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Science Mathematics Calculus and analysis Multivariable and vector calculus

Multivariable and vector calculus

Conservative vector field

Vector field that is the gradient of some function

Curl (mathematics)

Vector operator describing circulation density at a point in a 3D vector field

Vector differential operator

Differential form

Expression that may be integrated over a region

Directional derivative

Instantaneous rate of change of the function

Vector operator that measures how much a field vector is growing or fading

Divergence theorem

Theorem in calculus which relates the flux of closed surfaces to divergence over their volume

Generalized Stokes theorem

Statement about the integration of differential forms on manifolds

Multi-variable generalization of the derivative of a function

Gradient theorem

Evaluates a line integral through a gradient field using the original scaler field

Green's theorem

Theorem in calculus relating line and double integrals

Helmholtz decomposition

Certain vector fields are the sum of an irrotational and a solenoidal vector field

Iterated integral

Type of integral of functions of multiple variables

Jacobian matrix and determinant

Matrix of all first-order partial derivatives of a vector-valued function

Lagrange multiplier

A method to solve constrained optimization problems

Laplace operator

Differential operator

Laplace's equation

Second order partial differential equation

Definite integral of a scalar or vector field along a path

Multiple integral

Generalization of definite integrals to functions of multiple variables

Multivariable calculus

Calculus of functions of several independent variables

Partial derivative

Derivative of a function of several variables with respect to one variable, with the others held constant

Poisson's equation

elliptic partial differential equation

Extension of vector calculus to tensors

Solenoidal vector field

Vector field with zero divergence

Surface integral

Integration over a non-flat region in 3D space

Total derivative

Derivative of a function of several variables with respect to one variable, without the others held constant

Vector calculus

Calculus of vector-valued functions

Assignment of a vector to each point in a subset of Euclidean space

Volume integral

Integral over a 3-D domain