Calculus, Part 3
What’s a Function?
•
Euler (1748): “[A] Function of a variable quantity is an analytical expression composed in
whatever way of that variable and of numbers and constant quantities.” This roughly corre
sponds today to what we call an
analytic
function, which is a function locally representable
by a power series.
•
Euler (1755): “Those quantities that depend on others .
. . , namely, those that undergo a
change when others change, are called functions of these quantities. This de±nition applies
rather widely and includes all ways in which one quantity can be determined by others.”
•
Fourier (1822)
◦
“The function
f(x)
represents a succession of values or ordinates each of which is
arbitrary.
. . . We do not suppose these ordinates to be subject to a common law; they
succeed each other in any manner whatever, and each of them is given as if it were a
single quantity.”
•
Dirichlet
◦
1829: “One supposes that
φ(x)
equals a determined constant
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This note was uploaded on 12/29/2011 for the course MATH 378 taught by Professor Wen during the Fall '10 term at SUNY Stony Brook.
 Fall '10
 wen
 Calculus

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