Course in Differential Equations with Modeling Applications
This course teaches differential equations via practical river pollution modelling, linking ODEs and PDEs for transport and decay. Learners will interpret parameters, evaluate models, and deliver clear insights for environmental and engineering decisions, building essential skills for real-world applications.
flexible workload of 4 to 360h
valid certificate in your country
What will I learn?
Gain hands-on skills in differential equations to model pollutant transport and decay in rivers. Derive ODE and PDE models using mass balance principles, solve advection-decay equations, examine steady states, and contrast compartment versus distributed models. Master handling units, parameter estimation, model limitations, and communicating risks effectively to non-experts.
Elevify advantages
Develop skills
- Develop mass-balance ODE models by converting inflow, outflow, and decay into dC/dt equations.
- Solve advection-decay PDEs using the method of characteristics for efficient river simulations.
- Compare ODE and PDE models to assess mixing assumptions and select appropriate approaches.
- Estimate and scale parameters like velocity, area, decay rate, flow, residence times, and safety thresholds.
- Communicate environmental risks simply by transforming model outputs into public advisories.
Suggested summary
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