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 (23 February...

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...

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

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...

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...

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...

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

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...

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...

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...

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...

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

of real vectors, and whose imaginary part is unconstrained. Tube domains are domains of the Laplace transform of a function of several real variables...

along the graph has a finite value. For a continuous function of several variables, the meaning of the definition is the same, except for the fact that...

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...

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

x_{2})}}\leq K.} For real-valued functions of several real variables, this holds if and only if the absolute value of the slopes of all secant lines are...

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...

If f {\displaystyle f} is a real-valued function of several real variables, the fibers of the function are the level sets of f {\displaystyle f} . If f...

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...

defining higher order differentials of functions of several variables. For example, if f is a function of two variables x and y, then d n f = ∑ k = 0 n (...

the special cases of discrete random variables and absolutely continuous random variables, corresponding to whether a random variable is valued in a countable...

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

exponential function is the unique real function which maps zero to one and has a derivative everywhere equal to its value. The exponential of a variable ⁠ x...