WELCOME TO OUR PRESENTATION

PRESENTATION ONBIOGRAPHY OF BROOK TAYLOR

BROOK TAYLOR (1685-1731)

CREDIT TO… 1. A K M Tanvir Rahman : 152-33-2674 2. Kaimul Islam RudDro : 152-33-2653 3. Monsur Ahmed : 152-33-2628 4. Shahedujjaman : 152-33-2643 5. Md Al Tarek : 152-33-2719

Biodata of Taylor Brook Taylor was born on 18 August 1685 at Edmonton area of London,England.

Residence:England Nationality: English Institution: St John’s college,Cambridge. Fields: Mathematician Known for: Taylor’s Theorem Or, Taylor Series. Died: 29 December,1731

Family Description Brook Taylor was the son of John Taylor of Bifrons House, Kent, and Olivia, daughter of Sir Nicholas Tempest, Bart. The family was fairly well-to-do, and was connected with the minor nobility. Brook’s grandfather, Nathaniel, had supported Oliver Cromwell. John Taylor was a stern parent from whom Brook became estranged in 1721 when he married a woman said to have been of good family but of no fortune.

In 1723 Brook returned home after his wife’s death in childbirth. He married again in 1725 with his father’s approval, but his second wife died in childbirth in 1730. The daughter born at that time survived.

Educational Description Taylor’s home life seems to have influenced his work in several ways. Two of his major scientific contributions deal with the vibrating string and with perspective drawing. His father was interested in music and art, and entertained many musicians in his home. The family archives were said to contain paintings by Brook, and there is an unpublished manuscript entitled On Musick among the Taylor materials at St. John’s College, Cambridge.

Educational Description This is not the paper said to have been presented to the Royal society prior to 1713, but a portion of a projected joint work by Taylor, Sir Isaac Newton, and Dr. Pepusch, who apparently was to write on the nonscientific aspects of music.

Taylor was tutored at home before entering St. John’s College in 1701, where the chief mathematicians were John Machin and John Keill. Taylor received the LL.B. degree in 1709, was elected to the Royal Society in 1712, and was awarded the LL.D. degree in 1714. He was elected secretary to the Royal Society in January 1714, but he resigned in October 1718 because of ill health and perhaps because of a loss of interest in this rather confining task. He visited France several times both for the sake of his health and for social reasons.

Out of these trips grew a scientific correspondence with Pierre Rémond de Montmort dealing with infinite series and Montmort’s work in probability. In this Taylor served on some occasions as an intermediary between Montmort and Abraham De Moivre. W. W. Rouse Ball reports that the problem of the knight’s tour was first solved by Montmort and De Moivre after it had been suggested by Taylor.

Way of Life The famous Taylor series was printed for the first time in the Methodus incrementorum directa et inversa (1715), although there is evidence that Gottfried Wilhelm Leibniz and Isaac Newton had known the result earlier. The series expresses the value of a function in the neighborhood of a point in terms of the derivatives at the point. Taylor derived the series by taking the limiting case of the general finite difference formula, but he failed to consider the problem of convergence.

He specifically mentioned the case x = 0, which is often known as Maclaurin's series. Joseph Louis Lagrange was the first to recognize fully the importance of the Taylor series, and the first correct proof was given by Augustin Louis Cauchy.

Publishing Theory In 1717 Taylor applied his series to the solution of numerical equations, observing that the method could be used to solve transcendental equations. Other contributions to the calculus included consideration of change of variable, the first singular solution of a differential equation, and the derivation of the differential equation relating to atmospheric refraction. He also contributed a solution to the problem of the center of oscillation.

Publishing Theory Taylor's theorem is taught in introductory level calculus courses and it is one of the central elementary tools in mathematical analysis. Within pure mathematics it is the starting point of more advanced asymptotic analysis, and it is commonly used in more applied fields of numerics as well as in mathematical physics.

Publishing Theory Taylor's theorem also generalizes to multivariate and vector valued functions   on any dimensions n and m. This generalization of Taylor's theorem is the basis for the definition of so-called jets which appear in differential geometry and partial differential equations.

Later Life In 1715 Taylor published his Linear Perspective, followed in 1719 by New Principles of ‘’Linear Perspective’’. These works contained the first general statement of the principle of vanishing points. In his later years he became interested in philosophy, writing” Contemplation philosophical”, which was printed and circulated privately in 1793.

THANKS EVEYRONE

HAVE A NICE DAY…