Preliminary Course.
Applied mathematics
In this applied mathematics sub-chapter, two different sections are presented:
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Notions in probabilities
Parameter estimation (for dynamic systems)
The objectives of these sections are practical and oriented to the development of plant growth models and their application in confrontation with experimental data.
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Notion in probabilities are introduced in order to be able to build a stochastic growth model of the plant organogenesis.
Parameter functions are more related to plant functioning, such as organ sink functions and modelling of photosynthesis.
Parameter estimation is oriented to the identification of some hidden parameters of the model.
Course content map
Applied Mathematics Sub-Chapter
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Definitions
Expected value and Variance
A few properties
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Bernoulli Process
Binomial Distribution
Geometrical Distribution
Negative binomial Distribution
Parameter estimation of dynamic systems
Some useful parametric functions
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Growth Functions
Beta density function
Negative exponential function
- A definition of dynamic systems: a little bit of systems theory
Mathematical definition of discrete dynamic systems
Parameter estimation using the generalized least squares method
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Identification of dynamic systems: definitions, exercise
Parameter estimation. Exercise.