Rates | Generalizations of the derivative | Multivariable calculus

Material derivative

In continuum mechanics, the material derivative describes the time rate of change of some physical quantity (like heat or momentum) of a material element that is subjected to a space-and-time-dependent macroscopic velocity field. The material derivative can serve as a link between Eulerian and Lagrangian descriptions of continuum deformation. For example, in fluid dynamics, the velocity field is the flow velocity, and the quantity of interest might be the temperature of the fluid. In which case, the material derivative then describes the temperature change of a certain fluid parcel with time, as it flows along its pathline (trajectory). (Wikipedia).

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Derivatives are the main object of study in differential calculus. They describe rates of change of functions. That makes them incredibly useful in all of science, as many models can be expressed by describing the changes over time (e.g. of physical quantities). However, the abstract defin

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From playlist CALCULUS 1 CH 2 WHAT IS A DERIVATIVE?

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From playlist Sect 2.7, Definition of Derivative

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From playlist CALCULUS 3 CH 4 PARTIAL DERIVATIVES

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From playlist Materials Sciences 101 - Introduction to Materials Science & Engineering 2020

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From playlist Lectures for Transport Phenomena course

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From playlist Mathematics

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From playlist Lectures for Transport Phenomena course

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From playlist Lectures for Transport Phenomena course

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From playlist Lectures for Transport Phenomena course

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Related pages

Scalar field | Covariant derivative | Temperature | Derivative | Gradient | Chain rule | Advection | Momentum | Partial derivative | Levi-Civita connection | Directional derivative | Cartesian coordinate system | Lie derivative | Tensor | Spatial gradient | Metric tensor | Navier–Stokes equations | Flow velocity | Tensor field | Orthogonal coordinates | Vector field | Total derivative