mathematical physics of water systems
This course provides a foundational understanding of the mathematical physics concepts that underpin process-based modeling in water engineering and management. It equips you with the essential tools to formulate, analyze, and solve mathematical models of physical processes relevant to water systems skills that are critical for both engineering consultancy and academic research.
Structured around the four key steps of mathematical physics: problem formulation, pre-analysis, solution (both analytical and numerical), and interpretation, this course prepares you to work effectively with differential equations commonly encountered in hydrodynamics, environmental modeling, and coastal engineering.
Key Topics Include:
- Classification of differential problems (ODEs and PDEs): linear vs. nonlinear, order, and dimensionality
- Relaxation and growth models
- Oscillatory systems
- Advection and transport processes
- Diffusion (parabolic PDEs)
- Wave phenomena (hyperbolic PDEs)
- Equilibrium problems (elliptic PDEs)
- Supplementary topics: complex numbers and Von Neumann stability analysis
By the end of the course, you will be able to:
- Identify and classify water-related differential equations and assess their mathematical properties (e.g., type, linearity, order, well-posedness)
- Derive, solve, and interpret ordinary differential equations (ODEs) related to relaxation and oscillation phenomena using analytical methods
- Derive, solve, and interpret partial differential equations (PDEs) describing advection, diffusion, and wave dynamics using analytical techniques
- Construct finite difference schemes for solving differential equations and assess their numerical properties, including consistency, stability, accuracy, and convergence
- Recognize nonlinear differential problems and, in simple cases, solve and interpret them analytically
For who? Professionals with at least HBO degree in Civil Engineering
When? 4 February 2026 - 2 April 2026
More in depth information on the course in our online course catalogue Osiris : link to osiris course information
Do you want to register for this course? Find the course registration form here
This course provides the mathematical foundation for more advanced, domain-specific courses such as Long Waves and Tidal Dynamics and Wave-Dominated Coastal Dynamics, and supports preparation for Morphology and related applied modeling courses. Want to see more courses related to this topic? Check out our overview to see which courses might be suitable.
