After successfully completing this course, the student is able to:
- Recognize (water-related) differential problems and classify their elementary mathematical properties (such as ODE/PDE, linear/nonlinear, order, well-posedness, dimensions)
- Derive, analyze, solve differential problems involving ODEs (ordinary differential equations describing relaxation and oscillation phenomena) using analytical techniques and to interpret the outcomes
- Derive, analyze, solve differential problems involving linear PDEs (partial differential equations describing advection, diffusion and wave phenomena) using analytical techniques and to interpret the outcomes
- To derive numerical finite difference schemes of differential problems and to analyze their fundamental properties (consistency, stability, accuracy, convergence)
- Recognize nonlinear differential problems and, in simple cases, to derive and interpret their solution analytically
|
|
This course deals with the aspects of mathematical physics that are commonly encountered in Water Engineering (and Management), and provides the essential mathematical background needed to conduct process-based modelling studies, e.g. of water-related problems. This is of value in both engineering consultancy and academic research. This course follows the four steps of mathematical physics problem formulation, pre-analysis, solution (analytically and numerically) and interpretation.
The main topics covered in this course are:
- Introduction to and classification of problems involving ordinary and partial differential equations,
- Relaxation and growth models,
- Oscillations,
- Advection,
- Diffusion (parabolic),
- Wave phenomena (hyperbolic),
- Equilibrium problems (elliptic).
- As intermezzos: Complex numbers and Von Neumann stability
The course is assessed by means of an individual assignment (weight 10%), a group assignment (30%) and a written exam (60%). For the written exam, a grade restriction (grade should be 5.0 or higher) applies.
Additional info
This course..
- ..provides the mathematical background helpful for the courses “Long Waves and Tidal Dynamics” and “Short Waves and Coastal Dynamics”
- ..through these courses, indirectly prepares also for “Morphology”.
|
 |
|