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

By Karel Hrbacek,Olivier Lessmann,Richard O'Donovan

Analysis with Ultrasmall Numbers provides an intuitive therapy of arithmetic utilizing ultrasmall numbers. With this contemporary method of infinitesimals, proofs develop into less complicated and extra thinking about the combinatorial center of arguments, not like conventional remedies that use epsilon–delta equipment. scholars can absolutely turn out basic effects, similar to the intense price Theorem, from the axioms instantly, while not having to grasp notions of supremum or compactness.

The publication is acceptable for a calculus direction on the undergraduate or highschool point or for self-study with an emphasis on nonstandard tools. the 1st a part of the textual content bargains fabric for an basic calculus direction whereas the second one half covers extra complicated calculus subject matters.

The textual content offers trouble-free definitions of uncomplicated ideas, permitting scholars to shape stable instinct and truly end up issues by means of themselves. It doesn't require any extra "black packing containers" as soon as the preliminary axioms were awarded. The textual content additionally contains quite a few routines all through and on the finish of every chapter.

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