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A History of Analysis
Analysis as an independent subject was created as part of the scientific revolution in the seventeenth century. Kepler, Galileo, Descartes, Fermat, Huygens, Newton, and Leibniz, to name but a few, contributed to its genesis. Since the end of the seventeenth century, the historical progress of mathematical analysis has displayed unique vitality and momentum. No other mathematical field has so profoundly influenced the development of modern scientific thinking. Describing this multidimensional historical development requires an in-depth discussion which includes a reconstruction of general trends and an examination of the specific problems. This volume is designed as a collective work of autho...
The Cambridge History of Science: Volume 5, The Modern Physical and Mathematical Sciences
A new and comprehensive examination of the history of the modern physical and mathematical sciences.
Heinrich Hertz: Classical Physicist, Modern Philosopher
The sub-title of this symposium is accurate and, in a curious way, promises more than it states: Classical Physicist, Modem Philosopher. Heinrich Hertz, as the con summate experimentalist of 19th century technique and as brilliant clarifying critic of physical theory of his time, achieved one of the fulfilments but at the same time opened one of the transition points of classical physics. Thus, in his 'popular' lecture 'On the Relations Between Light and Electricity' at Heidelberg in the Fall of 1889, Hertz identified the ether as henceforth the most fundamental problem of physics, as the conceptual mystery but also the key to understanding mass, electric ity, and gravity. Of Hertz's demonst...
Lacroix and the Calculus
Silvestre François Lacroix was not a prominent mathematical researcher, but he was certainly a most influential mathematical book author. His most famous work is the three-volume Traité du calcul différentiel et du calcul intégral, which is an encyclopedic appraisal of 18th-century calculus that remained the standard reference on the subject through much of the 19th century. This book provides the first global and detailed study of Lacroix's Traité Traité du calcul.
Number Theory in the Spirit of Liouville
A gentle introduction to Liouville's powerful method in elementary number theory. Suitable for advanced undergraduate and beginning graduate students.
An Imaginary Tale
Today complex numbers have such widespread practical use--from electrical engineering to aeronautics--that few people would expect the story behind their derivation to be filled with adventure and enigma. In An Imaginary Tale, Paul Nahin tells the 2000-year-old history of one of mathematics' most elusive numbers, the square root of minus one, also known as i. He recreates the baffling mathematical problems that conjured it up, and the colorful characters who tried to solve them. In 1878, when two brothers stole a mathematical papyrus from the ancient Egyptian burial site in the Valley of Kings, they led scholars to the earliest known occurrence of the square root of a negative number. The pa...
From Natural Philosophy to the Sciences
During the 19th century, much of the modern scientific enterprise took shape: scientific disciplines were formed, institutions and communities were founded and unprecedented applications to and interactions with other aspects of society and culture occurred. taught us about this exciting time and identify issues that remain unexamined or require reconsideration. They treat scientific disciplines - biology, physics, chemistry, the earth sciences, mathematics and the social sciences - in their specific intellectual and sociocultural contexts as well as the broader topics of science and medicine; science and religion; scientific institutions and communities; and science, technology and industry. From Natural Philosophy to the Sciences should be valuable for historians of science, but also of great interest to scholars of all aspects of 19th-century life and culture.
Change and Variations
This book presents a history of differential equations, both ordinary and partial, as well as the calculus of variations, from the origins of the subjects to around 1900. Topics treated include the wave equation in the hands of d’Alembert and Euler; Fourier’s solutions to the heat equation and the contribution of Kovalevskaya; the work of Euler, Gauss, Kummer, Riemann, and Poincaré on the hypergeometric equation; Green’s functions, the Dirichlet principle, and Schwarz’s solution of the Dirichlet problem; minimal surfaces; the telegraphists’ equation and Thomson’s successful design of the trans-Atlantic cable; Riemann’s paper on shock waves; the geometrical interpretation of me...
The Significance of the Hypothetical in the Natural Sciences
Naturwissenschaftler und Philosophen haben im Lauf der Wissenschaftsgeschichte unterschiedliche Auffassungen vom Hypothesencharakter empirischer Theorien entwickelt. Der Band widmet sich drei verschiedenen Epochen, in denen der Erkenntnisoptimismus erfolgreicher Wissenschaftspraxis auf ein wachsendes Bewusstsein der Grenzen naturwissenschaftlicher Einsicht trifft: der Frühen Neuzeit (Kopernikus, Kepler, Bacon, Galilei, Descartes, Boyle, Newton, Locke, mit einem Rückblick auf die mittelalterlichen Autoren Maimonides und Gersonides), dem mechanistischen Weltbild des 19. Jahrhunderts (Herschel, Whewell, Mill, C. G. J. Jacobi, Carl Neumann, Boutroux, Ch. S. Peirce, mit einem Rückblick auf Lagrange und d'Alembert) und dem 20. Jahrhundert mit dem Aufkommen der modernen Physik (Hertz, Poincaré, Vaihinger, Duhem, Heisenberg, Popper). Abgerundet wird der Band durch Studien zur Gegenwartsdiskussion des wissenschaftlichen Realismus und den Chancen einer hypothetischen Metaphysik der Natur.
The Probability Interpretation and the Statistical Transformation Theory, the Physical Interpretation, and the Empirical and Mathematical Foundations of Quantum Mechanics 1926–1932
Quantum Theory, together with the principles of special and general relativity, constitute a scientific revolution that has profoundly influenced the way in which we think about the universe and the fundamental forces that govern it. The Historical Development of Quantum Theory is a definitive historical study of that scientific work and the human struggles that accompanied it from the beginning. Drawing upon such materials as the resources of the Archives for the History of Quantum Physics, the Niels Bohr Archives, and the archives and scientific correspondence of the principal quantum physicists, as well as Jagdish Mehra's personal discussions over many years with most of the architects of quantum theory, the authors have written a rigorous scientific history of quantum theory in a deeply human context. This multivolume work presents a rich account of an intellectual triumph: a unique analysis of the creative scientific process. The Historical Development of Quantum Theory is science, history, and biography, all wrapped in the story of a great human enterprise. Its lessons will be an aid to those working in the sciences and humanities alike.
