Functions and mappings

2017-07-27T17:51:57+03:00[Europe/Moscow] en true Weierstrass function, Dirac delta function, Function (mathematics), Homeomorphism, Integral, Primitive recursive function, Tensor field, Window function, Identity function, Linear map, Möbius transformation, Exponential growth, Recursion (computer science), Curve sketching, Empty function, Minkowski's question mark function, Splitting lemma (functions), 3D projection, Pfaffian function, Constant function, Partial function, Two-dimensional graph, Morphism of algebraic varieties, Unimodality flashcards Functions and mappings
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  • Weierstrass function
    In mathematics, the Weierstrass function is an example of a pathological real-valued function on the real line.
  • Dirac delta function
    In mathematics, the Dirac delta function, or δ function, is a generalized function, or distribution, on the real number line that is zero everywhere except at zero, with an integral of one over the entire real line.
  • Function (mathematics)
    In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output.
  • Homeomorphism
    In the mathematical field of topology, a homeomorphism or topological isomorphism or bi continuous function is a continuous function between topological spaces that has a continuous inverse function.
  • Integral
    In mathematics, an integral assigns numbers to functions in a way that can describe displacement, area, volume, and other concepts that arise by combining infinitesimal data.
  • Primitive recursive function
    In computability theory, primitive recursive functions are a class of functions that are defined using primitive recursion and composition as central operations and are a strict subset of the total µ-recursive functions (µ-recursive functions are also called partial recursive).
  • Tensor field
    In mathematics, physics, and engineering, a tensor field assigns a tensor to each point of a mathematical space (typically a Euclidean space or manifold).
  • Window function
    In signal processing, a window function (also known as an apodization function or tapering function) is a mathematical function that is zero-valued outside of some chosen interval.
  • Identity function
    In mathematics, an identity function, also called an identity relation or identity map or identity transformation, is a function that always returns the same value that was used as its argument.
  • Linear map
    In mathematics, a linear map (also called a linear mapping, linear transformation or, in some contexts, linear function) is a mapping V → W between two modules (including vector spaces) that preserves (in the sense defined below) the operations of addition and scalar multiplication.
  • Möbius transformation
    In geometry and complex analysis, a Möbius transformation of the complex plane is a rational function of the form of one complex variable z; here the coefficients a, b, c, d are complex numbers satisfying ad − bc ≠ 0.
  • Exponential growth
    Exponential growth is a phenomenon that occurs when the growth rate of the value of a mathematical function is proportional to the function's current value, resulting in its growth with time being an exponential function.
  • Recursion (computer science)
    Recursion in computer science is a method where the solution to a problem depends on solutions to smaller instances of the same problem (as opposed to iteration).
  • Curve sketching
    In geometry, curve sketching (or curve tracing) includes techniques that can be used to produce a rough idea of overall shape of a plane curve given its equation without computing the large numbers of points required for a detailed plot.
  • Empty function
    In mathematics, an empty function is a function whose domain is the empty set ∅.
  • Minkowski's question mark function
    In mathematics, the Minkowski question mark function (or the slippery devil's staircase), denoted by ?(x), is a function possessing various unusual fractal properties, defined by Hermann Minkowski (, pages 171–172).
  • Splitting lemma (functions)
    In mathematics, especially in singularity theory the splitting lemma is a useful result due to René Thom which provides a way of simplifying the local expression of a function usually applied in a neighbourhood of a degenerate critical point.
  • 3D projection
    3D projection is any method of mapping three-dimensional points to a two-dimensional plane.
  • Pfaffian function
    In mathematics, Pfaffian functions are a certain class of functions introduced by Askold Georgevich Khovanskiǐ in the 1970s.
  • Constant function
    In mathematics, a constant function is a function whose (output) value is the same for every input value.
  • Partial function
    In mathematics, a partial function from X to Y (written as f: X ↛ Y) is a function f: X ′ → Y, for some subset X ′ of X.
  • Two-dimensional graph
    A two-dimensional graph is a set of points in two-dimensional space.
  • Morphism of algebraic varieties
    In algebraic geometry, a morphism between algebraic varieties is a function between the varieties that is given locally by polynomials.
  • Unimodality
    In mathematics, unimodality means possessing a unique mode.