By Ovidiu Furdui

This e-book gains tough difficulties of classical research that invite the reader to discover a number of ideas and instruments used for fixing difficulties of contemporary subject matters in genuine research. This quantity bargains an strange choice of difficulties — a lot of them unique — focusing on 3 themes of mathematical research: limits, sequence, and fractional half integrals.

The paintings is split into 3 components, each one containing a bankruptcy facing a selected challenge sort in addition to a really brief part of tricks to pick difficulties. the 1st bankruptcy collects difficulties on limits of distinctive sequences and Riemann integrals; the second one chapter focuses on the calculation of fractional half integrals with a unique part referred to as ‘Quickies’ which includes difficulties that experience had unforeseen succinct recommendations. the ultimate bankruptcy deals the reader an collection of issues of a taste in the direction of the computational features of countless sequence and specified items, a lot of that are new to the literature. every one bankruptcy includes a component to tricky difficulties that are stimulated by way of different difficulties within the booklet. those ‘Open difficulties’ can be thought of learn initiatives for college students who're learning complicated calculus, and which are meant to stimulate creativity and the invention of latest and unique tools for proving identified effects and setting up new ones.

This stimulating choice of difficulties is meant for undergraduate scholars with a robust heritage in research; graduate scholars in arithmetic, physics, and engineering; researchers; and a person who works on themes on the crossroad among natural and utilized arithmetic. additionally, the extent of difficulties is acceptable for college students enthusiastic about the Putnam festival and different excessive point mathematical contests.

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