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Author: Ivor Grattan-Guinness
Publisher:
ISBN: 9780262571784
Category : Biography & Autobiography
Languages : en
Pages : 530
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Book Description
Beyond being the first substantial publication on Fourier, this work contains the text of Fourier's seminal paper of 1807 on the propagation of heat, marking the first time it has ever appeared in print. This paper incorporates many of the mathematical creations on which Fourier's fame rests, including derivation of the diffusion equation, the separation of the treatment of surface phenomena from internal phenomena, the use of boundary values and initial conditions, and the development of "Fourier series" and the so-called "Bessel functions."When submitted to the examiners of the Institut de France, the originality of the paper and the surprising nature of some of its mathematical revelations caused great controversy, and it was denied publication both in 1807 and in later years. Fourier had the support, among the examiners, of Laplace and Monge, but Lagrange was adamantly in opposition, so that Fourier's work did not appear in print until 1822, reworked into book form.Fourier's mathematical discoveries are intimately related to his interest in the solution of physical problems and their experimental verification. The mathematical methods he developed in connection with heat diffusion apply to physical situations far beyond the boundaries of this area. Generally, Fourier may be credited with one of the first major extensions of mathematical physics beyond the applications of Newton's laws of motion and universal gravitation.The opening biographical chapter of this book follows Fourier's career up to the submission of the 1807 paper, and the two closing chapters take up his life and work from that point on. Fourier had strong political motivations and spent much of his life in the public service. These chapters trace his political difficulties, both before and after 1807, when he was the prefect of a department of France and was subjected to the dislocations of Napoleon's ups and downs. These chapters also describe aspects of the turbulent but productive development of French science from the Revolution to 1830.The core of the book presents the paper of 1807 in its original French and with the original notation. Grattan-Guinness has divided the paper into sections by the sequence of the problems taken up, and he introduces and, where necessary, closes each section with commentary relevant to Fourier's later work in these areas. The paper itself (cllows the chronology of Fourier's discoveries, and among the topics treated are, in this order: heat diffusion between disjoint bodies and in continuous bodies; the appearance of partial differential equations; the special solution for the lamina; sine and cosine series for an arbitrary function; reflections on the vibrating string problem; solution for the annulus; the full Fourier series for an arbitrary function; reflections on n-body analysis; solution for the sphere; solution for the cylinder; steady-state diffusion in the rectangular prism; time-dependent diffusion in the cube; and Fourier's experimental work.
Author: Ivor Grattan-Guinness
Publisher:
ISBN: 9780262571784
Category : Biography & Autobiography
Languages : en
Pages : 530
Get Book Here
Book Description
Beyond being the first substantial publication on Fourier, this work contains the text of Fourier's seminal paper of 1807 on the propagation of heat, marking the first time it has ever appeared in print. This paper incorporates many of the mathematical creations on which Fourier's fame rests, including derivation of the diffusion equation, the separation of the treatment of surface phenomena from internal phenomena, the use of boundary values and initial conditions, and the development of "Fourier series" and the so-called "Bessel functions."When submitted to the examiners of the Institut de France, the originality of the paper and the surprising nature of some of its mathematical revelations caused great controversy, and it was denied publication both in 1807 and in later years. Fourier had the support, among the examiners, of Laplace and Monge, but Lagrange was adamantly in opposition, so that Fourier's work did not appear in print until 1822, reworked into book form.Fourier's mathematical discoveries are intimately related to his interest in the solution of physical problems and their experimental verification. The mathematical methods he developed in connection with heat diffusion apply to physical situations far beyond the boundaries of this area. Generally, Fourier may be credited with one of the first major extensions of mathematical physics beyond the applications of Newton's laws of motion and universal gravitation.The opening biographical chapter of this book follows Fourier's career up to the submission of the 1807 paper, and the two closing chapters take up his life and work from that point on. Fourier had strong political motivations and spent much of his life in the public service. These chapters trace his political difficulties, both before and after 1807, when he was the prefect of a department of France and was subjected to the dislocations of Napoleon's ups and downs. These chapters also describe aspects of the turbulent but productive development of French science from the Revolution to 1830.The core of the book presents the paper of 1807 in its original French and with the original notation. Grattan-Guinness has divided the paper into sections by the sequence of the problems taken up, and he introduces and, where necessary, closes each section with commentary relevant to Fourier's later work in these areas. The paper itself (cllows the chronology of Fourier's discoveries, and among the topics treated are, in this order: heat diffusion between disjoint bodies and in continuous bodies; the appearance of partial differential equations; the special solution for the lamina; sine and cosine series for an arbitrary function; reflections on the vibrating string problem; solution for the annulus; the full Fourier series for an arbitrary function; reflections on n-body analysis; solution for the sphere; solution for the cylinder; steady-state diffusion in the rectangular prism; time-dependent diffusion in the cube; and Fourier's experimental work.
Author: Walter William Rouse Ball
Publisher:
ISBN:
Category : Mathematicians
Languages : en
Pages : 576
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Book Description
Author: Solym Mawaki Manou-Abi
Publisher: John Wiley & Sons
ISBN: 1786304546
Category : Mathematics
Languages : en
Pages : 308
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Book Description
This book highlights mathematical research interests that appear in real life, such as the study and modeling of random and deterministic phenomena. As such, it provides current research in mathematics, with applications in biological and environmental sciences, ecology, epidemiology and social perspectives. The chapters can be read independently of each other, with dedicated references specific to each chapter. The book is organized in two main parts. The first is devoted to some advanced mathematical problems regarding epidemic models; predictions of biomass; space-time modeling of extreme rainfall; modeling with the piecewise deterministic Markov process; optimal control problems; evolution equations in a periodic environment; and the analysis of the heat equation. The second is devoted to a modelization with interdisciplinarity in ecological, socio-economic, epistemological, demographic and social problems. Mathematical Modeling of Random and Deterministic Phenomena is aimed at expert readers, young researchers, plus graduate and advanced undergraduate students who are interested in probability, statistics, modeling and mathematical analysis.
Author: John Herivel
Publisher: Oxford University Press, USA
ISBN:
Category : Biography & Autobiography
Languages : en
Pages : 380
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Book Description
Author: John Bird
Publisher: Routledge
ISBN: 1136347119
Category : Technology & Engineering
Languages : en
Pages : 998
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Book Description
Electrical Circuit Theory and Technology is a fully comprehensive text for courses in electrical and electronic principles, circuit theory and electrical technology. The coverage takes students from the fundamentals of the subject, to the completion of a first year degree level course. Thus, this book is ideal for students studying engineering for the first time, and is also suitable for pre-degree vocational courses, especially where progression to higher levels of study is likely. John Bird's approach, based on 700 worked examples supported by over 1000 problems (including answers), is ideal for students of a wide range of abilities, and can be worked through at the student's own pace. Theory is kept to a minimum, placing a firm emphasis on problem-solving skills, and making this a thoroughly practical introduction to these core subjects in the electrical and electronic engineering curriculum. This revised edition includes new material on transients and laplace transforms, with the content carefully matched to typical undergraduate modules. Free Tutor Support Material including full worked solutions to the assessment papers featured in the book will be available at http://textbooks.elsevier.com/. Material is only available to lecturers who have adopted the text as an essential purchase. In order to obtain your password to access the material please follow the guidelines in the book.
Author: Timothy Gowers
Publisher: Princeton University Press
ISBN: 1400830397
Category : Mathematics
Languages : en
Pages : 1057
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Book Description
The ultimate mathematics reference book This is a one-of-a-kind reference for anyone with a serious interest in mathematics. Edited by Timothy Gowers, a recipient of the Fields Medal, it presents nearly two hundred entries—written especially for this book by some of the world's leading mathematicians—that introduce basic mathematical tools and vocabulary; trace the development of modern mathematics; explain essential terms and concepts; examine core ideas in major areas of mathematics; describe the achievements of scores of famous mathematicians; explore the impact of mathematics on other disciplines such as biology, finance, and music—and much, much more. Unparalleled in its depth of coverage, The Princeton Companion to Mathematics surveys the most active and exciting branches of pure mathematics. Accessible in style, this is an indispensable resource for undergraduate and graduate students in mathematics as well as for researchers and scholars seeking to understand areas outside their specialties. Features nearly 200 entries, organized thematically and written by an international team of distinguished contributors Presents major ideas and branches of pure mathematics in a clear, accessible style Defines and explains important mathematical concepts, methods, theorems, and open problems Introduces the language of mathematics and the goals of mathematical research Covers number theory, algebra, analysis, geometry, logic, probability, and more Traces the history and development of modern mathematics Profiles more than ninety-five mathematicians who influenced those working today Explores the influence of mathematics on other disciplines Includes bibliographies, cross-references, and a comprehensive index Contributors include: Graham Allan, Noga Alon, George Andrews, Tom Archibald, Sir Michael Atiyah, David Aubin, Joan Bagaria, Keith Ball, June Barrow-Green, Alan Beardon, David D. Ben-Zvi, Vitaly Bergelson, Nicholas Bingham, Béla Bollobás, Henk Bos, Bodil Branner, Martin R. Bridson, John P. Burgess, Kevin Buzzard, Peter J. Cameron, Jean-Luc Chabert, Eugenia Cheng, Clifford C. Cocks, Alain Connes, Leo Corry, Wolfgang Coy, Tony Crilly, Serafina Cuomo, Mihalis Dafermos, Partha Dasgupta, Ingrid Daubechies, Joseph W. Dauben, John W. Dawson Jr., Francois de Gandt, Persi Diaconis, Jordan S. Ellenberg, Lawrence C. Evans, Florence Fasanelli, Anita Burdman Feferman, Solomon Feferman, Charles Fefferman, Della Fenster, José Ferreirós, David Fisher, Terry Gannon, A. Gardiner, Charles C. Gillispie, Oded Goldreich, Catherine Goldstein, Fernando Q. Gouvêa, Timothy Gowers, Andrew Granville, Ivor Grattan-Guinness, Jeremy Gray, Ben Green, Ian Grojnowski, Niccolò Guicciardini, Michael Harris, Ulf Hashagen, Nigel Higson, Andrew Hodges, F. E. A. Johnson, Mark Joshi, Kiran S. Kedlaya, Frank Kelly, Sergiu Klainerman, Jon Kleinberg, Israel Kleiner, Jacek Klinowski, Eberhard Knobloch, János Kollár, T. W. Körner, Michael Krivelevich, Peter D. Lax, Imre Leader, Jean-François Le Gall, W. B. R. Lickorish, Martin W. Liebeck, Jesper Lützen, Des MacHale, Alan L. Mackay, Shahn Majid, Lech Maligranda, David Marker, Jean Mawhin, Barry Mazur, Dusa McDuff, Colin McLarty, Bojan Mohar, Peter M. Neumann, Catherine Nolan, James Norris, Brian Osserman, Richard S. Palais, Marco Panza, Karen Hunger Parshall, Gabriel P. Paternain, Jeanne Peiffer, Carl Pomerance, Helmut Pulte, Bruce Reed, Michael C. Reed, Adrian Rice, Eleanor Robson, Igor Rodnianski, John Roe, Mark Ronan, Edward Sandifer, Tilman Sauer, Norbert Schappacher, Andrzej Schinzel, Erhard Scholz, Reinhard Siegmund-Schultze, Gordon Slade, David J. Spiegelhalter, Jacqueline Stedall, Arild Stubhaug, Madhu Sudan, Terence Tao, Jamie Tappenden, C. H. Taubes, Rüdiger Thiele, Burt Totaro, Lloyd N. Trefethen, Dirk van Dalen, Richard Weber, Dominic Welsh, Avi Wigderson, Herbert Wilf, David Wilkins, B. Yandell, Eric Zaslow, and Doron Zeilberger
Author: Naomi Oreskes
Publisher: A&C Black
ISBN: 1408828774
Category : Technology & Engineering
Languages : en
Pages : 368
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Book Description
The U.S. scientific community has long led the world in research on such areas as public health, environmental science, and issues affecting quality of life. These scientists have produced landmark studies on the dangers of DDT, tobacco smoke, acid rain, and global warming. But at the same time, a small yet potent subset of this community leads the world in vehement denial of these dangers. Merchants of Doubt tells the story of how a loose-knit group of high-level scientists and scientific advisers, with deep connections in politics and industry, ran effective campaigns to mislead the public and deny well-established scientific knowledge over four decades. Remarkably, the same individuals surface repeatedly-some of the same figures who have claimed that the science of global warming is "not settled" denied the truth of studies linking smoking to lung cancer, coal smoke to acid rain, and CFCs to the ozone hole. "Doubt is our product," wrote one tobacco executive. These "experts" supplied it. Naomi Oreskes and Erik M. Conway, historians of science, roll back the rug on this dark corner of the American scientific community, showing how ideology and corporate interests, aided by a too-compliant media, have skewed public understanding of some of the most pressing issues of our era.
Author: Ioan James
Publisher: Mathematical Association of America
ISBN: 9780521817776
Category : Mathematics
Languages : en
Pages : 286
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Book Description
Ioan James introduces and profiles sixty mathematicians from the era when mathematics was freed from its classical origins to develop into its modern form. The subjects, all born between 1700 and 1910, come from a wide range of countries, and all made important contributions to mathematics, through their ideas, their teaching, and their influence. James emphasizes their varied life stories, not the details of their mathematical achievements. The book is organized chronologically into ten chapters, each of which contains biographical sketches of six mathematicians. The men and women James has chosen to portray are representative of the history of mathematics, such that their stories, when read in sequence, convey in human terms something of the way in which mathematics developed. Ioan James is a professor at the Mathematical Institute, University of Oxford. He is the author of Topological Topics (Cambridge, 1983), Fibrewise Topology (Cambridge, 1989), Introduction to Uniform Spaces (Cambridge, 1990), Topological and Uniform Spaces (Springer-Verlag New York, 1999), and co-author with Michael C. Crabb of Fibrewise Homotopy Theory (Springer-Verlag New York, 1998). James is the former editor of the London Mathematical Society Lecture Note Series and volume editor of numerous books. He is the organizer of the Oxford Series of Topology symposia and other conferences, and co-chairman of the Task Force for Mathematical Sciences of Campaign for Oxford.
Author: Harold Hill
Publisher: Cambridge University Press
ISBN: 9780521542081
Category : Art
Languages : en
Pages : 272
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Book Description
Harold Hill's achievement is to awaken us to the stark, compelling beauty of the moon, with its mighty ringwalls and glistening highlands. Each image tells its own story. Each is constructed with precision and attention to detail.
Author: David Lindley
Publisher: National Academies Press
ISBN: 0309096189
Category : Science
Languages : en
Pages : 383
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Book Description
LORD KELVIN. In 1840, a precocious 16-year-old by the name of William Thomson spent his summer vacation studying an extraordinarily sophisticated mathematical controversy. His brilliant analysis inspired lavish praise and made the boy an instant intellectual celebrity. As a young scholar William dazzled a Victorian society enthralled with the seductive authority and powerful beauty of scientific discovery. At a time when no one really understood heat, light, electricity, or magnetism, Thomson found key connections between them, laying the groundwork for two of the cornerstones of 19th century science-the theories of electromagnetism and thermodynamics. Charismatic, confident, and boyishly handsome, Thomson was not a scientist who labored quietly in a lab, plying his trade in monkish isolation. When scores of able tinkerers were flummoxed by their inability to adapt overland telegraphic cables to underwater, intercontinental use, Thomson took to the high seas with new equipment that was to change the face of modern communications. And as the world's navies were transitioning from wooden to iron ships, they looked to Thomson to devise a compass that would hold true even when surrounded by steel. Gaining fame and wealth through his inventive genius, Thomson was elevated to the peerage by Queen Victoria for his many achievements. He was the first scientist ever to be so honored. Indeed, his name survives in the designation of degrees Kelvin, the temperature scale that begins with absolute zero, the point at which atomic motion ceases and there is a complete absence of heat. Sir William Thomson, Lord Kelvin, was Great Britain's unrivaled scientific hero. But as the century drew to a close and Queen Victoria's reign ended, this legendary scientific mind began to weaken. He grudgingly gave way to others with a keener, more modern vision. But the great physicist did not go quietly. With a ready pulpit at his disposal, he publicly proclaimed his doubts over the existence of atoms. He refused to believe that radioactivity involved the transmutation of elements. And believing that the origin of life was a matter beyond the expertise of science and better left to theologians, he vehemently opposed the doctrines of evolution, repeatedly railing against Charles Darwin. Sadly, this pioneer of modern science spent his waning years arguing that the Earth and the Sun could not be more than 100 million years old. And although his early mathematical prowess had transformed our understanding of the forces of nature, he would never truly accept the revolutionary changes he had helped bring about, and it was others who took his ideas to their logical conclusion. In the end Thomson came to stand for all that was old and complacent in the world of 19th century science. Once a scientific force to be reckoned with, a leader to whom others eagerly looked for answers, his peers in the end left him behind-and then meted out the ultimate punishment for not being able to keep step with them. For while they were content to bury him in Westminster Abbey alongside Isaac Newton, they used his death as an opportunity to write him out of the scientific record, effectively denying him his place in history. Kelvin's name soon faded from the headlines, his seminal ideas forgotten, his crucial contributions overshadowed. Destined to become the definitive biography of one of the most important figures in modern science, Degrees Kelvin unravels the mystery of a life composed of equal parts triumph and tragedy, hubris and humility, yielding a surprising and compelling portrait of a complex and enigmatic man.
