A History of the Calculus of Variations in the Eighteenth Century
Shortly after the invention of differential and integral calculus, the calculus of variations was developed. The new calculus looks for functions that minimize or maximize some quantity, such as the brachistochrone problem, which was solved by Johann Bernoulli, Leibniz, Newton, Jacob Bernoulli and l'Hopital and is sometimes considered as the starting point of the calculus of variations. In Woodhouse's book, first published in 1810, he has interwoven the historical progress with the scientific development of the subject. The reader will have the opportunity to see how calculus, during its first one hundred years, developed by seemingly tiny increments to become the highly polished subject that we know today. Here, Woodhouse's interweaving of history and science gives his special point of view on the mathematics. As he states in his preface: ``Indeed the authors who write near the beginnings of science are, in general, the most instructive; they take the reader more along with them, show him the real difficulties and, which is the main point, teach him the subject, the way they themselves learned it.''
What people are saying - Write a review
We haven't found any reviews in the usual places.
Other editions - View all
abscissa Acad amongst analytical expression axis Bernoulli's method brachystochrone Brook Taylor c.dp Calc Calculus of Variations catenary condition consequently constant curve of quickest cycloid deduced determined differential calculus differential coefficients differential equation equal equation of limits Euler Euler's formula Euler's method f Vdx f(Pb former formula of solution function fundamental equation fVdx given Hence instance integral expressions integral sign Isoperimetrical problems James Bernoulli John Bernoulli JVdx Lagrange length limiting curve maxima and minima maximum or minimum maximum property memoir Methodus Inveniendi Novi Comm ordinate P.bg Petrop principle Prob quickest descent R.bg reduced relative maxima Required the curve resulting equation Sciences similar equations Simpson solid of least solution of problems solved substituting suppose symbols tangent terms involving tion torn treatise vary velocity whence