• function of several real variables or real multivariate function is a function with more than one argument, with all arguments being real variables....
    47 KB (7,467 words) - 06:18, 12 January 2025
  • ))={\mathfrak {c}}} . Real analysis Function of several real variables Complex analysis Function of several complex variables R. Courant (23 February...
    21 KB (3,563 words) - 08:09, 8 April 2025
  • 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...
    124 KB (17,717 words) - 22:01, 1 July 2025
  • 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...
    26 KB (4,588 words) - 16:08, 7 January 2025
  • Thumbnail for Real-valued function
    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...
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  • 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...
    23 KB (3,821 words) - 05:35, 7 June 2025
  • function of several real variables or of a function of several complex variables. There are various standard ways for denoting functions. The most commonly...
    76 KB (11,410 words) - 20:15, 22 May 2025
  • Thumbnail for Critical point (mathematics)
    Critical point (mathematics) (category Smooth functions)
    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...
    20 KB (2,990 words) - 14:23, 5 July 2025
  • Thumbnail for Stationary point
    point where the function "stops" increasing or decreasing (hence the name). For a differentiable function of several real variables, a stationary point...
    10 KB (1,162 words) - 18:47, 27 February 2024
  • Thumbnail for Multiple integral
    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...
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  • of the system is generally determined by a finite set of coordinates, and the parametrization thus consists of one function of several real variables...
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  • Thumbnail for Complex analysis
    analytic functions of a complex variable, that is, holomorphic functions. The concept can be extended to functions of several complex variables. Complex...
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  • of real analysis studies the behavior of real numbers, sequences and series of real numbers, and real functions. Some particular properties of real-valued...
    49 KB (7,670 words) - 19:52, 25 June 2025
  • Thumbnail for Analytic function
    power series). Analytic functions of several variables have some of the same properties as analytic functions of one variable. However, especially for...
    16 KB (2,233 words) - 09:22, 10 July 2025
  • Thumbnail for Derivative
    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...
    58 KB (7,403 words) - 01:20, 3 July 2025
  • Thumbnail for Differentiable function
    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...
    13 KB (1,884 words) - 01:18, 9 June 2025
  • Thumbnail for Convex function
    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...
    35 KB (5,856 words) - 19:37, 21 May 2025
  • Thumbnail for Holomorphic function
    holomorphic function is a complex-valued function of one or more complex variables that is complex differentiable in a neighbourhood of each point in...
    25 KB (3,490 words) - 21:26, 15 June 2025
  • Thumbnail for Real coordinate space
    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...
    31 KB (4,248 words) - 16:09, 26 June 2025
  • 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...
    61 KB (8,441 words) - 20:55, 29 April 2025
  • Tube domain (category Several complex variables)
    of real vectors, and whose imaginary part is unconstrained. Tube domains are domains of the Laplace transform of a function of several real variables...
    7 KB (947 words) - 16:51, 7 September 2022
  • Thumbnail for Cumulative distribution function
    cumulative distribution function (CDF) of a real-valued random variable X {\displaystyle X} , or just distribution function of X {\displaystyle X} , evaluated...
    26 KB (4,110 words) - 15:38, 29 June 2025
  • Thumbnail for Graph of a function
    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...
    7 KB (961 words) - 07:13, 5 March 2025
  • Thumbnail for Lipschitz continuity
    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...
    18 KB (2,630 words) - 12:17, 25 May 2025
  • Thumbnail for Cauchy–Riemann equations
    Cauchy–Riemann equations (category Harmonic functions)
    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...
    34 KB (5,011 words) - 18:33, 3 July 2025
  • 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...
    5 KB (795 words) - 05:03, 16 June 2025
  • Thumbnail for Exponential function
    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...
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  • meaning and denotes an argument of a function. Free variables and bound variables A random variable is a kind of variable that is used in probability theory...
    31 KB (3,784 words) - 15:16, 7 June 2025
  • 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...
    22 KB (2,135 words) - 04:00, 8 April 2025
  • Thumbnail for Cauchy's integral formula
    circle. In fact, giving just the real part on the boundary of a holomorphic function is enough to determine the function up to an imaginary constant — there...
    25 KB (4,364 words) - 04:10, 17 May 2025