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Topic: Partial derivative

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  The Derivative   (Site not responding. Last check: 2007-10-12)
The ordinary derivative of a function of one variable can be carried out because everything else in the function is a constant and does not affect the process of differentiation.
One example of the use of the derivative is in obtaining the velocity and acceleration from a position equation.
The derivative of a polynomial is the sum of the derivatives of its terms, and for a general term of a polynomial such as
hyperphysics.phy-astr.gsu.edu /hbase/deriv.html   (203 words)

 PlanetMath: derivative notation
is the derivative with respect to the first variable of the derivative with respect to the second variable.
The second of these notations represents the derivative matrix, which in most cases is the Jacobian, but in some cases, does not exist, even though the Jacobian exists.
This is version 10 of derivative notation, born on 2001-11-14, modified 2006-08-10.
planetmath.org /encyclopedia/DerivativeNotation.html   (249 words)

 Partial derivative - Wikipedia, the free encyclopedia
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).
Equations involving an unknown function's partial derivatives are called partial differential equations and are common in physics and engineering.
However, if all partial derivatives exist in a neighborhood of a and are continuous there, then f is totally differentiable in that neighborhood and the total derivative is continuous.
en.wikipedia.org /wiki/Partial_derivative   (450 words)

 PlanetMath: partial derivative
is simply its derivative with respect to only one variable, keeping all other variables constant (which are not functions of the variable in question).
In fact, as long as an equal number of partials are taken with respect to each variable, changing the order of differentiation will produce the same results in the above condition.
This is version 21 of partial derivative, born on 2001-11-14, modified 2006-10-04.
planetmath.org /encyclopedia/PartialDerivative.html   (204 words)

 lecture 6   (Site not responding. Last check: 2007-10-12)
Geometric interpretation of partial derivatives: The partial derivative of a function f(x,y) with respect to x can be interpreted as the slope of the curve obtained by cutting the graph of f(x,y) (i.e., the surface z=f(x,y)) at a fixed y-value; a similar interpretation holds for the partial derivative with respect to y.
Computation of partial derivatives: If, as is usually the case, f(x,y) is given by a formula, the computation of the partial derivatives of f boils down to ordinary differentiation.
Partial differential equations (PDE's): A PDE is an equation for a function of several variables involving partial derivatives of that function.
www.math.uiuc.edu /~dikim/m242/lec6.html   (752 words)

 partial derivative - Search Results - MSN Encarta   (Site not responding. Last check: 2007-10-12)
- derivative of single variable: the derivative of a function of two or more mathematical variables calculated with respect to one of the variables and on the assumption that the others are fixed
Derivatives (financial), financial instrument whose value is based on an underlying asset.
Partial pressure is the term applied to the effective pressure a single constituent exerts in a mixture of gases.
encarta.msn.com /partial+derivative.html   (139 words)

 What is a Directional Derivative?
the partial derivative of f with respect to y at the point (x0,y0) is denoted by fy(x0,y0).
The partial derivative fy(x0,y0) is a special case of a directional derivative.
The gradient of f is the vector of partial derivatives.
omega.albany.edu:8008 /calc3/directional-derivatives-dir/define-m2h.html   (725 words)

 Derivative - Wikipedia, the free encyclopedia
Jerk is the derivative (with respect to time) of an object's acceleration, that is, the third derivative (with respect to time) of an object's position, and second derivative (with respect to time) of an object's velocity.
Partial derivatives can be thought of informally as taking the derivative of the function with all but one variable held temporarily constant near a point.
The common thread is that the derivative at a point serves as a linear approximation of the function at that point.
en.wikipedia.org /wiki/Derivative   (2381 words)

 Partial Derivatives -- Pictorial Representation   (Site not responding. Last check: 2007-10-12)
Partial derivatives are particularly confusing in non-Cartesian coordinate systems, such as are commonly encountered in thermodynamics.
In contrast, it is risky to ask for the partial derivative of G with respect to R, because your readers might not know whether you intended to hold B constant (as on the first line of equation 5) or hold V constant (as on the second line of equation 5).
One argument is that the form of equation 7 is well-nigh unforgettable, and provides a clear recipe for calculating the desired partial derivative.
www.av8n.com /physics/partial-derivative.htm   (3896 words)

 Partial Derivative -- from Wolfram MathWorld
Partial derivatives are defined as derivatives of a function of multiple variables when all but the variable of interest are held fixed during the differentiation.
A differential equation expressing one or more quantities in terms of partial derivatives is called a partial differential equation.
Partial differential equations are extremely important in physics and engineering, and are in general difficult to solve.
mathworld.wolfram.com /PartialDerivative.html   (227 words)

 PARTIAL-DEMO   (Site not responding. Last check: 2007-10-12)
As part of the motivation for the derivative of a function y = f(x) of a single variable at a value x = a, we often draw a set of secant lines which 'settle' into the tangent line position.
Then the partial derivative of f with respect to y when x = 0.35 corresponds to the slope of a tangent line moving along this curve.
The MATLAB routine which generated the animation at the top of this demo, and the animations in the gallery of partials which can be accessed by clicking here, provide lecture tools that has been used successfully in large and small classes for both math/science and non-science majors.
astro.temple.edu /~dhill001/partial-demo   (656 words)

 World Web Math: Vector Calculus: Partial Differentiation
A partial function is a one-variable function obtained from a function of several variables by assigning constant values to all but one of the independent variables.
A partial derivative is the rate of change of a multi-variable function when we allow only one of the variables to change.
To get an intuitive grasp of partial derivatives, suppose you were an ant crawling over some rugged terrain (a two-variable function) where the x-axis is north-south with positive x to the north, the y-axis is east-west and the z-axis is up-down.
web.mit.edu /wwmath/vectorc/scalar/partial.html   (706 words)

 The Directional Derivatives   (Site not responding. Last check: 2007-10-12)
derivative of f with respect to that coordinate as the other coordinates are constant.
One is calculating a partial derivative simply by considering the other variables being just as any other constant.
The derivative of f with respect to s is not a partial derivative because as s changes, all of the coordinates usually
hemsidor.torget.se /users/m/mauritz/math/field/dirder.htm   (454 words)

 The Partial Derivative
and the partial derivatives being "velocity" relative to a single changing parameter (a.k.a.
The book calles the partial of a parametric function the speed, but it does not call a function in terms of x,y the speed, which is why I ask about the rigidity (is that a word?) of the use of the term speed.
The partial derivative is the rate of change of the vector S with respect to a change in the spatial variable x.
www.physicsforums.com /showthread.php?t=77896   (1803 words)

 Partial Differentiation - HMC Calculus Tutorial
The rate of change of f with respect to x (holding y constant) is called the partial derivative of f with respect to x and is denoted by f
Similarly, the rate of change of f with respect to y is called the partial derivative of f with respect to y and is denoted by f
Consider the partial derivative of f with respect to x at a point (x
www.math.hmc.edu /calculus/tutorials/partialdifferentiation   (371 words)

 Calculus III (Math 2415) - Partial Derivatives - Parital Derivatives
We will need to develop ways, and notations, for dealing with all of these cases.  In this section we are going to concentrate exclusively on only changing one of the variables at a time, while the remaining variable(s) are held fixed.  We will deal with allowing multiple variables to change in a later section.
Since we can think of the two partial derivatives above as derivatives of single variable functions it shouldn’t be too surprising that the definition of each is very similar to the definition of the derivative for single variable functions.  Here are the formal definitions of the two definitions partial derivatives we looked at above.
For the fractional notation for the partial derivative notice the difference between the partial derivative and the ordinary derivative from single variable calculus.
tutorial.math.lamar.edu /AllBrowsers/2415/PartialDerivatives.asp   (1868 words)

 6.4 Derivatives in Two Dimensions: Directional Derivative and Partial Derivatives   (Site not responding. Last check: 2007-10-12)
The directional derivative in the direction of the x-axis is called the partial derivative of f with respect to x, and is written as
Similarly the directional derivative of f in the direction of the y-axis is called the partial derivative of f with respect to y, and is written as
When computing the partial derivative with respect to x, you treat y as a constant, and differentiate with respect to x exactly as you do in one dimension.
ocw.mit.edu /ans7870/18/18.013a/textbook/HTML/chapter06/section04.html   (261 words)

 Exact Equations
Using the fact that these partial derivatives are of the same function will be the key to the method used to solve these equations.
To test for exactness, equate the partial derivative with respect to y of M and the partial derivative with respect to x of N. Notice that these partials are with respect to the exact opposite variables as those used to determine the total derivative in the last example.
The previous four examples demonstrate a method of finding the solution to an exact differential equation by confirming that the partial derivatives with respect to y of M and x of N are equal.
homepage.mac.com /nshoffner/nsh/ODE/Exact.html   (2156 words)

 Partial derivative examples
(x, y), we simply view y as being a fixed number and calculate the ordinary derivative with respect to x.
The first time you do this, it might be easiest to set y = b, where b is a constant, to remind you that you should treat y as though it were number rather than a variable.
The derivative of a constant is zero, so that term drops out.
www.math.umn.edu /~nykamp/m2374/readings/pderivex/index.html   (219 words)

 partial derivative
The ordinary derivative of a function of two or more variables with respect to one of the variables, the others being considered constants.
If the variables are x and y,the partial derivatives of f(x, y) are written (delta f)/(delta x) and (delta f)/(delta y), or D
The partial derivative of a variable with respect to time is known as the local derivative.
www.daviddarling.info /encyclopedia/P/partial_derivative.html   (132 words)

 Math Tutorial - Partial Derivatives
In order to understand the generalization of Newtonian mechanics to two and three dimensions, we first need to understand a new type of derivative called the partial derivative.
'' and the derivative is called a partial derivative.
Notice that the partial derivative is actually simpler to evaluate than an ordinary derivative, because only the explicit dependence of the function on the differentiating variable need be considered -- all other variables are taken to be constant.
www.physics.nmt.edu /~raymond/classes/ph13xbook/node88.html   (122 words)

 Partial Derivative Quantities from Phase Equilibria Relationships for Mixtures -- from Mathematica Information Center
A systematic formulation of multicomponent/multiphase phase equilibria as a linear algebra problem in the fugacities, mole fractions, partial molar volumes, and partial molar enthalpies is given.
These algorithmic steps allow current symbolic manipulation packages to generate useful partial derivative relationships in terms of measurable thermodynamic quantities.
Features of the algorithm are demonstrated by applying a computer implementation of the method to a simple two-phase/two-component system and to the more complicated examples of a two-phase/three-component supercritical fluid chromatography experiment and a mass-conserving closed system.
library.wolfram.com /infocenter/Articles/2217   (129 words)

 Partial Differentiation
Although a partial derivative is itself a function of several variables, we often want to evaluate it at some fixed point, such as (x
Because the definitions are really just version of the 1-variable result, these examples are quite typical; most of the usual rules for differentiation apply in the obvious way to partial derivatives exactly as you would expect.
, and suppose that all the partial derivatives of f are continuous.
www.maths.abdn.ac.uk /~igc/tch/ma2001/notes/node67.html   (615 words)

Specifically we explore an application to a temperature function (this example does have a geometric aspect in terms of the physical model itself) and a second application to electrical circuits, where no geometry is involved.
Since the temperature function is defined on two variables we will be computing a partial derivative.
Our verbal conclusion becomes: If the EMF is fixed at 120 volts, the current is decreasing with respect to resistance at the rate of 0.5333 amperes per ohm when the resistance is 15 ohms.
www.usna.edu /MathDept/website/courses/calc_labs/hill/Application.html   (546 words)

 Multivariable Partial Derivative: dp()
Single and mixed partial derivatives of one or higher orders.
The order of the derivative is specified with an exponent for each variable(s).
I have seen several other functions available on the Internet that will return partial derivatives of higher orders, but none of them will calculate mixed partial derivatives at higher orders as this one does (9/11/99).
www.ibiblio.org /technicalc/fpw/dp.html   (139 words)

 If the derivative is the slope of a curve, what's the partial derivative?   (Site not responding. Last check: 2007-10-12)
When doing ordinary differentiation we found that the derivative of a function gave us the slope of the curve of that function.
In this case the partial derivative represents the slope in a particular direction.
Similarly if we cut parallel to the x-axis, fixing t, then the slope of that cross-section is the partial derivative with respect to x, which is tcos(x).
www.ucl.ac.uk /Mathematics/geomath/level2/pdiff/pd6.html   (370 words)

 On the inverse scattering problem for characterization of agglomerated particulates: partial derivative formulation   (Site not responding. Last check: 2007-10-12)
All possible combinations of the scattering/extinction quantities with respect to the incident/scattered polarization state of the radiation field as well as the scattering angle are considered.
Closed form (exact) expressions for the partial derivatives are presented for the selected quantities and the most suitable sets for data inversion are selected using the criteria for maximum sensitivity and maximum accuracy.
The depolarization ratio in the vertical polarization state and the extinction normalized differential scattering intensities were identified as the most suitable set for inverting the corresponding measured quantities for the real and imaginary parts of the refractive index.
stacks.iop.org /0022-3727/28/2585   (389 words)

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