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Typically linear operator defined in terms of differentiation of functions
In mathematics, a differential operator is an operator defined as a function of the differentiation operator. It is helpful, as a matter of notation first
Differential_operator
Type of differential operator
mathematical analysis a pseudo-differential operator is an extension of the concept of differential operator. Pseudo-differential operators are used extensively
Pseudo-differential_operator
Elliptic differential operators in geometry mathematics
In differential geometry there are a number of second-order, linear, elliptic differential operators bearing the name Laplacian. This article provides
Laplace operators in differential geometry
Laplace_operators_in_differential_geometry
Vector differential operator
Del, or nabla, is an operator used in mathematics (particularly in vector calculus) as a vector differential operator, usually represented by ∇ (the nabla
Del
Differential equation that is linear with respect to the unknown function
(abbreviated, in this article, as linear operator or, simply, operator) is a linear combination of basic differential operators, with differentiable functions as
Linear_differential_equation
Type of differential operator
the theory of partial differential equations, elliptic operators are differential operators that generalize the Laplace operator. They are defined by the
Elliptic_operator
Operator generalizing the Laplacian in differential geometry
In differential geometry, the Laplace–Beltrami operator is a generalization of the Laplace operator to functions defined on submanifolds in Euclidean space
Laplace–Beltrami_operator
Circulation density in a vector field
{\displaystyle \nabla } is taken as a vector differential operator del. Such notation involving operators is common in physics and algebra. Expanded in
Curl_(mathematics)
Exterior algebraic map taking tensors from p forms to n-p forms
{n}{k}}={\tbinom {n}{n-k}}} . The naturality of the star operator means it can play a role in differential geometry when applied to the cotangent bundle of a
Hodge_star_operator
Polynomial sequence
{He} _{\lambda }(x)} may be understood as eigenfunctions of the differential operator L [ u ] {\displaystyle L[u]} . This eigenvalue problem is called
Hermite_polynomials
Function acting on function spaces
are built from them are called differential operators, integral operators or integro-differential operators. Operator is also used for denoting the symbol
Operator_(mathematics)
Type of functional equation (mathematics)
pseudo-differential equations use pseudo-differential operators instead of differential operators. A differential algebraic equation (DAE) is a differential
Differential_equation
Concept in mathematics
allows the importation of Casimir operators into other areas of mathematics, specifically, those that have a differential algebra. They also play a central
Universal_enveloping_algebra
Differential operator in mathematics
In mathematics, the Laplace operator or Laplacian is a differential operator given by the divergence of the gradient of a scalar function on Euclidean
Laplace_operator
Mathematical symbol used for partial derivatives and other concepts
boundary of a set, the boundary operator in a chain complex, and the conjugate of the Dolbeault operator on smooth differential forms over a complex manifold
Partial_differential
In mathematics and theoretical physics, an invariant differential operator is a kind of mathematical map from some objects to an object of similar type
Invariant differential operator
Invariant_differential_operator
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 as
Differential_algebra
Type of differential equation
In mathematics, a partial differential equation (PDE) is an equation which involves a multivariable function and one or more of its partial derivatives
Partial_differential_equation
Collection of mathematical theories
line is in one sense the spectral theory of differentiation as a differential operator. But for that to cover the phenomena one has already to deal with
Spectral_theory
Mathematics of smooth surfaces
In mathematics, the differential geometry of surfaces deals with the differential geometry of smooth surfaces with various additional structures, most
Differential geometry of surfaces
Differential_geometry_of_surfaces
Type of partial differential equations
particular kind of differential equation under consideration. There is a well-developed theory for linear differential operators, due to Lars Gårding
Hyperbolic partial differential equation
Hyperbolic_partial_differential_equation
Linear operator equal to its own adjoint
{\displaystyle V} . Differential operators are an important class of unbounded operators. The structure of self-adjoint operators on infinite-dimensional
Self-adjoint_operator
Type of problem involving ODEs or PDEs
problems, in the linear case, involves the eigenfunctions of a differential operator. To be useful in applications, a boundary value problem should be
Boundary_value_problem
Class of ordinary differential equations
correspond to the eigenvalues and eigenfunctions of a Hermitian differential operator in an appropriate Hilbert space of functions with inner product
Sturm–Liouville_theory
Symbol used to indicate the del operator
notation, in the Mathematical Operators block. As a mathematical operator, it is often called del. The differential operator given in Cartesian coordinates
Nabla_symbol
Concepts from linear algebra
take many forms. For example, the linear transformation could be a differential operator like d d x {\displaystyle {\tfrac {d}{dx}}} , in which case the
Eigenvalues_and_eigenvectors
Branch of functional analysis
representation theory, differential geometry, quantum statistical mechanics, quantum information, and quantum field theory. Operator algebras can be used
Operator_algebra
Differential operator used in vector calculus
A vector operator is a differential operator used in vector calculus. Vector operators include: Gradient is a vector operator that operates on a scalar
Vector_operator
Part of spectral theory
quantum mechanics, operator theory and harmonic analysis on semisimple Lie groups. Spectral theory for second order ordinary differential equations on a compact
Spectral theory of ordinary differential equations
Spectral_theory_of_ordinary_differential_equations
Fundamental construction of differential calculus
in the context of differential equations defined by a vector valued function Rn to Rm, the Fréchet derivative A is a linear operator on R considered as
Generalizations of the derivative
Generalizations_of_the_derivative
Specific mathematical differential form
differential operator. Consequently, a quantity with an inexact differential cannot be expressed as a function of only the variables within the differential. I
Inexact_differential
Type of ordinary differential equation
form of a linear homogeneous differential equation is L ( y ) = 0 {\displaystyle L(y)=0} where L is a differential operator, a sum of derivatives (defining
Homogeneous differential equation
Homogeneous_differential_equation
Mathematical result in differential geometry
applications to theoretical physics. The index problem for elliptic differential operators was posed by Israel Gel'fand. He noticed the homotopy invariance
Atiyah–Singer_index_theorem
Multivariate derivative (mathematics)
an upside-down triangle and pronounced "del", denotes the vector differential operator. When a coordinate system is used in which the basis vectors are
Gradient
Method of solution to differential equations
Green function) is the impulse response of an inhomogeneous linear differential operator defined on a domain with specified initial conditions or boundary
Green's_function
First-order differential linear operator on spinor bundle, whose square is the Laplacian
a Dirac operator is a first-order differential operator that is a formal square root, or half-iterate, of a second-order differential operator such as
Dirac_operator
Polynomial sequence
\cdots .} The Zernike polynomials are eigenfunctions of the Zernike differential operator, in modern formulation L [ f ] = ∇ 2 f − ( r ⋅ ∇ ) 2 f − 2 r ⋅ ∇
Zernike_polynomials
Module over a sheaf of differential operators
a ring D of differential operators. The major interest of such D-modules is as an approach to the theory of linear partial differential equations. Since
D-module
Type of discrete calculus
discrete operators on graphs which are analogous to differential operators in calculus, such as graph Laplacians (or discrete Laplace operators) as discrete
Calculus on finite weighted graphs
Calculus_on_finite_weighted_graphs
Branch of mathematical analysis
1832. Oliver Heaviside introduced the practical use of fractional differential operators in electrical transmission line analysis circa 1890. The theory
Fractional_calculus
Mathematical study of linear operators
mathematics, operator theory is the study of linear operators on function spaces, beginning with differential operators and integral operators. The operators may
Operator_theory
Topics referred to by the same term
Del squared may refer to: Laplace operator, a differential operator often denoted by the symbol ∇2 Hessian matrix, sometimes denoted by ∇2 Aitken's delta-squared
Del_squared
Second-order differential operator
d'Alembert operator (denoted by a box: ◻ {\displaystyle \Box } ), also called the d'Alembertian, wave operator, box operator or sometimes quabla operator (cf
D'Alembert_operator
Vector operator in vector calculus
In vector calculus, divergence is a vector operator that operates on a vector field, producing a scalar field giving the rate that the vector field alters
Divergence
Relates 2 second-order elliptic operators on a manifold with the same principal symbol
the Laplacian on differential forms over an oriented compact Riemannian manifold M. The first definition uses the divergence operator δ defined as the
Weitzenböck_identity
Type of continuous linear operator
Fredholm alternative, in the spectral theory of linear operators, and in applications to differential equations and Sobolev spaces. For example, compactness
Compact_operator
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
Class of integral and differential operator
values of λ. Oscillatory integral operators often appear in many fields of mathematics (analysis, partial differential equations, integral geometry, number
Oscillatory_integral_operator
Method for solving certain nonlinear partial differential equations
solve linear partial differential equations. Using a pair of differential operators, a 3-step algorithm may solve nonlinear differential equations; the initial
Inverse_scattering_transform
Mathematical manifold theory
cohomology class has a canonical representative, a differential form that vanishes under the Laplacian operator of the metric. Such forms are called harmonic
Hodge_theory
Mathematical function often applied to matrices
vector fields in nonlinear analysis, and strong ellipticity in differential operators on function spaces, subject to specific boundary conditions. The
Logarithmic_norm
Calculus of vector-valued functions
studies various differential operators defined on scalar or vector fields, which are typically expressed in terms of the del operator ( ∇ {\displaystyle
Vector_calculus
Mathematical function of a linear operator
multiplicity. A widely used class of linear operators acting on infinite dimensional spaces are differential operators on the space C∞ of infinitely differentiable
Eigenfunction
Broad concept generalizing scalars in mathematics and physics
differentiation and integration of vector fields Vector differential, or del, a vector differential operator represented by the nabla symbol ∇ {\displaystyle
Vector (mathematics and physics)
Vector_(mathematics_and_physics)
Equation for the velocity of a body in viscous fluid
Hessian matrix differential operator and S = I ∇ 2 − H {\displaystyle \mathrm {S} =\mathbf {I} \nabla ^{2}-\mathrm {H} } is a differential operator composed
Stokes's_law
Partial differential operator
In the theory of partial differential equations, a partial differential operator P {\displaystyle P} defined on an open subset U ⊂ R n {\displaystyle
Hypoelliptic_operator
Topics referred to by the same term
logic Operator (mathematics), mapping that acts on elements of a space to produce elements of another space, e.g.: Linear operator Differential operator Integral
Operator
Concept in complex analysis
the theory of functions of several complex variables, are partial differential operators of the first order which behave in a very similar manner to the
Wirtinger_derivatives
Measures coefficients, derivatives in second-order hyperbolic differential equations
In differential equations, the Laplace invariant of any of certain differential operators is a certain function of the coefficients and their derivatives
Laplace_invariant
Polynomial sequence
an Appell sequence (i.e. a Sheffer sequence for the ordinary derivative operator). For the Bernoulli polynomials, the number of crossings of the x-axis
Bernoulli_polynomials
curves of the operator, Brownian motion can be seen as a stochastic counterpart of a flow to a second-order partial differential operator. Stochastic analysis
Stochastic analysis on manifolds
Stochastic_analysis_on_manifolds
Topics referred to by the same term
delineavit in Wiktionary, the free dictionary. Del is a vector differential operator represented by the symbol ∇ (nabla). Del or DEL can also refer to:
Del_(disambiguation)
(exponential) shift theorem is a theorem about polynomial differential operators (D-operators) and exponential functions. It permits one to eliminate,
Shift_theorem
Area of mathematics
connection between geometry and (discrete) differential operators. Introductory text: K. Crane, "Discrete Differential Geometry: An Applied Introduction," 2025
Discrete differential geometry
Discrete_differential_geometry
a microdifferential operator is a linear operator on a cotangent bundle (phase space) that generalizes a differential operator and appears in the framework
Microdifferential_operator
Generalized function whose value is zero everywhere except at zero
the study of a linear partial differential equation L [ u ] = f , {\displaystyle L[u]=f,} where L is a differential operator on Rn, is to seek first a fundamental
Dirac_delta_function
Type of operator in Fourier analysis
family of commuting operators). They are also special cases of pseudo-differential operators, and more generally Fourier integral operators. There are natural
Multiplier_(Fourier_analysis)
Technique used in image processing and computer vision for edge detection
proposed by Lawrence Roberts in 1963. As a differential operator, the idea behind the Roberts cross operator is to approximate the gradient of an image
Roberts_cross
Type of distribution in mathematical analysis
integrals. It is possible to represent approximate solution operators for many differential equations as oscillatory integrals. An oscillatory integral
Oscillatory_integral
Topics referred to by the same term
Two-dimensional rotation operator Rot (operator) aka Curl, a differential operator in mathematics Rotation operator (quantum mechanics) This disambiguation
Rotation_operator
Topics referred to by the same term
{\mathrm {d} \over \mathrm {d} x}} , a common notation for the differential operator with respect to a variable x DD(X), former program name of a class
DDX
Operator in quantum mechanics
operator is the operator associated with the linear momentum. The momentum operator is, in the position representation, an example of a differential operator
Momentum_operator
Type of derivative in differential geometry
to X is denoted L X T {\displaystyle {\mathcal {L}}_{X}T} . The differential operator T ↦ L X T {\displaystyle T\mapsto {\mathcal {L}}_{X}T} is a derivation
Lie_derivative
Subject field of Boolean algebra discussing changes of Boolean variables and functions
Boolean functions. Boolean differential operators play a significant role in BDC. They allow the application of differentials as known from classical analysis
Boolean_differential_calculus
Differential operator acting on vector bundles
gauge symmetry of a Lagrangian L {\displaystyle L} is defined as a differential operator on some vector bundle E {\displaystyle E} taking its values in the
Gauge_symmetry_(mathematics)
Topics referred to by the same term
quarks alt-J (Δ), a British indie band Laplace operator (Δ), a differential operator Increment operator (∆) Symmetric difference, in mathematics, the set
∆
Differential operator in mathematics
specifically, in the theory of partial differential equations — a semi-elliptic operator is a partial differential operator satisfying a positivity condition
Semi-elliptic_operator
Derivative of a function with multiple variables
notation. Thus, in these cases, it may be preferable to use the Euler differential operator notation with D i {\displaystyle D_{i}} as the partial derivative
Partial_derivative
In the mathematical field of differential geometry, the Paneitz operator is a fourth-order differential operator defined on a Riemannian manifold of dimension
Paneitz_operator
Branch of mathematics
infinite-dimensional spaces. Many areas of analysis study operators, like differential operators, integral operators, or linear transformations on a function space
Mathematical_analysis
Linear operator defined on a dense linear subspace
functional analysis and operator theory, the notion of unbounded operator provides an abstract framework for dealing with differential operators, unbounded observables
Unbounded_operator
result of functional analysis that gives a characterisation of differential operators in terms of their effect on generalized function spaces, and without
Peetre_theorem
Technique for solving differential equations
{\displaystyle T} is a differential operator with respect to x {\displaystyle x} and S {\displaystyle S} is a differential operator with respect to t {\displaystyle
Separation_of_variables
Specification of a derivative along a tangent vector of a manifold
introducing and working with a connection on a manifold by means of a differential operator, to be contrasted with the approach given by a principal connection
Covariant_derivative
Concept in calculus of variations
functional differential (or variation or first variation) is defined. Then the functional derivative is defined in terms of the functional differential. Suppose
Functional_derivative
Determinant of the matrix of first derivatives of a set of functions
ordinary differential equation y ( n ) + L y = 0 {\displaystyle y^{(n)}+Ly=0} (where L {\displaystyle L} is a linear differential operator with respect
Wronskian
Integral transform in mathematics
The Radon transform and its dual are intertwining operators for these two differential operators in the sense that: R ( Δ f ) = L ( R f ) , R ∗ ( L g
Radon_transform
Numerical method for solving differential equations
is a numerical method for solving differential equations that are decomposable into a sum of differential operators. It is named after Gilbert Strang
Strang_splitting
Equation in Fourier analysis
of a unitary group of operators (e.g., the Schrödinger or wave propagator) which encodes the spectrum of a differential operator and the geometric side
Poisson_summation_formula
Distinguished element of a Lie algebra's center
first order differential operators on M. In this situation, the Casimir invariant of ρ is the G-invariant second order differential operator on M defined
Casimir_element
Differential operator
In mathematics, the eta invariant of a self-adjoint elliptic differential operator on a compact manifold is formally the number of positive eigenvalues
Eta_invariant
Mathematical theorem
that the ring of differential operators with constant coefficients, generated by the Di, is commutative; but this is only true as operators over a domain
Symmetry of second derivatives
Symmetry_of_second_derivatives
Class of differential equations expressible in differential algebra
according to the concept of differential algebra used. The intention is to include equations formed by means of differential operators, in which the coefficients
Algebraic differential equation
Algebraic_differential_equation
Expression that may be integrated over a region
In mathematics, differential forms provide a unified approach to define integrands over curves, surfaces, volumes, and higher-dimensional manifolds. The
Differential_form
Analog of the continuous Laplace operator
In mathematics, the discrete Laplace operator is an analog of the continuous Laplace operator, defined so that it has meaning on a graph or a discrete
Discrete_Laplace_operator
Swedish mathematician (1931–2012)
Exposition for his four-volume textbook Analysis of Linear Partial Differential Operators, which is considered a foundational work on the subject. Hörmander
Lars_Hörmander
Ordinary differential equation
write the second-order Cauchy-Euler equation in terms of a linear differential operator L {\displaystyle L} as L y = ( x 2 D 2 + a x D + b I ) y = 0 , {\displaystyle
Cauchy–Euler_equation
Techniques in mathematical analysis
connection with linear partial differential equations, Fourier transform methods, hyperfunctions and pseudo-differential operators. It is concerned with elliptic
Microlocal_analysis
Differential equations involving stochastic processes
evolution to temporal evolution of differential forms is provided by the concept of stochastic evolution operator. In physical science, there is an ambiguity
Stochastic differential equation
Stochastic_differential_equation
Matrix of partial derivatives of a vector-valued function
Jacobian matrix is the natural generalization of the derivative and the differential of a usual function to vector valued functions of several variables.
Jacobian matrix and determinant
Jacobian_matrix_and_determinant
DIFFERENTIAL OPERATOR
DIFFERENTIAL OPERATOR
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.
Girl/Female
Indian, Sanskrit
Name of Lord Shiva; The Operator; One who Maintains Balance Between Life and Death
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
Afghan, Arabic, Muslim, Pashtun
One who can Differentiate; Comely; One who Distinguishes Truth from Falsehood
Surname or Lastname
English
English : from the Old Norse female personal name Gunvǫr, composed of the elements gunn ‘battle’ + vǫr, the feminine form of varr ‘defender’, or possibly from the Old Norse male personal name Gunnarr.English : occupational name for an operator of heavy artillery (see Gunn).Americanized spelling of German Gönner, a habitational name for someone from any of numerous places named Gönne.
DIFFERENTIAL OPERATOR
DIFFERENTIAL OPERATOR
Female
Hebrew
(צִלָה) Hebrew name TSILLAH means "shade, shadow." In the bible, this is the name of Lamech's second wife.
Boy/Male
Arabic, Muslim
Argument; Proof; Reasoning
Girl/Female
Muslim
Rose
Boy/Male
Hindu
Last of Moksha
Boy/Male
Hindu, Indian, Kannada, Marathi, Oriya, Sanskrit, Telugu
Principal; Controller
Boy/Male
Christian & English(British/American/Australian)
Protective Friend
Boy/Male
Indian, Sanskrit
Flame
Girl/Female
Muslim
A narrator of Hadith
Girl/Female
Indian
History
Girl/Female
Australian, Christian, Dutch, French, German, Greek, Italian, Swedish
Gift of God
DIFFERENTIAL OPERATOR
DIFFERENTIAL OPERATOR
DIFFERENTIAL OPERATOR
DIFFERENTIAL OPERATOR
DIFFERENTIAL OPERATOR
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. t.
To obtain the differential, or differential coefficient, of; as, to differentiate an algebraic expression, or an equation.
v. t.
To define or limit by adding a differentia.
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.
n.
An increment, usually an indefinitely small one, which is given to a variable quantity.
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.
v. t.
A determining feature; a distinguishing characteristic; a differentia.
n.
A characteristic or essential attribute; a differential.
a.
That deduces; inferential.
a.
Of or pertaining to a differential, or to differentials.
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.
adv.
In the way of differentiation.
a.
Relating to differences of motion or leverage; producing effects by such differences; said of mechanism.
v. i.
To acquire a distinct and separate character.
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.
n.
The formal or distinguishing part of the essence of a species; the characteristic attribute of a species; specific difference.
pl.
of Differentia
n.
An expression which, being differentiated, will produce a given differential. See differential Differential, and Integration. Cf. Fluent.
a.
Relating to or indicating a difference; creating a difference; discriminating; special; as, differential characteristics; differential duties; a differential rate.
a.
Ready to obey; reverent; differential; also, servilely submissive.