Partial differential equation (nonfiction)
In mathematics, a partial differential equation (PDE) is a differential equation that contains beforehand unknown multivariable functions and their partial derivatives. PDEs are used to formulate problems involving functions of several variables, and are either solved by hand, or used to create a computer model. A special case is ordinary differential equations (ODEs), which deal with functions of a single variable and their derivatives.
PDEs can be used to describe a wide variety of phenomena such as sound, heat, diffusion, electrostatics, electrodynamics, fluid dynamics, elasticity, or quantum mechanics. These seemingly distinct physical phenomena can be formalized similarly in terms of PDEs.
Just as ordinary differential equations often model one-dimensional dynamical systems, partial differential equations often model multidimensional systems.
PDEs find their generalization in stochastic partial differential equations.
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Nonfiction cross-reference
- Differential equation (nonfiction) - a mathematical equation that relates some function with its derivatives. The functions usually represent physical quantities, the derivatives represent their rates of change, and the equation defines a relationship between the two.
- Mathematics (nonfiction)
- Nonlinear partial differential equation (nonfiction) - a partial differential equation with nonlinear terms. They describe many different physical systems, ranging from gravitation to fluid dynamics, and have been used in mathematics to solve problems such as the Poincaré conjecture and the Calabi conjecture. They are difficult to study: there are almost no general techniques that work for all such equations, and usually each individual equation has to be studied as a separate problem.
- Physics (nonfiction)
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