The material derivative

Main article: 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:

\frac{D}{Dt} \ \stackrel{\mathrm{def}}{=}\  \frac{\partial}{\partial t} + \mathbf{v}\cdot\nabla

where \mathbf{v} 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).

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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…


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


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

f^\prime_x,\ f_{,x},\ \partial_x f, \text{ or }  \frac{\partial f}{\partial x}

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

 y'+ P(x)y = Q(x)

The basic idea is to find some function M(x), 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

M(x) = e^{\int_{s_0}^{x} P(s) ds}
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.
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.
The doke is almost doke.  It’s Clare the higher the math, the more people give less of a fuck.
Partial differential equations (PDEs) are equations that involve rates of change with respect to continuous variables.
Two cents: a single variable without a computer is all I ask as your foe.
* foe is calling 704
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his ankle?
two days ago
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he’s limping


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Fuck you, Elizabeth.  This I know is creditable, without fortuitousness, stoic, unassail-
Major critique is feeling engineering ought not to charge for examples I can do in my mind every day.
Mount Roraima


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Toad, Roraima toad, Bufo GranulosoMount Roraima toad

What will happen?  Why didn’t I see what will happen to that kid?  I predict you’ll die, but for there’s more —
I am  a queer!
Never auth. Dunham Pinal
Spiggling off the spigot of your own giant pile of Yid female clunkers?  Let’s car pool.  I have the giant Yye Yye Yippee -Yah.
Falstaff.  Make it new again, player.
Rowing and bowing and pouring.  Those three busy verb-finders can pepper the text, undernining every thing. BLOGR TLNU HISN SIP BEER THE CT… Uh-huh.  I’ll and hurt you are welcome to pee again one time lie guess sane nuclear regulatory corporation.  Row now specifically rho faster.  Integrate to tau.
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A gianette of daytime tee-vee contacted.  Do I bet set refusal to bury her a nickel?
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-Bious, do narrator to busque
Richard Ramirez in the Ramones
Ready to Kidnap
Kidnapping turns wose woods than reading DNA backwards.  Now new worst is Ariel the Decade.  “Nid-dnap”.  This is false harelip.  It is actually a different sound children make (Rs took a powder).  Childlike
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3 Responses to “”

  1. sbillinghurst Says:

    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

  2. sbillinghurst Says:

    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.

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  3. sbillinghurst Says:

    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.

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