Download PDF by Karel Hrbacek,Olivier Lessmann,Richard O'Donovan: Analysis with Ultrasmall Numbers (Textbooks in Mathematics)

By Karel Hrbacek,Olivier Lessmann,Richard O'Donovan

ISBN-10: 1498702651

ISBN-13: 9781498702652

Analysis with Ultrasmall Numbers offers an intuitive therapy of arithmetic utilizing ultrasmall numbers. With this contemporary method of infinitesimals, proofs develop into easier and extra fascinated with the combinatorial middle of arguments, not like conventional remedies that use epsilon–delta tools. scholars can totally end up primary effects, similar to the extraordinary worth Theorem, from the axioms instantly, while not having to grasp notions of supremum or compactness.

The publication is appropriate for a calculus path on the undergraduate or highschool point or for self-study with an emphasis on nonstandard equipment. the 1st a part of the textual content deals fabric for an straight forward calculus direction whereas the second one half covers extra complicated calculus subject matters.

The textual content offers simple definitions of uncomplicated innovations, allowing scholars to shape sturdy instinct and really end up issues via themselves. It doesn't require any extra "black bins" as soon as the preliminary axioms were offered. The textual content additionally comprises quite a few routines all through and on the finish of every chapter.

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Analysis with Ultrasmall Numbers (Textbooks in Mathematics) by Karel Hrbacek,Olivier Lessmann,Richard O'Donovan

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