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→Introduction
== Introduction ==
== Introduction ==
引言
Partial differential equations (PDEs) are equations that involve rates of change with respect to [[continuous variables]]. For example, the position of a [[rigid body]] is specified by six parameters,<ref>{{Cite book|url=https://books.google.com/books?id=v9PLbcYd9aUC&pg=PA32|title=Modelling and Control of Robot Manipulators|last=Sciavicco|first=Lorenzo|last2=Siciliano|first2=Bruno|date=2001-02-19|publisher=Springer Science & Business Media|isbn=9781852332211|language=en}}</ref> but the configuration of a [[fluid]] is given by the [[continuous distribution]] of several parameters, such as the [[temperature]], [[pressure]], and so forth. The dynamics for the rigid body take place in a finite-dimensional [[Configuration space (physics)|configuration space]]; the dynamics for the fluid occur in an infinite-dimensional configuration space. This distinction usually makes PDEs much harder to solve than ordinary differential equations (ODEs), but here again, there will be simple solutions for linear problems. Classic domains where PDEs are used include [[acoustics]], [[fluid dynamics]], [[electrodynamics]], and [[heat transfer]].
Partial differential equations (PDEs) are equations that involve rates of change with respect to [[continuous variables]]. For example, the position of a [[rigid body]] is specified by six parameters,<ref>{{Cite book|url=https://books.google.com/books?id=v9PLbcYd9aUC&pg=PA32|title=Modelling and Control of Robot Manipulators|last=Sciavicco|first=Lorenzo|last2=Siciliano|first2=Bruno|date=2001-02-19|publisher=Springer Science & Business Media|isbn=9781852332211|language=en}}</ref> but the configuration of a [[fluid]] is given by the [[continuous distribution]] of several parameters, such as the [[temperature]], [[pressure]], and so forth. The dynamics for the rigid body take place in a finite-dimensional [[Configuration space (physics)|configuration space]]; the dynamics for the fluid occur in an infinite-dimensional configuration space. This distinction usually makes PDEs much harder to solve than ordinary differential equations (ODEs), but here again, there will be simple solutions for linear problems. Classic domains where PDEs are used include [[acoustics]], [[fluid dynamics]], [[electrodynamics]], and [[heat transfer]].