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Derivative of a function
factor or coefficient of the differential dx in the differential df(x). A coefficient is usually a constant quantity, but the differential coefficient of f
Differential_coefficient
Differential equation that is linear with respect to the unknown function
A linear differential equation or a system of linear equations such that the associated homogeneous equations have constant coefficients may be solved
Linear_differential_equation
Multiplicative factor in a mathematical expression
rather than a constant coefficient. In particular, in a linear differential equation with constant coefficient, the constant coefficient term is generally
Coefficient
Type of functional equation (mathematics)
defined above. Inhomogeneous first-order linear constant-coefficient ordinary differential equation: d u d x = c u + x 2 . {\displaystyle {\frac {du}{dx}}=cu+x^{2}
Differential_equation
Differential equation containing derivatives with respect to only one variable
In mathematics, an ordinary differential equation (ODE) is a differential equation (DE) dependent on only a single independent variable. As with any other
Ordinary differential equation
Ordinary_differential_equation
Ratio of concentrations in a mixture at equilibrium
In the physical sciences, a partition coefficient (P) or distribution coefficient (D) is the ratio of concentrations of a compound in a mixture of two
Partition_coefficient
Differential equation parameter in thermal physics
A temperature coefficient describes the relative change of a physical property that is associated with a given change in temperature. For a property R
Temperature_coefficient
Type of differential equation
vector with m components, and the coefficient matrices Aν are m by m matrices for ν = 1, 2, …, n. The partial differential equation takes the form L u = ∑
Partial_differential_equation
Partial differential equations with random force terms and coefficients
Stochastic partial differential equations (SPDEs) generalize partial differential equations via random force terms and coefficients, in the same way ordinary
Stochastic partial differential equation
Stochastic_partial_differential_equation
Method of solution for inhomogeneous ODEs
method of undetermined coefficients is an approach to finding a particular solution to certain nonhomogeneous ordinary differential equations and recurrence
Method of undetermined coefficients
Method_of_undetermined_coefficients
Measure of inequality of a statistical distribution
In economics, the Gini coefficient (/ˈdʒiːni/ JEE-nee), also known as the Gini index or Gini ratio, is a measure of statistical dispersion intended to
Gini_coefficient
Measure of a device's efficiency at allowing fluid flow
The flow coefficient of a device is a relative measure of its efficiency at allowing fluid flow. It describes the relationship between the pressure drop
Flow_coefficient
Differential equations involving stochastic processes
A stochastic differential equation (SDE) is a differential equation in which one or more of the terms is a stochastic process, resulting in a solution
Stochastic differential equation
Stochastic_differential_equation
Physical quantity of hot and cold
temperature is an intensive variable because it is equal to a differential coefficient of one extensive variable with respect to another, for a given
Temperature
Method for solving differential equations
series solution to certain differential equations. In general, such a solution assumes a power series with unknown coefficients, then substitutes that solution
Power series solution of differential equations
Power_series_solution_of_differential_equations
Tendency of matter to change volume in response to a change in temperature
strain) divided by the change in temperature is called the material's coefficient of linear thermal expansion. For small temperature changes, this is nearly
Thermal_expansion
Number of subsets of a given size
the binomial coefficients are the positive integers that occur as coefficients in the binomial theorem. Commonly, a binomial coefficient is indexed by
Binomial_coefficient
Notation of differential calculus
derivative is referred to as the "differential coefficient" (the coefficient of dx). Some authors and journals set the differential symbol d in roman type instead
Notation_for_differentiation
Class of second-order linear partial differential equations
A parabolic partial differential equation is a type of partial differential equation (PDE). Parabolic PDEs are used to describe a wide variety of time-dependent
Parabolic partial differential equation
Parabolic_partial_differential_equation
Measure of voltage induced by change of temperature
The Seebeck coefficient (also known as thermopower, thermoelectric power, and thermoelectric sensitivity) of a material is a measure of the magnitude
Seebeck_coefficient
Tendency of a particle to settle out of suspension during centrifugation
Sedimentation Centrifugation Differential centrifugation "Sedimentation Coefficient of Particle Calculator | Calculate Sedimentation Coefficient of Particle". www
Sedimentation_coefficient
Mathematical symbol used for partial derivatives and other concepts
chain complex, and the conjugate of the Dolbeault operator on smooth differential forms over a complex manifold. It should be distinguished from other
Partial_differential
Class of differential equations expressible in differential algebra
concept of differential algebra used. The intention is to include equations formed by means of differential operators, in which the coefficients are rational
Algebraic differential equation
Algebraic_differential_equation
Study of rates of change
mathematics, differential calculus is a subfield of calculus that studies the rates at which quantities change. The primary objects of study in differential calculus
Differential_calculus
Typically linear operator defined in terms of differentiation of functions
Any polynomial in D with function coefficients is also a differential operator. We may also compose differential operators by the rule ( D 1 ∘ D 2 )
Differential_operator
Identity relating to differential equations
homogeneous second-order linear ordinary differential equation in terms of a coefficient of the original differential equation. The relation can be generalised
Abel's_identity
Type of differential operator
In the theory of partial differential equations, elliptic operators are differential operators that generalize the Laplace operator. They are defined
Elliptic_operator
Type of ordinary differential equation
In mathematics, an ordinary differential equation is called a Bernoulli differential equation if it is of the form y ′ + P ( x ) y = Q ( x ) y n , {\displaystyle
Bernoulli differential equation
Bernoulli_differential_equation
Indian mathematician and astronomer (1114–1185)
18th century. Some preliminary ideas of differential calculus and suggested that the "differential coefficient" vanishes at the extreme end. Stated early
Bhāskara_II
Type of differential equation subject to a particular solution methodology
In mathematics, an exact differential equation or total differential equation is a certain kind of ordinary differential equation which is widely used
Exact_differential_equation
Type of ordinary differential equation
A differential equation can be homogeneous in either of two respects. A first order differential equation is said to be homogeneous if it may be written
Homogeneous differential equation
Homogeneous_differential_equation
Establish relationships between homology and cohomology theories
universal coefficient theorems (UCT) establish relationships between homology groups (or cohomology groups) with different coefficients. For instance
Universal_coefficient_theorem
Type of differential operator
understanding the theory of pseudo-differential operators. Consider a linear differential operator with constant coefficients, P ( D ) := ∑ α a α D α {\displaystyle
Pseudo-differential_operator
Topics referred to by the same term
The term differential coefficient has been mostly displaced by the modern term derivative. In computer arithmetics, the term coefficient (floating point
Coefficient_(disambiguation)
Matrix whose entries are the coefficients of a linear equation
In linear algebra, a coefficient matrix is a matrix consisting of the coefficients of the variables in a set of linear equations. The matrix is used in
Coefficient_matrix
Method of mathematical optimization
Differential evolution (DE) is an evolutionary algorithm to optimize a problem by iteratively trying to improve a candidate solution with regard to a given
Differential_evolution
Physical law relating heat loss to temperature difference
same. As such, it is equivalent to a statement that the heat transfer coefficient, which mediates between heat losses and temperature differences, is a
Newton's_law_of_cooling
Mathematical notion of infinitesimal difference
In mathematics, differential refers to several related notions derived from the early days of calculus, put on a rigorous footing, such as infinitesimal
Differential_(mathematics)
Electrical circuit component which amplifies the difference of two analog signals
A differential amplifier is a type of electronic amplifier that amplifies the difference between two input voltages but suppresses any voltage common to
Differential_amplifier
Probability of a given process occurring in a particle collision
specified as the differential limit of a function of some final-state variable, such as particle angle or energy, it is called a differential cross section
Cross_section_(physics)
Device for measuring or restricting fluid flow
minimum fluid pressure. The measured differential pressure differs for each combination and so the coefficient of discharge used in flow calculations
Orifice_plate
Class of partial differential equations
In mathematics, an elliptic partial differential equation is a type of partial differential equation (PDE). In mathematical modeling, elliptic PDEs are
Elliptic partial differential equation
Elliptic_partial_differential_equation
System of equations in mathematics
In mathematics, a differential-algebraic system of equations (DAE) is a system of equations that either contains differential equations and algebraic
Differential-algebraic system of equations
Differential-algebraic_system_of_equations
Procedure for solving differential equations
to solve inhomogeneous linear ordinary differential equations. For first-order inhomogeneous linear differential equations it is usually possible to find
Variation_of_parameters
Diagram showing the proportion of a receptor bound to a ligand
reversible Hill equation. The Hill coefficient is also intimately connected to the elasticity coefficient where the Hill coefficient can be shown to equal: n =
Hill_equation_(biochemistry)
of the coefficient functions in the SDEs. Consider the Itō diffusion X {\displaystyle X} satisfying the following Itō stochastic differential equation
Runge–Kutta_method_(SDE)
Mechanical analogue computer to solve differential equations
The differential analyser is a mechanical analogue computer designed to solve differential equations by integration, using wheel-and-disc mechanisms to
Differential_analyser
Japanese philosopher
theory of light [光の物理学的理論]; Differential [微分]; Differential coefficient [微分係数]; Infinitesimal method [微分法]; Differential equation [微分方程式]; Non-Euclidean
Hajime_Tanabe
Algebraic equation on which the solution of a differential equation depends
differential equation is linear and homogeneous, and has constant coefficients. Such a differential equation, with y as the dependent variable, superscript (n)
Characteristic equation (calculus)
Characteristic_equation_(calculus)
Expression that may be integrated over a region
k + 1 ) {\displaystyle (k+1)} -form defined by taking the differential of the coefficient functions: d ω = ∑ i = 1 n ∂ f ∂ x i d x i ∧ d x I . {\displaystyle
Differential_form
Type of differential equation
In mathematics, delay differential equations (DDEs) are a type of differential equation in which the derivative of the unknown function at a certain time
Delay_differential_equation
Class of ordinary differential equations
applications, a Sturm–Liouville problem is a second-order linear ordinary differential equation of the form d d x [ p ( x ) d y d x ] + q ( x ) y = − λ w (
Sturm–Liouville_theory
Algebraic study of differential equations
mathematics, differential algebra is, broadly speaking, the area of mathematics consisting in the study of differential equations and differential operators
Differential_algebra
Mathematical manifold theory
studying the cohomology groups of a smooth manifold M using partial differential equations. The key observation is that, given a Riemannian metric on
Hodge_theory
Method of separating particles in a mixture
proteins have larger frictional coefficients, and sediment more slowly to ensure accuracy. The difference between differential and density gradient centrifugation
Differential_centrifugation
Direct conversion of temperature differences to electric voltage and vice versa
create temperature differences), and the Thomson effect (the Seebeck coefficient varies with temperature). The Seebeck and Peltier effects are different
Thermoelectric_effect
Development of mathematics in South Asia
Calculus: Preliminary concept of differentiation Discovered the differential coefficient. Stated early form of Rolle's theorem, a special case of the mean
Indian_mathematics
Existence and uniqueness theorem for certain partial differential equations
the existence of solutions to a system of m differential equations in n dimensions when the coefficients are analytic functions. The theorem and its proof
Cauchy–Kovalevskaya_theorem
Financial Term
identify and explain the differential market response to earnings information of different firms. An Earnings response coefficient measures the extent of
Earnings_response_coefficient
Algebraic generalization of the derivative
to the coefficient a 1 {\displaystyle a_{1}} gives a derivation. In differential geometry derivations are tangent vectors Kähler differential Hasse derivative
Derivation (differential algebra)
Derivation_(differential_algebra)
Differential form on a manifold which is permitted to have complex coefficients
complex differential form is a differential form on a manifold (usually a complex manifold) which is permitted to have complex coefficients. Complex
Complex_differential_form
Type of problem involving ODEs or PDEs
In the study of differential equations, a boundary-value problem is a differential equation subjected to constraints called boundary conditions. A solution
Boundary_value_problem
Values which describe behavior of a linear electric circuit
as gain, return loss, voltage standing wave ratio (VSWR), reflection coefficient and amplifier stability. The term 'scattering' is more common to optical
Scattering_parameters
Statistical transformation
z-transformation) of a Pearson correlation coefficient is its inverse hyperbolic tangent (artanh). When the sample correlation coefficient r is near 1 or -1, its distribution
Fisher_transformation
Mathematical simplification technique in physical sciences
As an illustrative example, consider a first order differential equation with constant coefficients: a d x d t + b x = A f ( t ) . {\displaystyle a{\frac
Nondimensionalization
Generalization of the exponential function
constant coefficient ordinary differential equations, strongly continuous semigroups provide solutions of linear constant coefficient ordinary differential equations
C0-semigroup
Quantity characterizing the deviation of a solvent from ideal behavior
An osmotic coefficient ϕ {\displaystyle \phi } is a quantity which characterises the deviation of a solvent from ideal behaviour, referenced to Raoult's
Osmotic_coefficient
Lf=f^{(n)}+q_{1}f^{(n-1)}+\cdots +q_{n}f} be a linear differential operator of order n {\displaystyle n} with one valued coefficient functions q 1 , … , q n {\displaystyle
Fuchsian_theory
Notion in calculus
In calculus, the differential represents the principal part of the change in a function y = f ( x ) {\displaystyle y=f(x)} with respect to changes in the
Differential_of_a_function
Detection of tornado debris in weather radar
particles, debris balls typically produce a correlation coefficient (ρhv) less than 0.80. Differential reflectivity (ZDR) values associated with debris balls
Tornado_debris_signature
Equations describing classical electromagnetism
Maxwell's equations are a set of coupled partial differential equations that describe how electric and magnetic fields are generated by electric charges
Maxwell's_equations
Quantum optical theoretical system
) {\displaystyle n_{0}={\frac {1}{3}}(2m-2s+\alpha +1)} , and differential coefficient C x = s ( s + 1 ) − x ( x + 1 ) {\displaystyle C_{x}={\sqrt {s(s+1)-x(x+1)}}}
Tavis–Cummings_model
Type of mathematical function
functions, and all functions obtained by roots of a polynomial whose coefficients are elementary. The elementary functions were originally defined by Joseph
Elementary_function
Monotone maps have countable discontinuities
William Henry; Young, Grace Chisholm (1911). "On the Existence of a Differential Coefficient". Proc. London Math. Soc. 2. 9 (1): 325–335. doi:10.1112/plms/s2-9
Discontinuities of monotone functions
Discontinuities_of_monotone_functions
Berthing mechanism used to connect ISS modules
thermal standoff: Foster, Cook, Smudde & Henry (2004). The effect of differential Coefficient of Thermal Expansion is a simple matter of physics given the difference
Common_Berthing_Mechanism
Technique for solving linear ordinary differential equations
Consider the general, homogeneous, second-order linear constant coefficient ordinary differential equation. (ODE) a y ″ ( x ) + b y ′ ( x ) + c y ( x ) = 0
Reduction_of_order
Concept in differential equation mathematics
points, at which the equation's coefficients are analytic functions, and singular points, at which some coefficient has a singularity. Then amongst singular
Regular_singular_point
Methods used to find numerical solutions of ordinary differential equations
methods for ordinary differential equations are methods used to find numerical approximations to the solutions of ordinary differential equations (ODEs).
Numerical methods for ordinary differential equations
Numerical_methods_for_ordinary_differential_equations
Partial differential equation
the Beltrami equation, named after Eugenio Beltrami, is the partial differential equation ∂ w ∂ z ¯ = μ ∂ w ∂ z . {\displaystyle {\frac {\partial w}{\partial
Beltrami_equation
Exponential representation for differential equations
Given the n × n coefficient matrix A(t), one wishes to solve the initial-value problem associated with the linear ordinary differential equation Y ′ (
Magnus_expansion
Uniqueness for linear partial differential equations with real analytic coefficients
(1873–1943), is a uniqueness result for linear partial differential equations with real analytic coefficients. We will use the multi-index notation: Let α = {
Holmgren's_uniqueness_theorem
Circulation density in a vector field
dx\wedge dz+a_{23}\,dy\wedge dz;} and a differential 3-form is defined by a single term with one function as coefficient: a 123 d x ∧ d y ∧ d z . {\displaystyle
Curl_(mathematics)
Differential equation exhibiting high rate of dissipation
for nonlinear stiff equations below. For a linear system with constant coefficients u ˙ = A u {\displaystyle {\dot {u}}=Au} , the divergence is constant
Stiff_equation
Scientific law describing absorption of light
μ is the (Napierian) attenuation coefficient, which yields the following first-order linear, ordinary differential equation: d Φ e ( z ) d z = − μ (
Beer–Lambert_law
Can all boundary value problems be solved
case where along the boundary there are prescribed either the differential coefficients or any relations between these and the values of the function
Hilbert's_twentieth_problem
Simple polynomial map exhibiting chaotic behavior
{\displaystyle x_{f2}^{(2)}} . When we actually calculate the differential coefficients of two periodic points for the logistic map, we get When this
Logistic_map
Numerical method for solving stochastic differential equations
stochastic differential equation. It is named after Grigori Milstein who first published it in 1974. Consider the autonomous Itō stochastic differential equation:
Milstein_method
Roughly, the number of k-dimensional holes on a topological surface
homology group in this case is a vector space over Q. The universal coefficient theorem, in a very simple torsion-free case, shows that these definitions
Betti_number
Differential form in commutative algebra
In mathematics, Kähler differentials provide an adaptation of differential forms to arbitrary commutative rings or schemes. The notion was introduced
Kähler_differential
Method for solving certain nonlinear partial differential equations
reflection coefficients, transmission coefficient, eigenvalue data, and normalization constants of the eigenfunction solutions for this differential equation
Inverse_scattering_transform
System of complete and orthogonal polynomials
also be defined as the coefficients in a formal expansion in powers of t {\displaystyle t} of the generating function The coefficient of t n {\displaystyle
Legendre_polynomials
Solution method for linear differential equations
technique for finding approximate solutions to linear differential equations with spatially varying coefficients. It is typically used for a semiclassical calculation
WKB_approximation
Differential equations play a prominent role in many scientific areas: mathematics, physics, engineering, chemistry, biology, medicine, economics, etc
List of named differential equations
List_of_named_differential_equations
Array of numbers describing a metric connection
with a metric, allowing distances to be measured on that surface. In differential geometry, an affine connection can be defined without reference to a
Christoffel_symbols
Method for solving ordinary differential equations
restriction on the coefficient for the term z 0 , {\displaystyle z^{0},} which can be set arbitrarily. If it is set to zero then with this differential equation
Frobenius_method
Parameter used to calculate the volume change of a fluid or solid in response to pressure
thermodynamics and fluid mechanics, the compressibility (also known as the coefficient of compressibility or, if the temperature is held constant, the isothermal
Compressibility
Mathematical relation defining a sequence
linear algebra, and dynamical systems), a linear recurrence with constant coefficients (also known as a linear recurrence relation or linear difference equation)
Linear recurrence with constant coefficients
Linear_recurrence_with_constant_coefficients
Partial differential equation with nonlinear terms
In mathematics and physics, a nonlinear partial differential equation is a partial differential equation with nonlinear terms. They describe many different
Nonlinear partial differential equation
Nonlinear_partial_differential_equation
Determinant of the matrix of first derivatives of a set of functions
Di(fj) (with 0 ≤ i < n), where each Di is some constant coefficient linear partial differential operator of order i. If the functions are linearly dependent
Wronskian
Polynomial sequence
power-series coefficients of the exponential are well known, and higher-order derivatives of the monomial xn can be written down explicitly, this differential-operator
Hermite_polynomials
DIFFERENTIAL COEFFICIENT
DIFFERENTIAL COEFFICIENT
Boy/Male
Afghan, Arabic, Muslim, Pashtun
One who can Differentiate; Comely; One who Distinguishes Truth from Falsehood
Boy/Male
Irish
From the Latin patricius “â€nobly born.â€â€ The patron saint of Ireland, it is hard to differentiate between fact and myth. What is probably true is that he was born in Britain around 373 AD and was brought to Ireland as a slave at the age of seven, possibly by Niall of the Nine Hostages (read the legend). Forced to guard sheep on the Slemish Mountains in Country Antrim for six years he had a vision urging him to convert his captors. He escaped to France where he trained as a priest before returning to Ireland where he banished the snakes (i.e. paganism) and converted the population to Christianity. Both Patrick and Padraig are very popular names in Ireland.
Boy/Male
Irish
From the Latin patricius “â€nobly born.â€â€ The patron saint of Ireland, it is hard to differentiate between fact and myth. What is probably true is that he was born in Britain around 373 AD and was brought to Ireland as a slave at the age of seven, possibly by Niall of the Nine Hostages (read the legend). Forced to guard sheep on the Slemish Mountains in Country Antrim for six years he had a vision urging him to convert his captors. He escaped to France where he trained as a priest before returning to Ireland where he banished the snakes (i.e. paganism) and converted the population to Christianity. Both Patrick and Padraig are very popular names in Ireland.
DIFFERENTIAL COEFFICIENT
DIFFERENTIAL COEFFICIENT
Male
Hebrew
(מְתוּש×Ö¸×ֵל) Hebrew name METHUWSHAEL means "man of God." In the bible, this is the name of a descendant of Cain.
Male
English
Variant spelling of English Mattaniah, MATANIA means "gift of God."Â
Boy/Male
Tamil
Boy/Male
Muslim/Islamic
Light (Also pronounced Ziya)
Boy/Male
Hindu
Indra devta
Girl/Female
Indian
Moon light or a river, Star
Boy/Male
Australian, Celtic, Christian, Irish
Little Fair One
Male
English
King-like
Boy/Male
Hindu, Indian, Sanskrit
Life
Boy/Male
Tamil
Chief, Leader, Joy, Delight
DIFFERENTIAL COEFFICIENT
DIFFERENTIAL COEFFICIENT
DIFFERENTIAL COEFFICIENT
DIFFERENTIAL COEFFICIENT
DIFFERENTIAL COEFFICIENT
n.
An expression which, being differentiated, will produce a given differential. See differential Differential, and Integration. Cf. Fluent.
v. t.
To define or limit by adding a differentia.
v. t.
To obtain the differential, or differential coefficient, of; as, to differentiate an algebraic expression, or an equation.
v. t.
A determining feature; a distinguishing characteristic; a differentia.
n.
An increment, usually an indefinitely small one, which is given to a variable quantity.
pl.
of Differentia
v. t.
To distinguish or mark by a specific difference; to effect a difference in, as regards classification; to develop differential characteristics in; to specialize; to desynonymize.
n.
One of two coils of conducting wire so related to one another or to a magnet or armature common to both, that one coil produces polar action contrary to that of the other.
v. i.
To acquire a distinct and separate character.
a.
Ready to obey; reverent; differential; also, servilely submissive.
n.
The formal or distinguishing part of the essence of a species; the characteristic attribute of a species; specific difference.
n.
A characteristic or essential attribute; a differential.
v. t.
To express the specific difference of; to describe the properties of (a thing) whereby it is differenced from another of the same class; to discriminate.
a.
Relating to differences of motion or leverage; producing effects by such differences; said of mechanism.
n.
A small difference in rates which competing railroad lines, in establishing a common tariff, allow one of their number to make, in order to get a fair share of the business. The lower rate is called a differential rate. Differentials are also sometimes granted to cities.
a.
Of or pertaining to a differential, or to differentials.
n.
A form of conductor used for dividing and distributing the current to a series of electric lamps so as to maintain equal action in all.
a.
That deduces; inferential.
adv.
In the way of differentiation.
a.
Relating to or indicating a difference; creating a difference; discriminating; special; as, differential characteristics; differential duties; a differential rate.