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

By Karel Hrbacek,Olivier Lessmann,Richard O'Donovan

Analysis with Ultrasmall Numbers provides an intuitive remedy of arithmetic utilizing ultrasmall numbers. With this contemporary method of infinitesimals, proofs develop into less complicated and extra all for the combinatorial center of arguments, in contrast to conventional remedies that use epsilon–delta equipment. scholars can totally turn out primary effects, similar to the extraordinary worth Theorem, from the axioms instantly, with no need to grasp notions of supremum or compactness.

The e-book is acceptable for a calculus path on the undergraduate or highschool point or for self-study with an emphasis on nonstandard tools. the 1st a part of the textual content deals fabric for an trouble-free calculus direction whereas the second one half covers extra complicated calculus issues.

The textual content presents simple definitions of simple techniques, permitting scholars to shape sturdy instinct and truly turn out issues by way of themselves. It doesn't require any extra "black bins" as soon as the preliminary axioms were provided. The textual content additionally contains various routines all through and on the finish of every chapter.

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