Nomina si nescis, perit et cognitio rerum - Carl von Linn

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Nomina si nescis, perit et cognitio rerum- Carl
von Linné

• Who knows not the names, knows not the subject

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• What do the following have in common?
• ab cd
• for similar
• Functions
• promoting the use of Recordes symbol rather
  than Descartes symbol

Gottfried Wilhelm Leibniz
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• What do the following have in common?

B
Leonhard Euler (1734)
c
a
C
b
A
f(x)
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Functions

• The word FUNCTION first appears in a Latin
  manuscript "Methodus tangentium inversa, seu de
  fuctionibus" written by Gottfried Wilhelm Leibniz
  (1646-1716) in 1673. Leibniz used the word in the
  non-analytical sense, as a magnitude which
  performs a special duty. He considered a function
  in terms of "mathematical job"--the "employee"
  being just a curve. He apparently conceived of a
  line doing "something" in a given figura. From
  the beginning of his manuscript, however, Leibniz
  demonstrated that he already possessed the idea
  of function, a term he denominates relatio.
• The phrase FUNCTION OF x was introduced by
  Leibniz.

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Functions

• On July 5, 1698, Johann Bernoulli, in another
  letter to Leibniz, for the first time
  deliberately assigned a specialized use of the
  term function in the analytical sense, writing
  "earum applicatarum quaecunque functiones per
  alias applicatas PZ expressae." At the end of
  that month, Leibniz replied (p. 526), showing his
  approval.
• Function is found in English in 1779 in Chambers'
  Cyclopedia "The term function is used in
  algebra, for an analytical expression any way
  compounded of a variable quantity, and of
  numbers, or constant quantities.

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Functions

• The origin of Function is in the Latin word fungi
  which means perform. It is not related to the
  modern word fungi, which came from the Greek word
  for sponge.
• The performance root base of function helps
  explain the meaning of related language terms
  like defunct for "no longer in use", that is, it
  is no longer performing. Dysfunctional, not
  performing properly, is another simple example.
• Perform is an appropriate root for the idea of a
  mathematical function as an operation, or
  operations, to be performed on a appropriate set
  of values, the domain of the function.

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• The function symbol f(x) was first used by
  Leonhard Euler (1707-1783) in 1734 in Commentarii
  Academiae Scientiarum Petropolitanae
• Absolute value function. Karl Weierstrass
  (1815-1897) used in an 1841 essay "Zur
  Theorie der Potenzreihen," in which the symbol
  appears on page 67.

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Functions

• DOMAIN was used in 1886 by Arthur Cayley in "On
  Linear Differential Equations" in the Quarterly
  Journal of Pure and Applied Mathematics "... for
  points x within the domain of the point a.
• Domain, in the sense of the values that an
  independent variable of a function can take,
  appears in the Encyclopaedia Britannica of 1902
  (OED2).
• RANGE (of a function). In 1865, The Differential
  Calculus by John Spare has "It is useful to
  become acquainted with the methods of fully
  examining the entire history of a function of one
  or more variables, in respect to the range of
  values which the function and its variable may
  sustain, and to their mutual dependence.

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• DOMAIN RANGE
• Alphabetical order
• x
  y
• Domain Range

Range
Is this always the case?
Domain
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Find the range of the function g x
x²-4x5
g(1) 2 g(5) 10 Range
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RANGE
Range
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Functions

• The creator of the symbol f is Joseph Louis
  Lagrange. He also was responsible for the prime
  notation, f', f" etc to represent the cascade of
  derived functions or derivatives of a function.
• If I had been rich, I probably would not have
  devoted myself to mathematics.

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Ideas taken fromhttp//www.pballew.net/etyindex
.html http//members.aol.com/jeff570/mathword.ht
ml http//mathforum.org/library/drmath/view/5379
7.html