Faster access than browser!
76 relations: Basis (linear algebra), Bipolar cylindrical coordinates, Bispherical coordinates, Boundary value problem, Cartesian coordinate system, Chemical species, Classical electromagnetism, Complex number, Conformal map, Conical coordinates, Covariance and contravariance of vectors, Cross product, Curl (mathematics), Curvilinear coordinates, Cylindrical coordinate system, Del, Diffusion, Divergence, Dot product, Einstein notation, Ellipsoidal coordinates, Elliptic cylindrical coordinates, Eric W. Weisstein, Euclidean space, Exponentiation, Fluid dynamics, Gradient, Heat, Helmholtz equation, Holomorphic function, Imaginary unit, Infinitesimal, Interval (mathematics), Jacobian matrix and determinant, Kronecker delta, Laplace operator, Laplace's equation, Length, Levi-Civita symbol, Line element, Line integral, Linear elasticity, Mathematics, MathWorld, Metric tensor, Normal (geometry), Oblate spheroidal coordinates, Ordinary differential equation, Orthogonal trajectory, Orthogonality, ..., Orthonormality, Parabolic cylindrical coordinates, Paraboloidal coordinates, Parametric equation, Partial differential equation, Pi (letter), Product (mathematics), Prolate spheroidal coordinates, Quantum mechanics, Reciprocal length, Scalar field, Separation of variables, Sigma, Skew coordinates, Spherical coordinate system, Summation, Surface (mathematics), Surface integral, Tensor, Toroidal coordinates, Unit vector, Vector area, Vector field, Vector Laplacian, Volume, Volume element. Expand index (26 more) »
Basis (linear algebra)
In mathematics, a set of elements (vectors) in a vector space V is called a basis, or a set of, if the vectors are linearly independent and every vector in the vector space is a linear combination of this set.
New!!: Orthogonal coordinates and Basis (linear algebra) · See more »
Bipolar cylindrical coordinates
Bipolar cylindrical coordinates are a three-dimensional orthogonal coordinate system that results from projecting the two-dimensional bipolar coordinate system in the perpendicular z-direction.
New!!: Orthogonal coordinates and Bipolar cylindrical coordinates · See more »
Bispherical coordinates
Bispherical coordinates are a three-dimensional orthogonal coordinate system that results from rotating the two-dimensional bipolar coordinate system about the axis that connects the two foci.
New!!: Orthogonal coordinates and Bispherical coordinates · See more »
Boundary value problem
In mathematics, in the field of differential equations, a boundary value problem is a differential equation together with a set of additional constraints, called the boundary conditions.
New!!: Orthogonal coordinates and Boundary value problem · See more »
Cartesian coordinate system
A Cartesian coordinate system is a coordinate system that specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular directed lines, measured in the same unit of length.
New!!: Orthogonal coordinates and Cartesian coordinate system · See more »
Chemical species
A chemical species is a chemical substance or ensemble composed of chemically identical molecular entities that can explore the same set of molecular energy levels on a characteristic or delineated time scale.
New!!: Orthogonal coordinates and Chemical species · See more »
Classical electromagnetism
Classical electromagnetism or classical electrodynamics is a branch of theoretical physics that studies the interactions between electric charges and currents using an extension of the classical Newtonian model.
New!!: Orthogonal coordinates and Classical electromagnetism · See more »
Complex number
A complex number is a number that can be expressed in the form, where and are real numbers, and is a solution of the equation.
New!!: Orthogonal coordinates and Complex number · See more »
Conformal map
In mathematics, a conformal map is a function that preserves angles locally.
New!!: Orthogonal coordinates and Conformal map · See more »
Conical coordinates
Conical coordinates are a three-dimensional orthogonal coordinate system consisting of concentric spheres (described by their radius) and by two families of perpendicular cones, aligned along the - and -axes, respectively.
New!!: Orthogonal coordinates and Conical coordinates · See more »
Covariance and contravariance of vectors
In multilinear algebra and tensor analysis, covariance and contravariance describe how the quantitative description of certain geometric or physical entities changes with a change of basis.
New!!: Orthogonal coordinates and Covariance and contravariance of vectors · See more »
Cross product
In mathematics and vector algebra, the cross product or vector product (occasionally directed area product to emphasize the geometric significance) is a binary operation on two vectors in three-dimensional space \left(\mathbb^3\right) and is denoted by the symbol \times.
New!!: Orthogonal coordinates and Cross product · See more »
Curl (mathematics)
In vector calculus, the curl is a vector operator that describes the infinitesimal rotation of a vector field in three-dimensional Euclidean space.
New!!: Orthogonal coordinates and Curl (mathematics) · See more »
Curvilinear coordinates
In geometry, curvilinear coordinates are a coordinate system for Euclidean space in which the coordinate lines may be curved.
New!!: Orthogonal coordinates and Curvilinear coordinates · See more »
Cylindrical coordinate system
A cylindrical coordinate system is a three-dimensional coordinate system that specifies point positions by the distance from a chosen reference axis, the direction from the axis relative to a chosen reference direction, and the distance from a chosen reference plane perpendicular to the axis.
New!!: Orthogonal coordinates and Cylindrical coordinate system · See more »
Del
Del, or nabla, is an operator used in mathematics, in particular in vector calculus, as a vector differential operator, usually represented by the nabla symbol ∇.
New!!: Orthogonal coordinates and Del · See more »
Diffusion
Diffusion is the net movement of molecules or atoms from a region of high concentration (or high chemical potential) to a region of low concentration (or low chemical potential) as a result of random motion of the molecules or atoms.
New!!: Orthogonal coordinates and Diffusion · See more »
Divergence
In vector calculus, divergence is a vector operator that produces a scalar field, giving the quantity of a vector field's source at each point.
New!!: Orthogonal coordinates and Divergence · See more »
Dot product
In mathematics, the dot product or scalar productThe term scalar product is often also used more generally to mean a symmetric bilinear form, for example for a pseudo-Euclidean space.
New!!: Orthogonal coordinates and Dot product · See more »
Einstein notation
In mathematics, especially in applications of linear algebra to physics, the Einstein notation or Einstein summation convention is a notational convention that implies summation over a set of indexed terms in a formula, thus achieving notational brevity.
New!!: Orthogonal coordinates and Einstein notation · See more »
Ellipsoidal coordinates
Ellipsoidal coordinates are a three-dimensional orthogonal coordinate system (\lambda, \mu, \nu) that generalizes the two-dimensional elliptic coordinate system.
New!!: Orthogonal coordinates and Ellipsoidal coordinates · See more »
Elliptic cylindrical coordinates
Elliptic cylindrical coordinates are a three-dimensional orthogonal coordinate system that results from projecting the two-dimensional elliptic coordinate system in the perpendicular z-direction.
New!!: Orthogonal coordinates and Elliptic cylindrical coordinates · See more »
Eric W. Weisstein
Eric Wolfgang Weisstein (born March 18, 1969) is an encyclopedist who created and maintains MathWorld and Eric Weisstein's World of Science (ScienceWorld).
New!!: Orthogonal coordinates and Eric W. Weisstein · See more »
Euclidean space
In geometry, Euclidean space encompasses the two-dimensional Euclidean plane, the three-dimensional space of Euclidean geometry, and certain other spaces.
New!!: Orthogonal coordinates and Euclidean space · See more »
Exponentiation
Exponentiation is a mathematical operation, written as, involving two numbers, the base and the exponent.
New!!: Orthogonal coordinates and Exponentiation · See more »
Fluid dynamics
In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids - liquids and gases.
New!!: Orthogonal coordinates and Fluid dynamics · See more »
Gradient
In mathematics, the gradient is a multi-variable generalization of the derivative.
New!!: Orthogonal coordinates and Gradient · See more »
Heat
In thermodynamics, heat is energy transferred from one system to another as a result of thermal interactions.
New!!: Orthogonal coordinates and Heat · See more »
Helmholtz equation
In mathematics & physics, the Helmholtz equation, named for Hermann von Helmholtz, is the partial differential equation where ∇2 is the Laplacian, k is the wavenumber, and A is the amplitude.
New!!: Orthogonal coordinates and Helmholtz equation · See more »
Holomorphic function
In mathematics, a holomorphic function is a complex-valued function of one or more complex variables that is complex differentiable in a neighborhood of every point in its domain.
New!!: Orthogonal coordinates and Holomorphic function · See more »
Imaginary unit
The imaginary unit or unit imaginary number is a solution to the quadratic equation.
New!!: Orthogonal coordinates and Imaginary unit · See more »
Infinitesimal
In mathematics, infinitesimals are things so small that there is no way to measure them.
New!!: Orthogonal coordinates and Infinitesimal · See more »
Interval (mathematics)
In mathematics, a (real) interval is a set of real numbers with the property that any number that lies between two numbers in the set is also included in the set.
New!!: Orthogonal coordinates and Interval (mathematics) · See more »
Jacobian matrix and determinant
In vector calculus, the Jacobian matrix is the matrix of all first-order partial derivatives of a vector-valued function.
New!!: Orthogonal coordinates and Jacobian matrix and determinant · See more »
Kronecker delta
In mathematics, the Kronecker delta (named after Leopold Kronecker) is a function of two variables, usually just non-negative integers.
New!!: Orthogonal coordinates and Kronecker delta · See more »
Laplace operator
In mathematics, the Laplace operator or Laplacian is a differential operator given by the divergence of the gradient of a function on Euclidean space.
New!!: Orthogonal coordinates and Laplace operator · See more »
Laplace's equation
In mathematics, Laplace's equation is a second-order partial differential equation named after Pierre-Simon Laplace who first studied its properties.
New!!: Orthogonal coordinates and Laplace's equation · See more »
Length
In geometric measurements, length is the most extended dimension of an object.
New!!: Orthogonal coordinates and Length · See more »
Levi-Civita symbol
In mathematics, particularly in linear algebra, tensor analysis, and differential geometry, the Levi-Civita symbol represents a collection of numbers; defined from the sign of a permutation of the natural numbers, for some positive integer.
New!!: Orthogonal coordinates and Levi-Civita symbol · See more »
Line element
In geometry, the line element or length element can be informally thought of as a line segment associated with an infinitesimal displacement vector in a metric space.
New!!: Orthogonal coordinates and Line element · See more »
Line integral
In mathematics, a line integral is an integral where the function to be integrated is evaluated along a curve.
New!!: Orthogonal coordinates and Line integral · See more »
Linear elasticity
Linear elasticity is the mathematical study of how solid objects deform and become internally stressed due to prescribed loading conditions.
New!!: Orthogonal coordinates and Linear elasticity · See more »
Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
New!!: Orthogonal coordinates and Mathematics · See more »
MathWorld
MathWorld is an online mathematics reference work, created and largely written by Eric W. Weisstein.
New!!: Orthogonal coordinates and MathWorld · See more »
Metric tensor
In the mathematical field of differential geometry, a metric tensor is a type of function which takes as input a pair of tangent vectors and at a point of a surface (or higher dimensional differentiable manifold) and produces a real number scalar in a way that generalizes many of the familiar properties of the dot product of vectors in Euclidean space.
New!!: Orthogonal coordinates and Metric tensor · See more »
Normal (geometry)
In geometry, a normal is an object such as a line or vector that is perpendicular to a given object.
New!!: Orthogonal coordinates and Normal (geometry) · See more »
Oblate spheroidal coordinates
Oblate spheroidal coordinates are a three-dimensional orthogonal coordinate system that results from rotating the two-dimensional elliptic coordinate system about the non-focal axis of the ellipse, i.e., the symmetry axis that separates the foci.
New!!: Orthogonal coordinates and Oblate spheroidal coordinates · See more »
Ordinary differential equation
In mathematics, an ordinary differential equation (ODE) is a differential equation containing one or more functions of one independent variable and its derivatives.
New!!: Orthogonal coordinates and Ordinary differential equation · See more »
Orthogonal trajectory
In mathematics an orthogonal trajectory is.
New!!: Orthogonal coordinates and Orthogonal trajectory · See more »
Orthogonality
In mathematics, orthogonality is the generalization of the notion of perpendicularity to the linear algebra of bilinear forms.
New!!: Orthogonal coordinates and Orthogonality · See more »
Orthonormality
In linear algebra, two vectors in an inner product space are orthonormal if they are orthogonal and unit vectors.
New!!: Orthogonal coordinates and Orthonormality · See more »
Parabolic cylindrical coordinates
In mathematics, parabolic cylindrical coordinates are a three-dimensional orthogonal coordinate system that results from projecting the two-dimensional parabolic coordinate system in the perpendicular z-direction.
New!!: Orthogonal coordinates and Parabolic cylindrical coordinates · See more »
Paraboloidal coordinates
Paraboloidal coordinates are a three-dimensional orthogonal coordinate system (\lambda, \mu, \nu) that generalizes the two-dimensional parabolic coordinate system.
New!!: Orthogonal coordinates and Paraboloidal coordinates · See more »
Parametric equation
In mathematics, a parametric equation defines a group of quantities as functions of one or more independent variables called parameters.
New!!: Orthogonal coordinates and Parametric equation · See more »
Partial differential equation
In mathematics, a partial differential equation (PDE) is a differential equation that contains unknown multivariable functions and their partial derivatives.
New!!: Orthogonal coordinates and Partial differential equation · See more »
Pi (letter)
Pi (uppercase Π, lowercase π; πι) is the sixteenth letter of the Greek alphabet, representing the sound.
New!!: Orthogonal coordinates and Pi (letter) · See more »
Product (mathematics)
In mathematics, a product is the result of multiplying, or an expression that identifies factors to be multiplied.
New!!: Orthogonal coordinates and Product (mathematics) · See more »
Prolate spheroidal coordinates
Prolate spheroidal coordinates are a three-dimensional orthogonal coordinate system that results from rotating the two-dimensional elliptic coordinate system about the focal axis of the ellipse, i.e., the symmetry axis on which the foci are located.
New!!: Orthogonal coordinates and Prolate spheroidal coordinates · See more »
Quantum mechanics
Quantum mechanics (QM; also known as quantum physics, quantum theory, the wave mechanical model, or matrix mechanics), including quantum field theory, is a fundamental theory in physics which describes nature at the smallest scales of energy levels of atoms and subatomic particles.
New!!: Orthogonal coordinates and Quantum mechanics · See more »
Reciprocal length
Reciprocal length or inverse length is a measurement used in several branches of science and mathematics.
New!!: Orthogonal coordinates and Reciprocal length · See more »
Scalar field
In mathematics and physics, a scalar field associates a scalar value to every point in a space – possibly physical space.
New!!: Orthogonal coordinates and Scalar field · See more »
Separation of variables
In mathematics, separation of variables (also known as the Fourier method) is any of several methods for solving ordinary and partial differential equations, in which algebra allows one to rewrite an equation so that each of two variables occurs on a different side of the equation.
New!!: Orthogonal coordinates and Separation of variables · See more »
Sigma
Sigma (upper-case Σ, lower-case σ, lower-case in word-final position ς; σίγμα) is the eighteenth letter of the Greek alphabet.
New!!: Orthogonal coordinates and Sigma · See more »
Skew coordinates
A system of skew coordinates is a curvilinear coordinate system where the coordinate surfaces are not orthogonal, in contrast to orthogonal coordinates.
New!!: Orthogonal coordinates and Skew coordinates · See more »
Spherical coordinate system
In mathematics, a spherical coordinate system is a coordinate system for three-dimensional space where the position of a point is specified by three numbers: the radial distance of that point from a fixed origin, its polar angle measured from a fixed zenith direction, and the azimuth angle of its orthogonal projection on a reference plane that passes through the origin and is orthogonal to the zenith, measured from a fixed reference direction on that plane.
New!!: Orthogonal coordinates and Spherical coordinate system · See more »
Summation
In mathematics, summation (capital Greek sigma symbol: ∑) is the addition of a sequence of numbers; the result is their sum or total.
New!!: Orthogonal coordinates and Summation · See more »
Surface (mathematics)
In mathematics, a surface is a generalization of a plane which needs not be flat, that is, the curvature is not necessarily zero.
New!!: Orthogonal coordinates and Surface (mathematics) · See more »
Surface integral
In mathematics, a surface integral is a generalization of multiple integrals to integration over surfaces.
New!!: Orthogonal coordinates and Surface integral · See more »
Tensor
In mathematics, tensors are geometric objects that describe linear relations between geometric vectors, scalars, and other tensors.
New!!: Orthogonal coordinates and Tensor · See more »
Toroidal coordinates
Toroidal coordinates are a three-dimensional orthogonal coordinate system that results from rotating the two-dimensional bipolar coordinate system about the axis that separates its two foci.
New!!: Orthogonal coordinates and Toroidal coordinates · See more »
Unit vector
In mathematics, a unit vector in a normed vector space is a vector (often a spatial vector) of length 1.
New!!: Orthogonal coordinates and Unit vector · See more »
Vector area
In 3-dimensional geometry, for a finite planar surface of scalar area and unit normal, the vector area is defined as the unit normal scaled by the area: For an orientable surface composed of a set of flat facet areas, the vector area of the surface is given by where is the unit normal vector to the area.
New!!: Orthogonal coordinates and Vector area · See more »
Vector field
In vector calculus and physics, a vector field is an assignment of a vector to each point in a subset of space.
New!!: Orthogonal coordinates and Vector field · See more »
Vector Laplacian
In mathematics and physics, the vector Laplace operator, denoted by \nabla^2, named after Pierre-Simon Laplace, is a differential operator defined over a vector field.
New!!: Orthogonal coordinates and Vector Laplacian · See more »
Volume
Volume is the quantity of three-dimensional space enclosed by a closed surface, for example, the space that a substance (solid, liquid, gas, or plasma) or shape occupies or contains.
New!!: Orthogonal coordinates and Volume · See more »
Volume element
In mathematics, a volume element provides a means for integrating a function with respect to volume in various coordinate systems such as spherical coordinates and cylindrical coordinates.
New!!: Orthogonal coordinates and Volume element · See more »
Redirects here:
Orthogonal coordinate, Orthogonal coordinate system.
References
[1] https://en.wikipedia.org/wiki/Orthogonal_coordinates
