Sir Isaac Newton was an influential English scientist in the late 1600s. He developed calculus and described universal gravitation and the laws of motion, which dominated scientific views for centuries. Newton invented calculus to solve problems in physics involving instantaneous rates of change. He and Gottfried Leibniz are credited with developing calculus independently and establishing its modern foundations and applications.

2.  Sir Isaac Newton was an
English physicist, mathematician, astrono
mer, 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.

3.  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 Newton's 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.

4.  Newton was educated at The King's 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.

5.  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.

6. King school Trinity College

7.  Newton's work has been said "to distinctly
advance every branch of mathematics then
studied".
 His work on the subject usually referred to as
fluxions or calculus, seen in a manuscript of
October 1666, is now published among Newton's
mathematical papers.

11.  Calculus was invented by sir Isaac Newton
 Isaac Newton developed the use of calculus in
his laws of motion and gravitation.

12.  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.

13. Calculus has historically been called "the calculus
of infinitesimals", or "infinitesimal calculus".
 More generally, calculus refers to any method or system of
calculation guided by the symbolic manipulation of
expressions.
Some examples of other well-known calculi
are propositional calculus, variational calculus, lambda
calculus, pi calculus, and join calculus
.

14.  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.

16.  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.

17.  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 Cavalieri's
principle to find the volume of a sphere.

19.  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.

20.  In Europe, the foundational work was a treatise due
to Bonaventura Cavalieri, who argued that volumes and
areas should be computed as the sums of the volumes
and areas of infinitesimally thin cross-sections.
 The ideas were similar to Archimedes' in The Method,
but this treatise was lost until the early part of the
twentieth century.
 Cavalieri's work was not well respected since his
methods could lead to erroneous results, and the
infinitesimal quantities he introduced were disreputable
at first.

21.  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 Newton's time, the fundamental theorem of calculus was
known.

22.  When Newton and Leibniz first published their results, there was great
controversy over which mathematician (and therefore which country)
deserved credit.
 Newton derived his results first, but Leibniz published first.
 Newton claimed Leibniz stole ideas from his unpublished notes, which
Newton had shared with a few members of the Royal Society. This
controversy divided English-speaking mathematicians from continental
mathematicians for many years, to the detriment of English mathematics.
 A careful examination of the papers of Leibniz and Newton shows that they
arrived at their results independently, with Leibniz starting first with
integration and Newton with differentiation.
 Today, both Newton and Leibniz are given credit for developing calculus
independently.
 It is Leibniz, however, who gave the new discipline its name. Newton called
his calculus "the science of fluxions".

23.  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

24. Sir Isaac Newton portrait

25.  While some of the ideas of calculus had been
developed earlier
in Egypt, Greece, China, India, Iraq, Persia,
and Japan, the modern use of calculus began
in Europe, during the 17th century, when Isaac
Newton and Gottfried Wilhelm Leibniz built on the
work of earlier mathematicians to introduce its basic
principles.
 The development of calculus was built on earlier
concepts of instantaneous motion and area
underneath curves.

26.  In the 19th century, infinitesimals were replaced by limits.
Limits describe the value of a function at a certain input in
terms of its values at nearby input.
 They capture small-scale behavior, just like infinitesimals, but
use the ordinary real number system. In this treatment, calculus
is a collection of techniques for manipulating certain limits.
 Infinitesimals get replaced by very small numbers, and the
infinitely small behavior of the function is found by taking the
limiting behavior for smaller and smaller numbers.
 Limits are the easiest way to provide rigorous foundations for
calculus, and for this reason they are the standard approach.

27.  differential calculus is a subfield of calculus concerned with
the study of the rates at which quantities change. It is one of
the two traditional divisions of calculus, the other being
integral calculus.

28.  The primary objects of study in differential calculus are
the derivative of a function, related notions such as
the differential, and their applications.
 The derivative of a function at a chosen input value describes
the rate of change of the function near that input value. The
process of finding a derivative is called differentiation.
 Geometrically, the derivative at a point equals the slope of
the tangent line to the graph of the function at that point. For
a real-valued function of a single real variable, the derivative of
a function at a point generally determines the best linear
approximation to the function at that point.

30.  In calculus, Leibniz's notation, named in honor
of the 17th-
century German philosopher and mathematician
Gottfried Wilhelm Leibniz, uses the
symbols dx and dy to represent "infinitely small"
(or infinitesimal) increments of x and y, just as
Δx and Δy represent finite increments of x and y.

31.  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.

33.  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.

35.  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.

36. Tangent Tangent Tangent
graph circle line

38.  the maximum and minimum of a function, known
collectively as extrema are the largest and smallest
value that the function takes at a point either within a
given neighborhood or on the function domain in its
entirety
 More generally, the maximum and minimum of a set are
the greatest and least element in the set. Unbounded
infinite sets such as the set of real numbers have no
minimum and maximum.

41.  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 Newton's 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.

42.  Newton's formula is of interest because it is the
straightforward rate of change of its rate of
change, etc. at one particular x value.
 Newton's formula is Taylor's polynomial based
on finite differences instead of instantaneous
rates of change.

44.  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.

46.  There are many ways of formally defining an
integral, not all of which are equivalent.
 The differences exist mostly to deal with
differing special cases which may not be
integrable under other definitions, but also
occasionally for pedagogical reasons.
 The most commonly used definitions of integral
are Riemann integrals and Lévesque integrals.

47.  A "proper" Riemann integral assumes the integrand
is defined and finite on a closed and bounded
interval, bracketed by the limits of integration.
 An improper integral occurs when one or more of
these conditions is not satisfied.
 In some cases such integrals may be defined by
considering the limit of a sequence of
proper Riemann integrals on progressively larger
intervals.

49.  The multiple integral is a type
of definite integral extended to functions of
more than one real variable, for example, ƒ(x, y)
or ƒ(x, y, z).
 Integrals of a function of two variables over a
region in ℝ2 are called double integrals.

51.  The concept of an integral can be extended to more general
domains of integration, such as curved lines and surfaces.
 Such integrals are known as line integrals and surface integrals
respectively.
 These have important applications in physics, as when dealing
with vector fields.
 A line integral (sometimes called a path integral) is an integral
where the function to be integrated is evaluated along a curve.
 Various different line integrals are in use. In the case of a
closed curve it is also called a contour integral.

53.  A surface integral is a definite integral taken over
a surface (which may be a curved set in space); it can be
thought of as the double integral analog of the line
integral.
 The function to be integrated may be a scalar field or
a vector field. The value of the surface integral is the
sum of the field at all points on the surface.
 This can be achieved by splitting the surface into surface
elements, which provide the partitioning for Riemann
sums.

55.  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.

56.  In the 1690s, Newton wrote a number of religious tracts dealing with the
literal interpretation of the Bible.
 Henry Moore's belief in the Universe and rejection of Cartesian dualism may
have influenced Newton's 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.

58.  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, Newton's hair was examined and
found to contain mercury, probably resulting from
his alchemical pursuits. Mercury poisoning could
explain Newton's eccentricity in late life.

59.  French mathematician Joseph-Louis Lagrange often said that Newton
was the greatest genius who ever lived, and once added that Newton
was also "the most fortunate, for we cannot find more than once a
system of the world to establish." English poet Alexander Pope was
moved by Newton's accomplishments to write the famous epitaph:
 Nature and nature's laws lay hid in night;
God said "Let Newton be" and all was light.
 Newton himself had been rather more modest of his own
achievements, famously writing in a letter to Robert Hooke in
February 1676:
 If I have seen further it is by standing on the shoulders of giants.

60.  Newton's monument (1731) can be seen in Westminster Abbey, at the north
of the entrance to the choir against the choir screen, near his tomb.
 It was executed by the sculptor Michael Rysbrack(1694–1770) in white and
grey marble with design by the architect William Kent.
 The monument features a figure of Newton reclining on top of a
sarcophagus, his right elbow resting on several of his great books and his left
hand pointing to a scroll with a mathematical design.
 Above him is a pyramid and a celestial globe showing the signs of the Zodiac
and the path of the comet of 1680.
 A relief panel depicts putti using instruments such as a telescope and
prism.[71] The Latin inscription on the base translates as:

61.  Here is buried Isaac Newton, Knight, who by a strength
of mind almost divine, and mathematical principles
peculiarly his own, explored the course and figures of
the planets, the paths of comets, the tides of the sea,
the dissimilarities in rays of light, and, what no other
scholar has previously imagined, the properties of the
colours thus produced.
 Diligent, sagacious and faithful, in his expositions of
nature, antiquity and the holy Scriptures, he vindicated
by his philosophy the majesty of God mighty and good,
and expressed the simplicity of the Gospel in his
manners.