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
This is the end of the preview. Sign up
access the rest of the document.
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.