Mathematical Modelling with Ordinary and Partial Differential Equations
Learning goals with assessment weighting:
- Problem formulation, problem solving, and scientific exposition will be assessed in the form of assignments to be submitted to the instructor (30%).
- Theory and analytical skills will be tested with midterm (30%) and final (40%) exams.
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Description
The course is an introduction to mathematical modelling with ordinary and partial differential equations.
Mathematical modelling techniques are introduced in the context of applications. Non-dimensionalization and scaling facilitate the normalization of differential equation models and the identification of a minimal set of parameters. Perturbation methods allow us to obtain approximate solutions or to construct approximate models in the presence of a small parameter. We introduce two classes of ODE models: reaction kinetic equations prominent in chemistry, population dynamics and epidemiology; and molecular models as encountered in chemistry, astronomy and mechanical systems. Variational methods offer an elegant means of identifying conservation laws and treating mechanical contraints. Diffusion provides a natural bridge between ODE and PDE models. We introduce continuum models and conservation laws, and introduce reaction-diffusion equations. By studying traffic models, we introduce hyperbolic conservation laws and shock wave propagation. Finally we turn to materials, where we discuss the models of solid and fluid mechanics and wave propagation.
Format:
Lectures and work sessions
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