401-0373-00L Mathematics III: Partial Differential Equations
Semester | Autumn Semester 2016 |
Lecturers | F. Da Lio |
Periodicity | yearly recurring course |
Language of instruction | English |
Courses
Number | Title | Hours | Lecturers | |||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
401-0373-00 V | Mathematics III: Partial Differential Equations | 2 hrs |
| F. Da Lio | ||||||||||||
401-0373-00 U | Mathematics III: Partial Differential Equations | 1 hrs |
| F. Da Lio |
Catalogue data
Abstract | Examples of partial differential equations. Linear partial differential equations. Introduction to Separation of Variables method. Fourier Series, Fourier Transform, Laplace Transform and applications to the resolution to some partial differential equations (Laplace Equation, Heat Equation, Wave Equation). |
Objective | The main objective is that the students get a basic knowledge of the classical tools to solve explicitly linear partial differential equations. |
Content | ## Examples of partial differential equations - Classification of PDEs - Superposition principle ## One-dimensional wave equation - D'Alembert's formula - Duhamel's principle ## Fourier series - Representation of piecewise continuous functions via Fourier series - Examples and applications ## Separation of variables - Resolution of wave and heat equation - Homogeneous and inhomogeneous boundary conditions, Dirichlet and Neumann boundary conditions ## Laplace equation - Resolution of the Laplace equation on rectangle, disk and annulus - Poisson formula - Mean value theorem and maximum principle ## Fourier transform - Derivation and Definition - Inverse Fourier transformation and inversion formula - Interpretation and properties of the Fourier transform - Resolution of the heat equation ## Laplace transform - Definition, motivation and properties - Inverse Laplace transform of rational functions - Application to ordinary differential equations |
Lecture notes | There are available some Lecture Notes in English and also in German of the Professor. These can be found following the links provided under the tab 'Lernmaterialien'. |
Literature | 1) N. Hungerbühler, Einführung in partielle Differentialgleichungen für Ingenieure, Chemiker und Naturwissenschaftler, vdf Hochschulverlag, 1997. 2) Y. Pinchover and J. Rubinstein, An Introduction to Partial Differential Equations, Cambridge University Press 3) E. Kreyszig, Advanced Engineering Mathematics, John Wiley & Sons (only Chapters 1,2,6,11) 4) T. Westermann: Partielle Differentialgleichungen, Mathematik für Ingenieure mit Maple, Springer-Lehrbuch 1997. |
Prerequisites / Notice | It is required a minimal background of: 1) multivariables functions (Riemann integrals in two or three variables, change of variables in the integrals through the Jacobian, partial derivatives, differentiability, Jacobian) 2) numerical and functional sequences and series, 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 Chemistry 2005; Version 27.03.2018 (Examination Block I) Bachelor's Degree Programme in Interdisciplinary Sciences 2010; Version 27.03.2018 (Examination Block) |
ECTS credits | 4 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 |
Additional information on mode of examination | The exam is offered in English and in German. / Die Prüfung wird auf Deutsch und auf Englisch angeboten. |
Written aids | 20 A4 pages summary and formulary. No pocket calculator. / 20 A4-Seiten Zusammenfassung und Formelsammlung. 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
Additional links | Link zur Homepage Mathematik III von F. Da Lio mit Skripten und Literatur |
Only public learning materials are listed. |
Groups
No information on groups available. |
Restrictions
There are no additional restrictions for the registration. |