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term (s): 2
Status for math students:
commitment: 10 x 3 hours lectures + 9 x 1 hour support classes
Rating: course work (100%). Part of this course work requires some programming. These orders can be completed with either Matlab or Python. Support in the form of solution templates is only provided for MATLAB.
Requirements: MA133 Differential equations and MA124 math with the computer (or equivalent)
Mathematics not only arises nature, but also in social structures. A fundamental idea is that of mathematical modeling, in which natural issues are transformed into mathematical problems. Two types of mathematical models are (i) those resulting from the application of physical laws, and (ii) resulting from the analysis of data. In this module, we expose some basic aspects of mathematical modeling with normal differential equations. For example, fundamental principles in science such as conservation laws and force balances lead to initial value problems. These principles can also be extended in epidemiology to model the transmission of diseases.
Mathematical models are generally too complex to explicitly solve, so that approximation methods and calculation are essential tools. Therefore, this module also examines various methods for approximating the solution to Odes. Of particular interest and value are their mathematical properties, especially in compliance with the properties of the underlying model.
- demonstration of fundamental principles in deriving models (reaction kinetics and Hamiltonian principle as well as basic role of dimensional analysis theory for simplicity of complex models
approximation by discretization (runge-kutta and multistep) and the tools needed for analysis
- Analysis of discretization (stability and convergence)
- Examples of using these tools in applications.
At the end of the module, the student should be able to be:
- understand the central concepts of mathematical modeling
- derive fundamental numeric methods and analyze
- Implement and test numeric methods with a scripting language
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