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Intended for advanced undergraduates and graduate students, this concise text focuses on the convergence of real series. Definitions of the terms and summaries of those results in analysis that are of special importance in the theory of series are specified at the outset. In the interests of maintaining a succinct presentation, discussion of the question of the upper and lower limits of a function is confined to an outline of those properties with...
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One of the finest expositors in the field of modern mathematics, Dr. Konrad Knopp here concentrates on a topic that is of particular interest to 20th-century mathematicians and students. He develops the theory of infinite sequences and series from its beginnings to a point where the reader will be in a position to investigate more advanced stages on his own. The foundations of the theory are therefore presented with special care, while the developmental...
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Ideas and Explorations of the Meaning of InfinityWho has not wondered if there is something beyond the universe? Or if there is a biggest number? Or if there is something smaller than the smallest thing?These are questions about different infinities. Exploring the paradoxes and riddles of what infinity means is the invitation contained in this book. This classic book, written by the seminal Leapfrogs team, has been visually updated in this second...
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Originally prepared for the Office of Naval Research, this important monograph introduces various methods for the asymptotic evaluation of integrals containing a large parameter, and solutions of ordinary linear differential equations by means of asymptotic expansions. Author's preface. Bibliography.
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A mathematician and scientist in residence at the School of the Art Institute of Chicago helps readers explore the concept of infinity through unique concepts including chessboards, a chicken-sandwich sandwich and the creation of infinite cookies from an infinite dough ball.--
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