riemann integrals in two or three variables, change of variables 2) Sequences and series of numbers and of functions 3) Basic knowledge of ordinary differential equations |
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 Chemical Engineering 2006; Version 27.03.2018 (Examination Block I) Bachelor's Degree Programme in Chemical Engineering 2018; Version 26.09.2022 (Examination Block I) Bachelor's Degree Programme in Chemistry 2005; Version 27.03.2018 (Examination Block I) Bachelor's Degree Programme in Chemistry 2018; Version 26.09.2022 (Examination Block I) Bachelor's Degree Programme in Interdisciplinary Sciences 2010; Version 27.03.2018 (Examination Block) Bachelor's Degree Programme in Interdisciplinary Sciences 2018; Version 12.07.2022 (Examination Block) |
| ECTS credits | 4 credits |
| Examiners | T. Ilmanen, C. Busch |
| 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 |
| Additional information on mode of examination | The exam will actually be offered in both English and German. / Die Prüfung wird sowohl auf Deutsch als auch auf Englisch angeboten. |
| Written aids | 10 A4 pages summary in your own handwriting (or 5 A4 pages on both sides)..No pocket calculator. / 10 A4-Seiten Zusammenfassung in eigener Handschrift (oder 5 A4-Blätter beidseitig). Kein Taschenrechner. |
| 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 | Information |
| Only public learning materials are listed. | |
Groups
| 401-0373-00 U | Mathematics III: Partial Differential Equations | ||||||
| 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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Restrictions
| There are no additional restrictions for the registration. |
