The material derivative

Changes in properties of a moving fluid can be measured in two different ways. One can measure a given property by either carrying out the measurement on a fixed point in space as particles of the fluid pass by, or by following a parcel of fluid along its streamline. The derivative of a field with respect to a fixed position in space is called the *Eulerian* derivative while the derivative following a moving parcel is called the *advective* or *material* derivative.

The material derivative is defined as the operator:

where is the velocity of the fluid. The first term on the right-hand side of the equation is the ordinary Eulerian derivative (i.e. the derivative on a fixed reference frame, representing changes at a point with respect to time) whereas the second term represents changes of a quantity with respect to position (see advection). This “special” derivative is in fact the ordinary derivative of a function of many variables along a path following the fluid motion; it may be derived through application of the chain rule in which all independent variables are checked for change along the path (i.e. the total derivative).

(********** gh)ost as possible

To eliminate a partial in your mind in a good way is to lay claim to a latent fingerprint function rather than source’s. When Ian is to Sponge Bob as symmetry of the six sources ablates your face, speculator…

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Derivation of Navier-Stokes for fluids: Near take rip. Ever stones

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In mathematics, a **partial derivative** of a function of several variables is its derivative with respect to one of those variables, with the others held constant (as opposed to the total derivative, in which all variables are allowed to vary). Partial derivatives are used in vector calculus and differential geometry.

The partial derivative of a function *f* with respect to the variable *x* is variously denoted by

The partial-derivative symbol is ∂. One of the first known uses of the symbol in mathematics is by Marquis de Condorcet from 1770, who used it for partial differences. The modern **partial derivative** notation is by Adrien-Marie Legendre (1786), though he later abandoned it; Carl Gustav Jacob Jacobi re-introduced the symbol in 1841.^{[1]}

********* bowder Paris lose the partials you can find [0{ops} 10]******** assuming adding up to one meant about this reality being intuitionist, i.e. a plastic representation of a higher world ******* What did I miss? Thai? It’s on delusion. Talk about One. Scare it.

Use in solving first order linear ordinary differential equations

Integrating factors are useful for solving ordinary differential equations that can be expressed in the form

The basic idea is to find some function , called the “integrating factor,” which we can multiply through our DE in order to bring the left-hand side under a common derivative. For the canonical first-order, linear differential equation shown above, our integrating factor is chosen to be

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- In mathematics, an
**integrating factor**is a function that is chosen to facilitate the solving of a given equation involving differentials. It is commonly used to solve ordinary differential equations, but is also used within multivariable calculus when multiplying through by an integrating factor allows an inexact differential to be made into an exact differential (which can then be integrated to give a scalar field). This is especially useful in thermodynamics where temperature becomes the integrating factor that makes entropy an exact differential. - *****
- A drug integrating factor bled.
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- In mathematics, a
**partial differential equation**(**PDE**) is a differential equation that contains unknown multivariable functions and their partial derivatives. (This is in contrast to ordinary differential equations, which deal with functions of a single variable and their derivatives.) PDEs are used to formulate problems involving functions of several variables, and are either solved by hand, or used to create a relevant computer model. - ***
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- Partial differential equations (PDEs) are equations that involve rates of change with respect to continuous variables.
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Jack knife, in your sweaty hands - kidnaping Ralston, poison realm Pasadena
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Tags: Math

Thu, 09 May 2013 08:54:42 +0000 at 8:54 am |

That is funny, and to me, clock around, what I objected to was the typical hairsplitting GNI, “Gee, and if want me to move…”, PPANDIK, per Pandora’s box should cut it. Better still, why do you write me prescriptions? Joan Steddial, acid house pants-dropping penthouse family-jewels fondling…I love to cook. The recipe? One or two, and in the courthouse of ill-repute, we use a singleton in accusations pandora, psychological crew mate to the lunatic Martin Wegman. Ralston is his inductee for psychological warfare. I consider the whole affair torture. My blood may soon fly out and darken on the radiator, so…why does it not specify suicide does not do justice to the sting of a little NIP, KID NAP ING GNI PAN LOL

Thu, 09 May 2013 09:01:03 +0000 at 9:01 am |

The cocksucking idiot Ms. Ralston, correct. Height unit laudables forth with standing the stench of a back room justice a decade at a time. Pasadena steals! I wanted that child, Sabrina. That is whom you took.

Shermer is a piece of knackwurst.

Fri, 07 Jun 2013 17:56:28 +0000 at 5:56 pm |

It is like I am sentimental. I met Rich in the tunnels in the OC Courthouse in ’87. I said hi richard and he benchmarked me with disdain.

This was the last time I mentioned RR before he dies today in the metal.” Richard Ramirez in the Ramones Ready to Kidnap “. He also figures in when the sun is low, a Texas sunset drifter looming up black ‘n uh-and oily.