Howard P. 2005. Modeling with ODE. Notes. 48 pp.
Great exposition and lots of Modeling Scenarios almost laid out completely as exercises.
From the text
A wide variety of natural phenomena such as projectile motion, the flow of electric current, and the progression of chemical reactions are well described by equations that relate changing quantities. As the derivative of a function provides the rate at which that function is changing with respect to its independent variable, the equations describing these phenomena often involve one or more derivatives, and we refer to them as differential equations. In these notes we consider three critical aspects in the theory of ordinary differential equations:
1. Developing models of physical phenomena,
2. Determining whether our models are mathematically %5Cwell-posed" (do solutions exist? are these solutions unique? do the solutions we find for our equation genuinely correspond with the phenomenon we are modeling), and
3. Solving ODE numerically with MATLAB.
Keywords: differential equation, model, compartment, stability, population, mechanics, Matlab, first order, numerical methods, variational methods, Hamiltonian mechanics, stability, existence, uniqueness
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