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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) Fourier transform - Derivation and definition - Inverse Fourier transformation - Interpretation and properties of the Fourier transform - Solution of the heat equation 6) Laplace transform - Definition, motivation and properties - Inverse Laplace transform - Application to ordinary differential equations 7) Further topics...
Resources
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)
General Information
- Language
- German
- Levels
- BSC
- Frequency
- Yearly recurring
Examination
- Type
- session examination
- Mode
- written 120 minutes
- Aids
- 2 A4-Seiten handgeschriebene Notizen.Kein Taschenrechner.
- Digital
- The examination takes place on your own device. Installation of SEB required.
Course Components
| Type | Title | Time & Place | Hours |
|---|---|---|---|
| lecture | Mathematik III: Partielle Differentialgleichungen | No time listed | 2 h weekly |
| exercise | Mathematik III: Partielle Differentialgleichungen | No time listed | 1 h weekly |