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 remedy of arithmetic utilizing ultrasmall numbers. With this contemporary method of infinitesimals, proofs turn into less complicated and extra fascinated by the combinatorial middle of arguments, in contrast to conventional remedies that use epsilon–delta equipment. scholars can totally end up basic effects, resembling the extraordinary price Theorem, from the axioms instantly, without having to grasp notions of supremum or compactness.



The publication 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 easy calculus direction whereas the second one half covers extra complex calculus subject matters.



The textual content presents simple definitions of simple suggestions, permitting scholars to shape reliable instinct and really 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 comprises a number of workouts all through and on the finish of every chapter.

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