Function of a real variable (nonfiction): Difference between revisions
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In mathematical analysis | In mathematical analysis, a '''function of a real variable''' is a [[Function (mathematics) (nonfiction)|function]] whose domain is the real numbers ℝ, more specifically the subset of ℝ for which the function is defined. | ||
Functions of real variables have applications in [[Geometry (nonfiction)|geometry]], applied mathematics, engineering, and natural sciences. | |||
The "output", also called the "value of the function", could be anything: simple examples include a single real number, or a vector of real numbers (the function is "vector valued"). Vector-valued functions of a single real variable occur widely in applied mathematics and physics, particularly in classical mechanics of particles, as well as phase paths of dynamical systems. But we could also have a matrix of real numbers as the output (the function is "matrix valued"), and so on. The "output" could also be other number fields, such as complex numbers, quaternions, or even more exotic hypercomplex numbers. | The "output", also called the "value of the function", could be anything: simple examples include a single real number, or a vector of real numbers (the function is "vector valued"). Vector-valued functions of a single real variable occur widely in applied mathematics and physics, particularly in classical mechanics of particles, as well as phase paths of dynamical systems. But we could also have a matrix of real numbers as the output (the function is "matrix valued"), and so on. The "output" could also be other number fields, such as complex numbers, quaternions, or even more exotic hypercomplex numbers. | ||
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* [[Calculus (nonfiction)]] | * [[Calculus (nonfiction)]] | ||
* [[Function (mathematics) (nonfiction)]] | |||
* [[Mathematics (nonfiction)]] | * [[Mathematics (nonfiction)]] | ||
Revision as of 09:10, 27 November 2017
In mathematical analysis, a function of a real variable is a function whose domain is the real numbers ℝ, more specifically the subset of ℝ for which the function is defined.
Functions of real variables have applications in geometry, applied mathematics, engineering, and natural sciences.
The "output", also called the "value of the function", could be anything: simple examples include a single real number, or a vector of real numbers (the function is "vector valued"). Vector-valued functions of a single real variable occur widely in applied mathematics and physics, particularly in classical mechanics of particles, as well as phase paths of dynamical systems. But we could also have a matrix of real numbers as the output (the function is "matrix valued"), and so on. The "output" could also be other number fields, such as complex numbers, quaternions, or even more exotic hypercomplex numbers.
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Fiction cross-reference
Nonfiction cross-reference
External links:
- Function of a real variable @ Wikipedia