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The following are important identities involving derivatives and integrals in vectorcalculus. For a function f ( x , y , z ) {\displaystyle f(x,y,z)}...
Vectorcalculus or vector analysis is a branch of mathematics concerned with the differentiation and integration of vector fields, primarily in three-dimensional...
such as dot product, cross product, etc. Vector calculusidentities — regarding operations on vector fields such as divergence, gradient, curl, etc. This...
matrix calculus into two separate groups. The two groups can be distinguished by whether they write the derivative of a scalar with respect to a vector as...
trigonometric functions Logarithmic identities Summation identitiesVectorcalculusidentities List of inequalities List of set identities and relations – Equalities...
In mathematics, tensor calculus, tensor analysis, or Ricci calculus is an extension of vectorcalculus to tensor fields (tensors that may vary over a...
The following are important identities in vector algebra. Identities that involve the magnitude of a vector ‖ A ‖ {\displaystyle \|\mathbf {A} \|} , or...
or nabla, is an operator used in mathematics (particularly in vectorcalculus) as a vector differential operator, usually represented by the nabla symbol...
In vectorcalculus, a Laplacian vector field is a vector field which is both irrotational and incompressible. If the field is denoted as v, then it is...
In vectorcalculus and physics, a vector field is an assignment of a vector to each point in a space, most commonly Euclidean space R n {\displaystyle...
and can be shown to encompass other mathematical theories including vectorcalculus, differential geometry, and differential forms. With a geometric algebra...
theorem or the fundamental theorem of vectorcalculus states that any sufficiently smooth, rapidly decaying vector field in three dimensions can be resolved...
of multivariable calculus topics. See also multivariable calculus, vectorcalculus, list of real analysis topics, list of calculus topics. Closed and...
In vectorcalculus a solenoidal vector field (also known as an incompressible vector field, a divergence-free vector field, or a transverse vector field)...
This is a list of some vectorcalculus formulae for working with common curvilinear coordinate systems. This article uses the standard notation ISO 80000-2...
physics, and engineering, a Euclidean vector or simply a vector (sometimes called a geometric vector or spatial vector) is a geometric object that has magnitude...
space. The special case of calculus in three dimensional space is often called vectorcalculus. In single-variable calculus, operations like differentiation...
In vectorcalculus, the gradient of a scalar-valued differentiable function f {\displaystyle f} of several variables is the vector field (or vector-valued...
In vectorcalculus, the Jacobian matrix (/dʒəˈkoʊbiən/, /dʒɪ-, jɪ-/) of a vector-valued function of several variables is the matrix of all its first-order...
This article summarizes several identities in exterior calculus. The following summarizes short definitions and notations that are used in this article...
manipulating indices, such as using index notation to verify vectorcalculusidentities or identities of the Kronecker delta and Levi-Civita symbol (see also...
B_{z}\end{bmatrix}}.} This identity is a coordinate dependent result, and is not general. An example of the usage of the vector Laplacian is the Navier-Stokes...
In vectorcalculus and differential geometry the generalized Stokes theorem (sometimes with apostrophe as Stokes' theorem or Stokes's theorem), also called...
In vectorcalculus, divergence is a vector operator that operates on a vector field, producing a scalar field giving the quantity of the vector field's...
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