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Introducing calculus at the basic level, this text covers hyperreal numbers and hyperreal line, continuous functions, integral and differential calculus, fundamental theorem, infinite sequences and series, infinite polynomials, topology of the real line, and standard calculus and sequences of functions. Only high school mathematics needed. 1979 edition.

Introducing calculus at the basic level, this text covers hyperreal numbers and hyperreal line, continuous functions, integral and differential calculus, fundamental theorem, infinite sequences and series, infinite polynomials, topology of the real line, and standard calculus and sequences of functions. Only high school mathematics needed. 1979 edition.

"His "Calcul Infinitesimal" ... published in 1968 addresses the needs of a good undergraduate - and his instructor - in Calculus. This book is well- written, well-arranged and classroom-tested. It compares to the best classics like Whittaker and Watson" - Pierre Cartier. Note that the French version of Calculus for the undergraduate was more like today's (Complex and Real) Analysis for the American undergraduate.

"His "Calcul Infinitesimal" ... published in 1968 addresses the needs of a good undergraduate - and his instructor - in Calculus. This book is well- written, well-arranged and classroom-tested. It compares to the best classics like Whittaker and Watson" - Pierre Cartier. Note that the French version of Calculus for the undergraduate was more like today's (Complex and Real) Analysis for the American undergraduate.

This historical account begins with the Greek, Hindu, and Arabic sources that constituted the framework for the development of infinitesimal methods in the 17th century. Subsequent chapters discuss the arithmetization of integration methods, the role of investigation of special curves, concepts of tangent and arc, the composition of motions, more. 1969 edition.

One of the most remarkable recent occurrences in mathematics is the re-founding, on a rigorous basis, the idea of infinitesimal quantity, a notion which played an important role in the early development of the calculus and mathematical analysis. In this new and updated edition, basic calculus, together with some of its applications to simple physical problems, are presented through the use of a straightforward, rigorous, axiomatically formulated concept of 'zero-square', or 'nilpotent' infinitesimal - that is, a quantity so small that its square and all higher powers can be set, to zero. The systematic employment of these infinitesimals reduces the differential calculus to simple algebra and, at the same time, restores to use the "infinitesimal" methods figuring in traditional applications of the calculus to physical problems - a number of which are discussed in this book. This edition also contains an expanded historical and philosophical introduction.

One of the most remarkable recent occurrences in mathematics is the refounding, on a rigorous basis, of the idea of infinitesimal quantity, a notion that played an important role in the early development of the calculus and mathematical analysis. In this book, basic calculus, together with some of its applications to simple physical problems, are presented through the use of a straightforward, rigorous, axiomatically formulated concept of "zero-square", or "nilpotent" infinitesimal--that is, a quantity so small that its square and all higher powers can be set, literally, to zero. As the author shows, the systematic employment of these infinitesimals reduces the differential calculus to simple algebra and, at the same time, restores to use the "infinitesimal" methods figuring in traditional applications of the calculus to physical problems--a number of which are discussed in this book. The text also contains a historical and philosophical introduction, a chapter describing the logical features of the infinitesimal framework, and an Appendix sketching the developments in the mathematical discipline of category theory that have made the refounding of infinitesimals possible.

Gunon's early and abiding interest in mathematics, like that of Plato, Pascal, Leibnitz, and many other metaphysicians of note, runs like a scarlet thread throughout his doctrinal studies. In this late text published just five years before his death, Gunon devotes an entire volume to questions regarding the nature of limits and the infinite with respect to the calculus both as a mathematical discipline and as symbolism for the initiatic path. This book therefore extends and complements the geometrical symbolism he employs in other works, especially The Symbolism of the Cross, The Multiple States of the Being, and Symbols of Sacred Science. According to Gunon, the concept 'infinite number' is a contradiction in terms. Infinity is a metaphysical concept at a higher level of reality than that of quantity, where all that can be expressed is the indefinite, not the infinite. But although quantity is the only level recognized by modern science, the numbers that express it also possess qualities, their quantitative aspect being merely their outer husk. Our reliance today on a mathematics of approximation and probability only further conceals the 'qualitative mathematics' of the ancient world, which comes to us most directly through the Pythagorean-Platonic tradition.

One of the most remarkable recent occurrences in mathematics is the re-founding, on a rigorous basis, the idea of infinitesimal quantity, a notion which played an important role in the early development of the calculus and mathematical analysis. In this new and updated edition, basic calculus, together with some of its applications to simple physical problems, are presented through the use of a straightforward, rigorous, axiomatically formulated concept of 'zero-square', or 'nilpotent' infinitesimal - that is, a quantity so small that its square and all higher powers can be set, to zero. The systematic employment of these infinitesimals reduces the differential calculus to simple algebra and, at the same time, restores to use the "infinitesimal" methods figuring in traditional applications of the calculus to physical problems - a number of which are discussed in this book. This edition also contains an expanded historical and philosophical introduction.

Guénon's early and abiding interest in mathematics, like that of Plato, Pascal, Leibnitz, and many other metaphysicians of note, runs like a scarlet thread throughout his doctrinal studies. In this late text published just five years before his death, Guénon devotes an entire volume to questions regarding the nature of limits and the infinite with respect to the calculus both as a mathematical discipline and as symbolism for the initiatic path. This book therefore extends and complements the geometrical symbolism he employs in other works, especially The Symbolism of the Cross, The Multiple States of the Being, and Symbols of Sacred Science. According to Guénon, the concept 'infinite number' is a contradiction in terms. Infinity is a metaphysical concept at a higher level of reality than that of quantity, where all that can be expressed is the indefinite, not the infinite. But although quantity is the only level recognized by modern science, the numbers that express it also possess qualities, their quantitative aspect being merely their outer husk. Our reliance today on a mathematics of approximation and probability only further conceals the 'qualitative mathematics' of the ancient world, which comes to us most directly through the Pythagorean-Platonic tradition.

Gunon's early and abiding interest in mathematics, like that of Plato, Pascal, Leibnitz, and many other metaphysicians of note, runs like a scarlet thread throughout his doctrinal studies. In this late text published just five years before his death, Gunon devotes an entire volume to questions regarding the nature of limits and the infinite with respect to the calculus both as a mathematical discipline and as symbolism for the initiatic path. This book therefore extends and complements the geometrical symbolism he employs in other works, especially The Symbolism of the Cross, The Multiple States of the Being, and Symbols of Sacred Science. According to Gunon, the concept 'infinite number' is a contradiction in terms. Infinity is a metaphysical concept at a higher level of reality than that of quantity, where all that can be expressed is the indefinite, not the infinite. But although quantity is the only level recognized by modern science, the numbers that express it also possess qualities, their quantitative aspect being merely their outer husk. Our reliance today on a mathematics of approximation and probability only further conceals the 'qualitative mathematics' of the ancient world, which comes to us most directly through the Pythagorean-Platonic tradition.

The book has been read, but is in excellent condition. Pages are intact and not marred by notes or highlighting. The spine remains undamaged.

Book is in NEW condition. 5.76

The topic of this book is the historical struggle to define and defend a real number continuum which could do the work limit theory required of it. These definitions drew heavily on philosophical and foundational assumptions, and each raises numerous philosophical questions of its own. As we shall see, attempts to formulate a non-geometrical mathematical continuity raise questions such as: What is a number? What, in particular, is a real number? What is the true nature of continuity itself? Does a philosophically coherent definition of continuity logically commit us to infinitesimally small quantities? Is the concept of an infinitesimally small quantity even logically coherent? What is the relationship between this real number continuum and other well known continua, such as the geometrical straight line? The main question to be addressed, of course, is whether mathematical continuity exists at all.

From the author of The Joy of Pi and The Flying Book, an engaging new guide to the amazing unseen world around us.How can we understand the world of the atom or the size of our galaxy? How do we grasp a billionth of a second or a billion years; the freezing point of helium or the heat generated by the blast of an atomic bomb? Spectrums answers these questions and many more by exploring realms we are familiar with in our daily lives, but whose extremes boggle the mind and inspire a sense of wonder. With relish and insight, Blatner re-introduces us to six fundamental spectrums in the world around us: numbers, size, light, sound, heat, and time. Offering fascinating glimpses of hidden realities, full of comparisons, facts, and anecdotes, and illustrated by a wealth of diagrams, photographs, and sidebars, Spectrums illuminates the full range of the bizarre and beautiful world in which we live.

Embark on a breath-taking, cutting-edge voyage through the enormity of our reality - travelling one "power of ten" or order of magnitude at a time. Echoing the classic film by Charles and Ray Eames, acclaimed astrobiologist Caleb Scharf and artist Ron Miller guide us from the very edge of the observable universe - about 91 billion light-years away - to the subatomic realm, where the fabric of space-time itself behaves in a way that confounds all the rules of physics we currently know. Gorgeously designed and visually inspiring, The Zoomable Universe takes a truly unique approach toward explaining our place in the universe, charting an unforgettable course through galaxies, black holes, solar systems, stars and planets, oceans, plants and animals, microorganisms, atoms, quantum fields, and much more. Illustrated with stunning colour artwork and infographics, this is an unforgettable journey that will thrill readers who want to discover more about the incredible reality we inhabit.

The thing about France Jobin's music that never fails to impress is that it works on so many levels. Listen to it at the threshold of perception (the way it is mastered) or at very high volume, on headphones or through loudspeakers, and you will hear new sonic relationships, new structures, a new logic every time. Things simultaneously are and aren't as they seem; sounds you hear are and aren't really there.

In the late fifteenth century, clocks acquired minute hands. A century later, second hands appeared. But it wasn’t until the 1850s that instruments could recognize a tenth of a second, and, once they did, the impact on modern science and society was profound. Revealing the history behind this infinitesimal interval, A Tenth of a Second sheds new light on modernity and illuminates the work of important thinkers of the last two centuries.Tracing debates about the nature of time, causality, and free will, as well as the introduction of modern technologies—telegraphy, photography, cinematography—Jimena Canales locates the reverberations of this “perceptual moment” throughout culture. Once scientists associated the tenth of a second with the speed of thought, they developed reaction time experiments with lasting implications for experimental psychology, physiology, and optics. Astronomers and physicists struggled to control the profound consequences of results that were a tenth of a second off. And references to the interval were part of a general inquiry into time, consciousness, and sensory experience that involved rethinking the contributions of Descartes and Kant. Considering its impact on much longer time periods and featuring appearances by Henri Bergson, Walter Benjamin, and Albert Einstein, among others, A Tenth of a Second is ultimately an important contribution to history and a novel perspective on modernity.

The Twelve Tissue Salts have been used for well over 100 years as natural remedies in restoring the health of the body. These inorganic minerals are constituents of the physical tissues, and are given in the infinitesimal dose to adjust various disturbed conditions in the body cells and fluids, evidenced as inflammation, congestion, pain, disease. The author gives simple directions for their use in the home. The treatment with these Tissue Salts of the various types of rheumatism is another useful feature of this book, which also discusses food values in connection with the maintenance and improvement of health.

First Snow White encounters one of the Little People, then one of the Even Smaller People, and finally one of the Truly Infinitesimal People. And no matter how diligently she searches, the only dwarves she can find are collapsed stars! Clearly, she's not at home in her well-known Brothers Grimm fairy tale, but instead in a strange new landscape that features quantum behavior, the wavelike properties of particles, and the Uncertainty Principle. She (and we) must have entered, in short, one of the worlds created by Robert Gilmore, physicist and fabulist.