partial differential equation
1
9.6
- noun
- /ˈpɑːrʧəl ˌdɪfəˈrɛnʃəl ɪˈkweɪʒən/
- Specialized
:
ecuación diferencial parcial
- To determine the time evolution of the meat temperature requires the solution of this partial differential equation, with the appropriate conductive, convective, and radiative boundary conditions.
- solving a partial differential equation
- nonlinear partial differential equations
- coupled systems of partial differential equations
So physics is written in terms of partial differential equations.
- So physics is written in terms of partial differential equations.
- And the beauty is it solves that basic partial differential equation.
- Whatever you know, control, understanding the motion of fluids, it's partial differential equations, etcetera.
Examples
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Turbulence problems can easily be set up on the computer, since a turbulent system may be correctly described by a well-known partial differential equation, the Navier-Stokes equation.
Academic text (1995) -
The governing equation is a linear fourth-order parabolic partial differential equation with boundary and initial conditions.
Blog text (2) -
I will then solve a set of partial differential equations at most and figure out how those little things in the box actually work.
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Her research interests are in several complex variables, partial differential equations, and complex geometry.
Blog text (25) -
And then this is the package they sell for solving partial differential equations by finite elements.
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Scientists know the partial differential equations obeyed by any fluid in which variations in space and time are sufficiently gentle.
Academic text (2001) -
Researchers often need to solve a partial differential equation to model the behavior of fluids over time.
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In many engineering fields, the design process involves understanding partial differential equations that describe heat transfer.
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To accurately predict the flow of air over the wing, engineers rely on a partial differential equation that captures complex interactions.
Surface Forms
Morphology
partial + differential + equation
Each part contributes directly: 'differential equation' denotes an equation involving derivatives and the modifier 'partial' specifies that these are partial derivatives with respect to one variable of a multivariable function. The phrase is compositional and follows regular noun-modifier patterns (and has clear equivalents in other languages), so a learner who knows the constituent mathematical terms can derive the full meaning.
Etymology
The term partial differential equation comes from three simple ideas: partial means 'only part or one direction', differential means 'a very small change', and equation means 'a rule that connects things'. So it is a rule that connects small changes in different directions, which is why people use it to describe heat, waves and other changes over space and time.