function of several real variables or real multivariate function is a function with more than one argument, with all arguments being real variables....

))={\mathfrak {c}}} . Real analysis Function of several real variables Complex analysis Function of several complex variables R. Courant. Differential...

The theory of functions of several complex variables is the branch of mathematics dealing with functions defined on the complex coordinate space C n {\displaystyle...

Real-valued functions of a real variable (commonly called real functions) and real-valued functions of several real variables are the main object of study...

mathematics, a homogeneous function is a function of several variables such that the following holds: If each of the function's arguments is multiplied by...

calculus, the implicit function theorem is a tool that allows relations to be converted to functions of several real variables. It does so by representing...

derivative is equal to zero (or the function is not holomorphic). Likewise, for a function of several real variables, a critical point is a value in its...

point where the function "stops" increasing or decreasing (hence the name). For a differentiable function of several real variables, a stationary point...

differentiable function of one real variable is a function whose derivative exists at each point in its domain. In other words, the graph of a differentiable...

variables. For a real-valued function of several variables, the Jacobian matrix reduces to the gradient vector. A function of a real variable f ( x ) {\displaystyle...

of the system is generally determined by a finite set of coordinates, and the parametrization thus consists of one function of several real variables...

power series). Analytic functions of several variables have some of the same properties as analytic functions of one variable. However, especially for...

of real analysis studies the behavior of real numbers, sequences and series of real numbers, and real functions. Some particular properties of real-valued...

function of several real variables or of a function of several complex variables. There are various standard ways for denoting functions. The most commonly...

analytic functions of a complex variable, that is, holomorphic functions. The concept can be extended to functions of several complex variables. Complex...

definite integral of a function of several real variables, for instance, f(x, y) or f(x, y, z). Integrals of a function of two variables over a region in...

case of many variables, as some of them are not listed for functions of one variable. Suppose f {\displaystyle f} is a function of one real variable defined...

cumulative distribution function (CDF) of a real-valued random variable X {\displaystyle X} , or just distribution function of X {\displaystyle X} , evaluated...

In probability theory, there exist several different notions of convergence of sequences of random variables, including convergence in probability, convergence...

equations of several variables. For sufficiently smooth functions on the real line, the Legendre transform f ∗ {\displaystyle f^{*}} of a function f {\displaystyle...

holomorphic function is a complex-valued function of one or more complex variables that is complex differentiable in a neighbourhood of each point in...

a real number. So, in multivariable calculus, the domain of a function of several real variables and the codomain of a real vector valued function are...

positive-semidefinite real matrices are at the basis of convex optimization, since, given a function of several real variables that is twice differentiable...

a subset of three-dimensional space; for a continuous real-valued function of two real variables, its graph forms a surface, which can be visualized as...

distribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is f ( x ) =...

supposed to be real numbers, and the function is considered as a real function that maps real numbers to real numbers or as a complex function that maps complex...

single complex variable z = x + iy where x and y are real variables; u and v are real differentiable functions of the real variables. Then f is complex...

end of the alphabet such as (x, y, z) are commonly used for unknowns and variables of functions. In printed mathematics, the norm is to set variables and...

of functions of several real variables, a stationary point that is not a local extremum is called a saddle point. An example of a stationary point of...

the equation of the plane tangent to the graph of z = f(x, y) at (a, b). For a continuously differentiable function of several real variables, a point P...