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The Early Period of the Calculus of Variations (Hardcover, 1st ed. 2016)
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The Early Period of the Calculus of Variations (Hardcover, 1st ed. 2016)
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This monograph explores the early development of the calculus of
variations in continental Europe during the Eighteenth Century by
illustrating the mathematics of its founders. Closely following the
original papers and correspondences of Euler, Lagrange, the
Bernoullis, and others, the reader is immersed in the challenge of
theory building. We see what the founders were doing, the
difficulties they faced, the mistakes they made, and their
triumphs. The authors guide the reader through these works with
instructive commentaries and complements to the original proofs, as
well as offering a modern perspective where useful. The authors
begin in 1697 with Johann Bernoulli's work on the brachystochrone
problem and the events leading up to it, marking the dawn of the
calculus of variations. From there, they cover key advances in the
theory up to the development of Lagrange's -calculus, including: *
The isoperimetrical problems * Shortest lines and geodesics *
Euler's Methodus Inveniendi and the two Additamenta Finally, the
authors give the readers a sense of how vast the calculus of
variations has become in centuries hence, providing some idea of
what lies outside the scope of the book as well as the current
state of affairs in the field. This book will be of interest to
anyone studying the calculus of variations who wants a deeper
intuition for the techniques and ideas that are used, as well as
historians of science and mathematics interested in the development
and evolution of modern calculus and analysis.
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