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Yet Another Calculus Text - A Short Introduction With Infinitesimals by Dan Sloughter
Preface of the book
Yet Another Calculus Text - A Short Introduction With Infinitesimals by Dan Sloughter
Preface of the book
I intend this book to be, firstly, a introduction to calculus based on the hyperreal number system.
In other words, I will use infinitesimal and infinite numbers freely. Just as most beginning calculus
books provide no logical justification for the real number system, I will provide none for
the hyperreals. The reader interested in questions of foundations should consult books
such as Abraham Robinson's Non-standard Analysis or Robert Goldblatt's Lectures on the Hyperreals.
Secondly, I have aimed the text primarily at readers who already have some familiarity with
calculus. Although the book does not explicitly assume any prerequisites beyond basic
algebra and trigonometry, in practice the pace is too fast for most of those without some
acquaintance with the basic notions of calculus
In other words, I will use infinitesimal and infinite numbers freely. Just as most beginning calculus
books provide no logical justification for the real number system, I will provide none for
the hyperreals. The reader interested in questions of foundations should consult books
such as Abraham Robinson's Non-standard Analysis or Robert Goldblatt's Lectures on the Hyperreals.
Secondly, I have aimed the text primarily at readers who already have some familiarity with
calculus. Although the book does not explicitly assume any prerequisites beyond basic
algebra and trigonometry, in practice the pace is too fast for most of those without some
acquaintance with the basic notions of calculus
