Calculus: Difference between revisions
(Created page with "== Functions == No concept in mathematics, especially in calculus, is more fundamental than the concept of a function.") |
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No concept in mathematics, especially in calculus, is more fundamental than the concept of a function. | No concept in mathematics, especially in calculus, is more fundamental than the concept of a function. | ||
A function has different meanings based on the context. | |||
In scientific text, it is common to come across sentences along the lines: | |||
<blockquote>The plot displays Y as a function of X<sub>1</sub>, X<sub>2</sub>, and X<sub>3</sub>.</blockquote> | |||
This has the same meaning as Y is dependent on the independent variables X<sub>1</sub>, X<sub>2</sub>, and X<sub>3</sub>. | |||
In traditional calculus a function is defined as a relation between two terms called variables because their values vary. Call the terms ''x'' and ''y''. If every value of ''x'' is associated with exactly one value of ''y'', then ''y'' is said to be a function of ''x''; ''x'' can only one-to-one relationships, however ''y'' can have one-to-many relationships (different values of ''x'' can be associated with ''y''). It is customary to call ''x'' the ''independent variable'', and ''y'' the ''dependent variable'' because its value depends on ''x''. | |||
Letters at the end of the alphabet are traditionally applied to variables, and letters elsewhere in the alphabet (usually first letters such as ''a'',''b'',''c'',...) are applied to constants. Constants are terms in an equation that have a fixed value. they remain the same as ''x'' and ''y'' vary. | |||
Latest revision as of 00:09, 29 November 2022
Functions
No concept in mathematics, especially in calculus, is more fundamental than the concept of a function.
A function has different meanings based on the context.
In scientific text, it is common to come across sentences along the lines:
The plot displays Y as a function of X1, X2, and X3.
This has the same meaning as Y is dependent on the independent variables X1, X2, and X3.
In traditional calculus a function is defined as a relation between two terms called variables because their values vary. Call the terms x and y. If every value of x is associated with exactly one value of y, then y is said to be a function of x; x can only one-to-one relationships, however y can have one-to-many relationships (different values of x can be associated with y). It is customary to call x the independent variable, and y the dependent variable because its value depends on x.
Letters at the end of the alphabet are traditionally applied to variables, and letters elsewhere in the alphabet (usually first letters such as a,b,c,...) are applied to constants. Constants are terms in an equation that have a fixed value. they remain the same as x and y vary.