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

Analysis with Ultrasmall Numbers offers an intuitive remedy of arithmetic utilizing ultrasmall numbers. With this contemporary method of infinitesimals, proofs develop into easier and extra all in favour of the combinatorial middle of arguments, not like conventional remedies that use epsilon–delta tools. scholars can absolutely end up basic effects, similar to the intense worth Theorem, from the axioms instantly, with no need to grasp notions of supremum or compactness.

The ebook 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 simple calculus direction whereas the second one half covers extra complex calculus themes.

The textual content presents trouble-free definitions of easy ideas, allowing scholars to shape solid instinct and truly end up issues via themselves. It doesn't require any extra "black containers" as soon as the preliminary axioms were awarded. The textual content additionally comprises a number of 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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