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Careful presentation of fundamentals of the theory by one of the finest modern expositors of higher mathematics. Covers functions of real and complex variables, arbitrary and null sequences, convergence and divergence, Cauchy's limit theorem, more.
Based on lectures on Elementary Analysis given at Queen's College, Galway, from 1902-1907, this title includes a discussion of the solution of linear differential equations of the second order; a discussion of elliptic function formulae; expanded treatment of asymptomatic series; and a discussion of trigonometrical series.
This concise text focuses on the convergence of real series. Topics include functions and limits, real sequences and series, series of non-negative terms, general series, series of functions, the multiplication of series, more. 1959 edition.
This textbook covers the majority of traditional topics of infinite sequences and series, starting from the very beginning – the definition and elementary properties of sequences of numbers, and ending with advanced results of uniform convergence and power series. The text is aimed at university students specializing in mathematics and natural sciences, and at all the readers interested in infinite sequences and series. It is designed for the reader who has a good working knowledge of calculus. No additional prior knowledge is required. The text is divided into five chapters, which can be grouped into two parts: the first two chapters are concerned with the sequences and series of numbers,...
Robinson, the master of fast-paced stories blending horror, science fiction, and thrillers, tackles his most ambitious subject to date: reality itself. An amalgam of the works of J.J. Abrams and Ridley Scott, Infinite is a bold SF novel exploring the vastness of space and a man's desire to exist, find love, and alter the course of his life.
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Maya’s shocked to discover it’s not the heaven she imagined; in fact, a life of adventure begins the moment you die. Zachariah, her faithful spirit guide, explains the rules of the dead: in order to regain complete awareness and reunite with loved ones all souls must review their previous lives. Maya plunges warily into her turbulent pasts as a sociopathic High Priest in ancient Egypt; an independent mother protecting a dangerous secret in glorious Sparta; an Irish boy kidnapped and enslaved by Vikings; and a doctor’s wife forced to make an ethical stand in plague-ridden England. All the while, Maya yearns to be with those she cares about most and worries that she hasn’t learned all of heaven’s most vital lessons. Will she be forced to leave the tranquility of heaven to survive yet another painful and tumultuous life? Or worse, accept the bitter reality of having to go back alone? Free, freebie
This is a widely accessible introductory treatment of infinite series of real numbers, bringing the reader from basic definitions and tests to advanced results. An up-to-date presentation is given, making infinite series accessible, interesting, and useful to a wide audience, including students, teachers, and researchers. Included are elementary and advanced tests for convergence or divergence, the harmonic series, the alternating harmonic series, and closely related results. One chapter offers 107 concise, crisp, surprising results about infinite series. Another gives problems on infinite series, and solutions, which have appeared on the annual William Lowell Putnam Mathematical Competition. The lighter side of infinite series is treated in the concluding chapter where three puzzles, eighteen visuals, and several fallacious proofs are made available. Three appendices provide a listing of true or false statements, answers to why the harmonic series is so named, and an extensive list of published works on infinite series.
Trans from the 2nd German ed , pub 1923.
An informal and practically focused introduction for undergraduate students exploring infinite series and sequences in engineering and the physical sciences. With a focus on practical applications in real world situations, it helps students to conceptualize the theory with real-world examples and to build their skill set.