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Differential Equations - Preliminaries

In: Applied Calculus with R

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  • Thomas J. Pfaff

    (Ithaca College, Department of Mathematics)

Abstract

A differential equation is an equation involving a function or functions and their derivatives. Differential equations are used to model real world phenomenon. Before analyzing various differential equation models we have some preliminary work to do. In building differential equation we will use the language of variables beginning proportional. In analyzing differential equation we will use a for loop in R. We cover both of these concepts in this chapter. First is M-Box which translates the statement x is proportional to y into the equation $$x=ky$$ x = k y for some constant k. This will be helpful in translating statements about real world situation into differential equations to analyze. Note that there is not anything particularly special about using k as the constant. Other letters can be used especially if they make more sense in context, such as say r if the context is related to a growth rate.

Suggested Citation

  • Thomas J. Pfaff, 2023. "Differential Equations - Preliminaries," Springer Books, in: Applied Calculus with R, chapter 0, pages 271-275, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-28571-4_23
    DOI: 10.1007/978-3-031-28571-4_23
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