Flashcards: Multivariable calculus

In mathematics, a partial differential equation (PDE) is a differential equation that contains unknown multivariable functions and their partial derivatives.

In calculus, Leibniz's rule for differentiation under the integral sign, named after Gottfried Leibniz, states that for an integral of the form then for x in (x0, x1) the derivative of this integral is thus expressible as provided that f and its partial derivative fx are both continuous over a region in the form [x0, x1] × [y0, y1].

A contour line (also isoline, isopleth, or isarithm) of a function of two variables is a curve along which the function has a constant value.

In calculus (a branch of mathematics), a differentiable function of one real variable is a function whose derivative exists at each point in its domain.

In mathematics, the directional derivative of a multivariate differentiable function along a given vector v at a given point x intuitively represents the instantaneous rate of change of the function, moving through x with a velocity specified by v.

In mathematics, a volume element provides a means for integrating a function with respect to volume in various coordinate systems such as spherical coordinates and cylindrical coordinates.

In mathematics, real coordinate space of n dimensions, written Rn (/ɑːrˈɛn/ ar-EN) (also written ℝn with blackboard bold) is a coordinate space that allows several (n) real variables to be treated as a single variable.

In mathematics, the Laplace operator or Laplacian is a differential operator given by the divergence of the gradient of a function on Euclidean space.

In mathematics, a differential operator is an operator defined as a function of the differentiation operator.

In mathematics, a critical point or stationary point of a differentiable function of a real or complex variable is any value in its domain where its derivative is 0 or undefined.

The multiple integral is a generalization of the definite integral to functions of more than one real variable, for example, f(x, y) or f(x, y, z).