Title: Limits, limits everywhere : the tools of mathematical analysis /
Authors: Applebaum, David, 1956-
Publisher: Oxford University Press,
Year: 2012
Subjects: Mathematical analysis.; Mathematical analysis Problems, exercises, etc.
Abstract: A quantity can be made smaller and smaller without it ever vanishing. This fact has profound consequences for science, technology, and even the way we think about numbers. This book explores this idea by moving at an easy pace through an account of elementary real analysis and, in particular, focuses on numbers, sequences, and series.
Contents: A whole lot of numbers -- Let's get real -- The joy of inequality -- Where do you go to, my lovely? -- Bounds for glory -- You cannot be series -- Wonderful numbers: e, (pi) and y -- Infinite products -- Continued fractions -- How infinite can you get? -- Constructing the real numbers -- Where to next in analysis? The calculus -- Some brief remarks about the history of analysis.