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Differential Equations

In: Calculator Calculus

Author

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  • George McCarty

    (University of California)

Abstract

Applications of the calculus depend on interpretations of the derivative, such as the slope of a graph, a velocity or an acceleration, marginal profit or cost or revenue, a rate of growth or of decay. For example, acceleration is the derivative of speed for a moving vehicle. Thus if the acceleration of an object is known to be constantly 7, then its speed s(t) as a function of time satisfies the equation s’(t) = 7. This is called a differential equation: it is an equation involving the derivative of a function. The solution to this equation is not a number; it is the function s(t) = 7t + C, where 7 is the constant acceleration and C is the number s(0), the value of the speed at the time coordinate 0. In general, in differential equations the unknowns do not stand for numbers but for functions, and the solutions are functions.

Suggested Citation

  • George McCarty, 1982. "Differential Equations," Springer Books, in: Calculator Calculus, chapter 14, pages 202-219, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4684-6484-9_14
    DOI: 10.1007/978-1-4684-6484-9_14
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