Time-scale calculus

<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, time-scale calculus is a unification of the theory of <a href="/facts/Difference_equation/JolXC71M">difference equations</a> with that of <a href="/facts/Differential_equation/9MGbE3Ca">differential equations</a>, unifying <a href="/facts/Integral/4PeM0mJc">integral</a> and <a href="/facts/Differential_calculus/uU1AAc4N">differential calculus</a> with the <a href="/facts/Calculus_of_finite_differences/aY1txFhj">calculus of finite differences</a>, offering a formalism for studying <a href="/facts/Hybrid_system/wk7Dfdup">hybrid systems</a>.  It has applications in any field that requires simultaneous modelling of <a href="/facts/Discrete_time_and_continuous_time/RR8wpS9e">discrete and continuous</a> data. It gives a new definition of a <a href="/facts/Derivative/7Ito70Dh">derivative</a> such that if one differentiates a function defined on the <a href="/facts/Real_number/R02gw5Pb">real numbers</a> then the definition is equivalent to standard differentiation, but if one uses a function defined on the <a href="/facts/Integer/PUwwrawx">integers</a> then it is equivalent to the <a href="/facts/Forward_difference/aY1txFhj">forward difference</a> operator.
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Time-scale calculus open-in-new

Time-scale calculus