MATH213 Lecture : MATH 213 Spring 2014 First Week Course Notes
9 May 2014
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Di erential equations are equations involving derivatives with respect to some indepen- dant variable. In the classical approach, we suppose f is given as a function of time, and we solve for the dependant variable with respect to the independant one. The systems approach has less of an emphasis on the response to a speci c input and deals more with the overall relationships between the function and between the individual dependant variables. The population of an organism (given abundant resources) or the growth of an economy (if the economy were to grow at a constant percentage rate) can be modelled as: Given that this function assumes that the population growth is not limited by resources, etc. , it is not very useful in the real world. More likely, we would nd for large populations. 2 a limit of some sort must be included. For example, the logistic equation is modelled as:
