The following are important identities involving derivatives and integrals in vector calculus. For a function f ( x , y , z ) {\displaystyle f(x,y,z)}...
40 KB (6,539 words) - 07:06, 26 April 2025
Vector calculus or vector analysis is a branch of mathematics concerned with the differentiation and integration of vector fields, primarily in three-dimensional...
22 KB (2,135 words) - 04:00, 8 April 2025
In mathematics, Green's identities are a set of three identities in vector calculus relating the bulk with the boundary of a region on which differential...
22 KB (3,781 words) - 15:51, 27 May 2025
such as dot product, cross product, etc. Vector calculus identities — regarding operations on vector fields such as divergence, gradient, curl, etc. This...
356 bytes (48 words) - 11:14, 12 October 2024
The following are important identities in vector algebra. Identities that only involve the magnitude of a vector ‖ A ‖ {\displaystyle \|\mathbf {A} \|}...
14 KB (2,287 words) - 21:44, 4 May 2025
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...
85 KB (7,062 words) - 19:08, 25 May 2025
Del (redirect from Vector differential)
or nabla, is an operator used in mathematics (particularly in vector calculus) as a vector differential operator, usually represented by the nabla symbol...
22 KB (3,923 words) - 07:28, 22 May 2025
of trigonometric identities Inverse trigonometric functions Logarithmic identities Summation identities Vector calculus identities List of inequalities...
2 KB (175 words) - 11:10, 21 June 2024
In vector calculus, a conservative vector field is a vector field that is the gradient of some function. A conservative vector field has the property...
23 KB (3,529 words) - 10:53, 16 March 2025
manipulating indices, such as using index notation to verify vector calculus identities or identities of the Kronecker delta and Levi-Civita symbol (see also...
46 KB (7,275 words) - 03:10, 13 January 2025
In vector calculus, a Laplacian vector field is a vector field which is both irrotational and incompressible. If the field is denoted as v, then it is...
7 KB (958 words) - 12:05, 30 April 2025
This article summarizes several identities in exterior calculus, a mathematical notation used in differential geometry. The following summarizes short...
29 KB (5,477 words) - 00:13, 17 May 2024
Differentiation rules (redirect from List of differentiation identities)
Matrix calculus – Specialized notation for multivariable calculus Trigonometric functions – Functions of an angle Vector calculus identities – Mathematical...
18 KB (2,820 words) - 03:07, 20 April 2025
Curl (mathematics) (redirect from Curl (vector calculus))
In vector calculus, the curl, also known as rotor, is a vector operator that describes the infinitesimal circulation of a vector field in three-dimensional...
34 KB (5,050 words) - 04:31, 3 May 2025
Product rule (redirect from Product Rule (Calculus))
displaying short descriptions of redirect targets Vector calculus identities – Mathematical identities "Leibniz rule – Encyclopedia of Mathematics". Michelle...
20 KB (4,162 words) - 03:09, 20 April 2025
In vector calculus and physics, a vector field is an assignment of a vector to each point in a space, most commonly Euclidean space R n {\displaystyle...
28 KB (4,076 words) - 01:44, 23 February 2025
Helmholtz decomposition (redirect from Fundamental theorem of vector calculus)
theorem of vector calculus states that certain differentiable vector fields can be resolved into the sum of an irrotational (curl-free) vector field and...
44 KB (7,266 words) - 03:08, 20 April 2025
In vector calculus a solenoidal vector field (also known as an incompressible vector field, a divergence-free vector field, or a transverse vector field)...
4 KB (430 words) - 08:36, 28 November 2024
Quotient rule (redirect from Quotient Rule (calculus))
Rules for computing derivatives of functionsPages displaying short descriptions of redirect targets Vector calculus identities – Mathematical identities...
7 KB (1,880 words) - 03:09, 20 April 2025
Gradient (redirect from Gradient (calculus))
In vector calculus, the gradient of a scalar-valued differentiable function f {\displaystyle f} of several variables is the vector field (or vector-valued...
38 KB (5,701 words) - 13:15, 12 March 2025
Laplace operator (redirect from Vector Laplacian)
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...
30 KB (4,682 words) - 03:20, 8 May 2025
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...
61 KB (9,116 words) - 12:01, 7 May 2025
of multivariable calculus topics. See also multivariable calculus, vector calculus, list of real analysis topics, list of calculus topics. Closed and...
2 KB (156 words) - 12:13, 30 October 2023
is the negative gradient of the electric potential, as well as vector calculus identities in a way that resembles integration by parts. These two integrals...
19 KB (2,613 words) - 18:35, 27 May 2025
Matrix multiplication (redirect from Matrix–vector multiplication)
Matrix calculus, for the interaction of matrix multiplication with operations from calculus Nykamp, Duane. "Multiplying matrices and vectors". Math Insight...
41 KB (6,581 words) - 13:39, 28 February 2025
Reciprocal rule (category Theorems in calculus)
Rules for computing derivatives of functionsPages displaying short descriptions of redirect targets Vector calculus identities – Mathematical identities...
6 KB (1,345 words) - 03:10, 20 April 2025
Derivative (redirect from Derivative (calculus))
variables, with the others held constant. Partial derivatives are used in vector calculus and differential geometry. As with ordinary derivatives, multiple notations...
57 KB (7,280 words) - 20:54, 25 May 2025
Del in cylindrical and spherical coordinates (category Vector calculus)
This is a list of some vector calculus formulae for working with common curvilinear coordinate systems. This article uses the standard notation ISO 80000-2...
34 KB (2,828 words) - 18:09, 23 February 2025
related fields, Malliavin calculus is a set of mathematical techniques and ideas that extend the mathematical field of calculus of variations from deterministic...
16 KB (2,660 words) - 13:14, 11 May 2025
calculus in three dimensional space is often called vector calculus. In single-variable calculus, operations like differentiation and integration are...
19 KB (2,369 words) - 21:13, 2 February 2025