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:
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.
- Introduction to and classification of problems involving ordinary and partial differential equations,
- Relaxation and growth models,
- Diffusion (parabolic),
- Wave phenomena (hyperbolic),
- Equilibrium problems (elliptic).
- As intermezzos: Complex numbers and Von Neumann stability
- ..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”.