Robert Woodhouse: Method

Robert Woodhouse was English mathematician. Explore interesting quotes on method.
Robert Woodhouse: 14   quotes 0   likes

“The methods of the Bernoullis and of Taylor, were held, at the time of their invention, to be most complete and exact. Several imperfections, however, belong to them. They do not apply to problems involving three or more properties; nor do they extend to cases involving differentials of a higher order than the first: for instance, they will not solve the problem, in which a curve is required, that with its radius of curvature and evolute shall contain the least area. Secondly, they do not extend to cases, in which the analytical expression contains, besides x, y, and their differentials, integral expressions; for instance, they will not solve the second case proposed in James Bernoulli's Programma if the Isoperimetrical condition be excluded; for then the arc s, an integral, since it =\int \! dx \sqrt(1+\frac{dy^2}{dx^2}), is not given. Thirdly, they do not extend to cases, in which the differential function, expressing the maximum should depend on a quantity, not given except under the form of a differential equation, and that not integrable; for instance, they will not solve the case of the curve of the quickest descent, in a resisting medium, the descending body being solicited by any forces whatever.”

Robert Woodhouse

A Treatise on Isoperimetrical Problems, and the Calculus of Variations (1810)

Problem , Time , Dependency

“Taylor's method… has no recommendation from its neatness and perspicuity, but is justly censured by John Bernoulli for its obscure conciseness.”

Robert Woodhouse

A Treatise on Isoperimetrical Problems, and the Calculus of Variations (1810)

“To history we shall adhere no farther, than is sufficient to preserve an unbroken series of methods gradually becoming more exact and extensive; the series beginning with the first rude, though perfectly just, method of James Bernoulli, and ending with Lagrange's exquisite and refined Calculus of Variations.”

Robert Woodhouse

p, 125
A Treatise on Isoperimetrical Problems, and the Calculus of Variations (1810)

History