This book concludes the outstanding series of historical studies of the mathematics in the nineteenth century. Previous volumes have studied logic, algebra, number theory, probability, geometry, and analytic functions. The third volume encompasses: an essay on the development of Chebyshev's theory of approximation of functions, later called "Constructive function theory", a systematic analysis of the history of the theory of ordinary differential equations from Chauchy and certain of his predecessors up to Poincaré and A.M. Lyapunov, an essay of the development of the calculus of variations, and a study of the history of finite differences, in whose development Soviet mathematicians have played a prominent role. This book will be a valuable source of understanding the development of these areas. It provides the general reader, as well as historians of science, not only with the descriptive history but also with a good understanding of the outer and inner motivations and the results and effects of the presented concepts and methods.
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Language Notes
Text: English (translation)
Original Language: Russian
Original Language: Russian
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3 of 3 people found the following review helpful:
5.0 out of 5 stars
Long shadow.,
By Palle E T Jorgensen "Palle Jorgensen" (Iowa City, Iowa United States) - See all my reviews (VINE VOICE) (REAL NAME)
This review is from: Mathematics of the 19th Century: Vol. III: Function Theory According to Chebyshev; Ordinary Differential Equations; Calculus of Variations; Theory of Finite Differences (v. 3) (Hardcover)
(It is now in paperback!) I like this book because it highlights how several of the central questions and ideas in mathematics from the 19th century still cast a long shadow into the present. It is as true for the pioneering work of Abel and Galois, from the early part of the period which is covered, as it is for the discoveries of Chebychev, Markov, and Kolmogorov toward the end. The period starts roughly at the time of the Napoleon wars, and extends up to the Second World War. The articles in this well written book go into mathematical detail (for example, Kummer's theory and work on Fermat's Last Theorem, Dedekin's ideal theory, and cuts,...)and they represent a well chosen treat of papers, written by major players.
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Inside This Book
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First Sentence:
The following judgment of Chebyshev, from his paper "The drawing of geographical maps" ([B11], Vol. 5, pp. 150-157; Oeuvres, Vol. 1, pp. 239-247), is well-known: The majority of practical problems lead to maximum and minimum problems that are completely new to science, and only by solving those problems can we satisfy the requirements of practice, which always and everywhere seeks the best and most advantageous. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
simplest variational problem, interpolating series, movable endpoints, strong extremum, enveloping series, fonctions fuchsiennes, minimal deviation, topographical system, équations différentielles linéaires, calculi integralis, équations différentielles ordinaires, für reine, développement des fonctions, analytic function theory, symbolic calculus, les équations différentielles, integral residues, certaines équations, interpolation series, geometric locus, isoperimetric problem, multiplier rule, independence theorem, calcul des variations, cylindrical functions Key Phrases - Capitalized Phrases (CAPs): (learn more)
Paris Academy of Sciences, Moscow University, Petersburg Academy of Sciences, Petersburg University, University of Berlin, Berlin Academy of Sciences, Collège de France, Paris Ecole Polytechnique, University of Bologna, International Congress of Mathematicians, Oliver Heaviside, Technische Hochschule, Turin Academy New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
The following judgment of Chebyshev, from his paper "The drawing of geographical maps" ([B11], Vol. 5, pp. 150-157; Oeuvres, Vol. 1, pp. 239-247), is well-known: The majority of practical problems lead to maximum and minimum problems that are completely new to science, and only by solving those problems can we satisfy the requirements of practice, which always and everywhere seeks the best and most advantageous. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
simplest variational problem, interpolating series, movable endpoints, strong extremum, enveloping series, fonctions fuchsiennes, minimal deviation, topographical system, équations différentielles linéaires, calculi integralis, équations différentielles ordinaires, für reine, développement des fonctions, analytic function theory, symbolic calculus, les équations différentielles, integral residues, certaines équations, interpolation series, geometric locus, isoperimetric problem, multiplier rule, independence theorem, calcul des variations, cylindrical functions Key Phrases - Capitalized Phrases (CAPs): (learn more)
Paris Academy of Sciences, Moscow University, Petersburg Academy of Sciences, Petersburg University, University of Berlin, Berlin Academy of Sciences, Collège de France, Paris Ecole Polytechnique, University of Bologna, International Congress of Mathematicians, Oliver Heaviside, Technische Hochschule, Turin Academy New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 27
books:
See all 27 books this book cites
3
books
cite this book:
- Divergent Series (AMS Chelsea Publishing) by G. H. Hardy in Back Matter (1), and Back Matter (2)
- Ordinary Differential Equations by Augustin Cauchy on page 128, and page 160
- Electrical Papers by Oliver Heaviside on page 133, and Back Matter
- A Treatise on Differential Equations by George Boole on page 130, and page 134
- Analytical Mechanics (Boston Studies in the Philosophy of Science) by J.L. Lagrange in Back Matter (1), and Back Matter (2)
See all 27 books this book cites
- An Imaginary Tale: The Story of i [the square root of minus one] by Paul J. Nahin in Back Matter
- Mathematical Evolutions (Spectrum Series) by Abe Shenitzer on page 126
- The Beginnings and Evolution of Algebra (Dolciani Mathematical Expositions) by I. G. Bashmakova in Back Matter
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