CBE Interdisciplinary Glossary

Example of a differential equation:

Let x(t) denote the concentration of a chemical in a compartment (e.g. continuous flow reactor). The so-called "first order elimination" of the chemical from the compartment means that the rate of elimination is proportional to the concentration. The corresponding differential equation is dx/dt=-kx', where k is a constant.

Mathematics

BOUNDARY CONDITIONS Requirements imposed on a dynamic model that describe how the external world acts on the real system under study:

Let B(t), where t denotes time and/or space, denote the set of all functions that satisfy the specified boundary conditions. Then any solution s(t) to the model equations must be a member of B(t).

DERIVATIVE The instantaneous rate of change of one variable with respect to another.

Example: Let x(t) denote the position (distance in meters) of a moving particle at time t (seconds). Then the derivative of position with respect to time, dx(t)/dt, is the velocity (meters per second) at time t.

DIFFERENTIAL EQUATION Any equation which has derivatives in it. Often used by engineers and scientists to represent models in the language of mathematics. (See example at left.)

INITIAL CONDITIONS The spatial profile s(to) of the output at time to, the initial time point; information required in order to use a dynamic model to calculate future behavior.

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Terms & Concepts by Discipline

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