Multivariable calculus

curve joining points with equal value on a 2D graphic representation

differential equation that contains unknown multivariable functions and their partial derivatives

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

infinite sum of monomials

thumb|A migrating wild-type Dictyostelium discoideum cell whose boundary is colored by curvature. Scale bar: 5 μm.

assignment of numbers to points in space

divergence of the gradient

integral over a multi-dimensional region of a function of several variables

function whose derivative exists at each point in its domain

parametric system of coordinates

generalization of a multiple integral to (possibly)-curved surfaces

the matrix of all first-order partial derivatives of a vector-valued function

a method to solve constrained optimization problems

stationary point that is not a local extremum

matrix of second derivatives

calculus of functions of several independent variables

function defined by a relation of the form 𝑅(𝑥,𝑦)=0, where 𝑅 is a function of several variables and there is a unique 𝑦 that satisfies the relation for every 𝑥

typically linear operator defined in terms of differentiation of functions

instantaneous rate of change of the function

in calculus, the points of an equation where the derivative is zero

geometric inequality which sets a lower bound on the surface area of a set given its volume

radius of a circle which best approximates a curve in a given point

definite integral of a vector function over a volume

theorem that, if a function is continuously differentiable with nonzero Jacobian determinant at a given point, then it is locally invertible near that point

subset of a function's domain on which its value is equal

differentiation under the integral sign formula

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

time rate of change of a physical quantity in a moving medium

formulas in differential geometry

theorem

thumb|Computed electrostatic equipotentials (black contours) between two electrically charged spheres

mathematics term

mathematical surface

theorem that the set of the critical values of a smooth function has measure zero

specialized notation for multivariable calculus

function whose domain a subset of real numbers

method for integrating a function with respect to its volume in different coordinate system

function with more than one argument, with all arguments being real variables

type of infinitesimal in calculus

functions of multiple variables which are complex numbers

Function in image processing

Type of mathematical function