What is function?

Some articles on functions, function:

Formal Definitions - Lebesgue Integral
... For instance, a sequence of functions can frequently be constructed that approximate, in a suitable sense, the solution to a problem ... Then the integral of the solution function should be the limit of the integrals of the approximations ... However, many functions that can be obtained as limits are not Riemann integrable, and so such limit theorems do not hold with the Riemann integral ...
Integral - Fundamental Theorem of Calculus - Statements of Theorems
... Let f be a continuous real-valued function defined on a closed interval ... Let F be the function defined, for all x in, by Then, F is continuous on, differentiable on the open interval (a, b), and for all x in (a, b) ... Let f be a real-valued function defined on a closed interval that admits an antiderivative g on ...
Integral - Methods - Numerical Quadrature
... Some integrals cannot be found exactly, some require special functions which themselves are a challenge to compute, and others are so complex that finding the exact answer is too slow ... book” approach divides the integration range into, say, 16 equal pieces, and computes function values ... Spaced function values x −2.00 −1.50 −1.00 −0.50 0.00 0.50 1.00 1.50 2.00 f(x) 2.22800 2.45663 2.67200 2.32475 0.64400 −0.92575 −0.94000 −0.16963 0.83600 x −1.75 −1.25 −0.75 −0.25 ...
Integral - Fundamental Theorem of Calculus
... differentiation and integration are inverse operations if a continuous function is first integrated and then differentiated, the original function is retrieved ... theorem of calculus, allows one to compute integrals by using an antiderivative of the function to be integrated ...
Integral - Extensions - Multiple Integration
... In general, an integral over a set E of a function f is written Here x need not be a real number, but can be another suitable quantity, for instance, a vector in R3 ... as the definite integral of a positive function of one variable represents the area of the region between the graph of the function and the x-axis, the double integral of a positive function of two variables ... The same volume can be obtained via the triple integral — the integral of a function in three variables — of the constant function f(x, y, z) = 1 over the above mentioned region ...

More definitions of "function":

  • (noun): The actions and activities assigned to or required or expected of a person or group.
    Example: "The function of a teacher"
    Synonyms: office, part, role
  • (verb): Serve a purpose, role, or function.
    Synonyms: serve
  • (noun): A mathematical relation such that each element of one set is associated with at least one element of another set.
    Synonyms: mathematical function
  • (noun): A formal or official social gathering or ceremony.
    Example: "It was a black-tie function"
  • (noun): What something is used for.
    Example: "The function of an auger is to bore holes"
    Synonyms: purpose, role, use
  • (verb): Perform duties attached to a particular office or place or function.
    Synonyms: officiate
  • (noun): A relation such that one thing is dependent on another.
    Example: "Height is a function of age"; "price is a function of supply and demand"

Famous quotes containing the word function:

    Our father has an even more important function than modeling manhood for us. He is also the authority to let us relax the requirements of the masculine model: if our father accepts us, then that declares us masculine enough to join the company of men. We, in effect, have our diploma in masculinity and can go on to develop other skills.
    Frank Pittman (20th century)

    Uses are always much broader than functions, and usually far less contentious. The word function carries overtones of purpose and propriety, of concern with why something was developed rather than with how it has actually been found useful. The function of automobiles is to transport people and objects, but they are used for a variety of other purposes—as homes, offices, bedrooms, henhouses, jetties, breakwaters, even offensive weapons.
    Frank Smith (b. 1928)

    The function of muscle is to pull and not to push, except in the case of the genitals and the tongue.
    Leonardo Da Vinci (1425–1519)