## Vector calculus

In vector calculus, curl is a vector operator that shows a vector field's rate of rotation: the direction of the axis of rotation and the magnitude of the rotation. It can also be described as the circulation density. ...more on Wikipedia about "Curl"

In vector calculus, del is a vector differential operator represented by the nabla symbol, ∇. ...more on Wikipedia about "Del"

In vector calculus, the divergence is an operator that measures a vector field's tendency to originate from or converge upon a given point. For instance, for a vector field that denotes the velocity of water flowing in a draining bathtub, the divergence would have a negative value over the drain because the water vanishes there (if we only consider two dimensions); away from the drain the divergence would be zero, since there are no other sinks or sources. ...more on Wikipedia about "Divergence"

In vector calculus, the divergence theorem, also known as Gauss' theorem, Ostrogradsky's theorem, or Ostrogradskyâ€“Gauss theorem is a result that relates the outward flow of a vector field on a surface to the behaviour of the vector field inside the surface. ...more on Wikipedia about "Divergence theorem"

The fundamental theorem of vector calculus, also known as Helmholtz's theorem, states that any vector field meeting certain conditions (of decaying towards infinity) can be resolved into irrotational (curl-free) and solenoidal (divergence-free) component vector fields. ...more on Wikipedia about "Fundamental theorem of vector analysis"

Gradient is commonly used to describe the measure of the slope (also called steepness, or incline) of a straight line. It is also sometimes used synonymously with grade, meaning the inclination of a surface along a given direction. ...more on Wikipedia about "Gradient"

Green's identities are a set of three identities in vector calculus. They are named after the mathematician George Green, who discovered Green's theorem. ...more on Wikipedia about "Green's identities"

In physics and mathematics, Green's theorem gives the relationship between a line integral around a simple closed curve C and a double integral over the plane region D bounded by C. Green's theorem was named after British scientist George Green and is a special case of the more general Stokes' theorem. ...more on Wikipedia about "Green's theorem"

In fluid mechanics, Helmholtz's theorems describe the behaviour of vortex lines in a fluid. The theorems apply to fluids that are inviscid (ie without viscosity), incompressible, of constant density and under the influence of a conservative body force (such as gravity). The theorems were published by Hermann von Helmholtz in 1858. ...more on Wikipedia about "Helmholtz's theorems"

In vector calculus, an irrotational or conservative vector field is a vector field whose curl is zero. If the field is denoted as v, then ...more on Wikipedia about "Irrotational vector field"

In vector analysis and in fluid dynamics, a lamellar vector field is a vector field with no rotational component. That is, if the field is denoted as v, then ...more on Wikipedia about "Lamellar vector field"

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 described by the following differential equations: ...more on Wikipedia about "Laplacian vector field"

In mathematical physics, a multipole expansion is a series expansion of the effect produced by localized source terms in a given partial differential equation, most commonly Poisson's equation (for electrostatics and gravity), in spherical coordinates or cylindrical coordinates. Typically, the expansion is in terms of spherical harmonics or related angular functions multiplied by an appropriate radial dependence. In order for the expansion to be convergent and useful, one relies on the property that the higher-order terms in the expansion decay increasingly quickly far away from the sources. In this case, the leading terms in a multipole expansion are generally the most significant, and the low-order behavior of the system at large distances can be approximated by the first few terms of the expansion, which are usually much easier to compute than the general solution. ...more on Wikipedia about "Multipole expansion"

This is a list of some vector calculus formulae of general use in working with standard coordinate systems. ...more on Wikipedia about "Nabla in cylindrical and spherical coordinates"

The parallelogram of forces is a method for solving (or visualizing) the results of applying several different forces to an object. It utilizes the principles of vectors to solve this problem called vector addition. ...more on Wikipedia about "Parallelogram of force"

In mathematics, a path integral (also known as a line integral) is an integral where the function to be integrated is evaluated along a path or curve. Various different path integrals are in use. In the case of a closed path it is also called a contour integral. ...more on Wikipedia about "Path integral"

This result can easily be proven by splitting the vectors into components and applying the product rule. Now using the definitions of velocity v = dr/dt, acceleration a = dv/dt and linear momentum p = mv, we can see that: ...more on Wikipedia about "Proof of angular momentum"

In physics and mathematics, a pseudovector (or axial vector) is a quantity that transforms like a vector under a proper rotation, but gains an additional sign flip under an improper rotation (a transformation that can be expressed as an inversion followed by a proper rotation). The conceptual opposite of a pseudovector is a (true) vector or a polar vector. ...more on Wikipedia about "Pseudovector"

The scalar resolute of a vector $\mathbf\left\{b\right\}$ in the direction of a vector $\mathbf\left\{a\right\}$ (also "$\mathbf\left\{b\right\}$ on $\mathbf\left\{a\right\}$"), is given by: ...more on Wikipedia about "Scalar resolute"

In vector calculus a solenoidal vector field is a vector field v with divergence zero: ...more on Wikipedia about "Solenoidal vector field"

Stokes' theorem in differential geometry is a statement about the integration of differential forms which generalizes several theorems from vector calculus. It is named after Sir George Gabriel Stokes ( 1819- 1903). The theorem acquired its name from Stokes' habit of including it in the Cambridge prize examinations. ...more on Wikipedia about "Stokes theorem"

A surface normal, or just normal to a ...more on Wikipedia about "Surface normal"