Sir Isaac Newton was an English physicist, mathematician, astronomer , natural philosopher, alchemist, and theologian, who has been considered by many to be the greatest and most influential scientist who ever lived. Newton described universal gravitation and the three laws of motion, which dominated the scientific view of the physical universe for the next three centuries.
Isaac Newton was born on what is retroactively considered 4 January 1643 at Woolsthorpe Manor in Woolsthorpe-by- Colsterworth, a hamlet in the county of Lincolnshire. At the time of Newtons birth, England had not adopted the Gregorian calendar and therefore his date of birth was recorded as Christmas Day, 25 December 1642. Newton was born three months after the death of his father, a prosperous farmer also named Isaac Newton.
Newton was educated at The Kings School, Grantham , and in October 1659 he was removed from school. In June 1661, he was admitted to Trinity College, Cambridge as a sizar – a sort of work-study role. In 1665, he discovered the generalized binomial theorem and began to develop a mathematical theory that later became infinitesimal calculus. Soon after Newton had obtained his degree in August 1665, the university temporarily closed as a precaution against the Great Plague.
Newton received a bachelor’s degree at Trinity College, Cambridge in 1665 The next two years Newton returned home where he came up with most of his discoveries. He returned to Trinity College in 1667, where he became a professor of mathematics in 1669.
King school Trinity College
Calculus was invented by sir Isaac Newton Isaac Newton developed the use of calculus in his laws of motion and gravitation.
Calculus is a branch of mathematics focused on limits, functions, derivatives, integrals, and infinite series. This subject constitutes a major part of modern mathematics education. It has two major branches, differential calculus and integral calculus, which are related by the fundamental theorem of calculus. Calculus is the study of change, in the same way that geometry is the study of shape and algebra is the study of operations and their application to solving equations.
Calculus has historically been called "the calculusof infinitesimals", or "infinitesimal calculus". More generally, calculus refers to any method or system ofcalculation guided by the symbolic manipulation ofexpressions.Some examples of other well-known calculiare propositional calculus, variational calculus, lambdacalculus, pi calculus, and join calculus .
A course in calculus is a gateway to other, more advanced courses in mathematics devoted to the study of functions and limits, broadly called mathematical analysis. Calculus has widespread applications in science, economics, and engineering and can solve many problems for which algebra alone is insufficient.
The ancient period introduced some of the ideas that led to integral calculus, but does not seem to have developed these ideas in a rigorous and systematic way. Calculations of volumes and areas, one goal of integral calculus, can be found in the Egyptian Moscow papyrus (c. 1820 BC), but the formulas are mere instructions, with no indication as to method, and some of them are wrong. From the age of Greek mathematics, Eudoxus (c. 408−355 BC) used the method of exhaustion, which prefigures the concept of the limit, to calculate areas and volumes, while Archimedes (c. 287−212 BC) developed this idea further, inventing heuristics which resembles the methods of integral calculus.
The method of exhaustion was later reinvented in China by Liu Hui in the 3rd century AD in order to find the area of a circle. In the 5th century AD, Zu Chongzhi established a method that would later be called Cavalieris principle to find the volume of a sphere.
In the 14th Century Indian mathematician Madhava of Sangamagrama and the Kerala school of astronomy and mathematics stated many components of calculus such as the Taylor series, infinite series approximations, an integral test for convergence, early forms of differentiation, term by term integration, iterative methods for solutions of non- linear equations, and the theory that the area under a curve is its integral. Some consider the Yuktibhāṣā to be the first text on calculus.
Leibniz and Newton are usually both credited with the invention of calculus. Newton was the first to apply calculus to general physics and Leibniz developed much of the notation used in calculus today. The basic insights that both Newton and Leibniz provided were the laws of differentiation and integration, second and higher derivatives, and the notion of an approximating polynomial series. By Newtons time, the fundamental theorem of calculus was known.
Since the time of Leibniz and Newton, many mathematicians have contributed to the continuing development of calculus. One of the first and most complete works on finite and infinitesimal analysis was written in 1748 by Maria Gaetana Agnesi
Sir Isaac Newton portrait
Integral calculus is the study of the definitions, properties, and applications of two related concepts, the indefinite integral and the definite integral. The process of finding the value of an integral is called integration. In technical language, integral calculus studies two related linear operators.
The fundamental theorem of calculus states that differentiation and integration are inverse operations. More precisely, it relates the values of antiderivatives to definite integrals. Because it is usually easier to compute an antiderivative than to apply the definition of a definite integral, the Fundamental Theorem of Calculus provides a practical way of computing definite integrals. It can also be interpreted as a precise statement of the fact that differentiation is the inverse of integration.
In geometry, the tangent line (or simply the tangent) to a plane curve at a given point is the straight line that "just touches" the curve at that point—that is, coincides with the curve at that point without crossing to the other side of the curve. More precisely, a straight line is said to be a tangent of a curve y = f(x) at a point x = c on the curve if the line passes through the point(c, f(c)) on the curve and has slope f(c) where f is the derivative of f. A similar definition applies to space curves and curves in n-dimensional Euclidean space.
Tangent Tangent Tangentgraph circle line
In the mathematical field of numerical analysis, a Newton polynomial, named after its inventor Isaac Newton, is the interpolation polynomial for a given set of data points in the Newton form. The Newton polynomial is sometimes called Newtons divided differences interpolation polynomial because the coefficients of the polynomial are calculated using divided differences. For any given set of data points, there is only one polynomial (of least possible degree) that passes through all of them. Thus, it is more appropriate to speak of "the Newton form of the interpolation polynomial" rather than of "the Newton interpolation polynomial". Like the Lagrange form, it is merely another way to write the same polynomial.
Newtons formula is of interest because it is the straightforward rate of change of its rate of change, etc. at one particular x value. Newtons formula is Taylors polynomial based on finite differences instead of instantaneous rates of change.
Integration is an important concept in mathematics and, together with its inverse, differentiation, is one of the two main operations in calculus. Given a function f of a real variable x and an interval [a, b] of the real line, the definite integral is defined informally to be the area of the region in the xy-plane bounded by the graph of f, the x-axis, and the vertical lines x = a and x = b, such that areas above the axis add to the total, and the area below the x axis subtract from the total.
A differential form is a mathematical concept in the fields of multivariable calculus, differential topology and tensors. The modern notation for the differential form, as well as the idea of the differential forms as being the wedge products of exterior derivatives forming an exterior algebra, was introduced by Élie Cartan.
In the 1690s, Newton wrote a number of religious tracts dealing with the literal interpretation of the Bible. Henry Moores belief in the Universe and rejection of Cartesian dualism may have influenced Newtons religious ideas. A manuscript he sent to John Locke in which he disputed the existence of the Trinity was never published. Later works – The Chronology of Ancient Kingdoms Amended (1728) and Observations Upon the Prophecies of Daniel and the Apocalypse of St. John (1733) – were published after his death. He also devoted a great deal of time to alchemy (see above). Newton was also a member of the Parliament of England from 1689 to 1690 and in 1701, but according to some accounts his only comments were to complain about a cold draught in the chamber and request that the window be closed.
Newton died in his sleep in London on 31 March 1727 and was buried in Westminster Abbey. Newton, a bachelor, had divested much of his estate to relatives during his last years, and died intestate. After his death, Newtons hair was examined and found to contain mercury, probably resulting from his alchemical pursuits. Mercury poisoning could explain Newtons eccentricity in late life.