PARISUKAT
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24
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Sir
Isaac
Newton
contributed
significantly to the field of science
over his lifetime. He invented
calculus and provided a clear
understanding of optics. But his most
significant work had to do with
forces, and specifically with the
development of a universal law of
gravitation and his laws of motion.
Isaac Newton was born on Christmas
Day to a poor farming family in
Woolsthorpe, England, in 1642. At
the time of Newton's birth England
used the Julian calendar, however,
when
England
adopted
the
Gregorian calendar in 1752, his
birthday became 4th January 1643.
Isaac Newton arrived in the world
only a few months after his father,
Isaac Newton Sr, had died. "The boy
expected to live managing the farm
in the place of the father he had
never known," wrote James Gleick in
"Isaac Newton" (Vintage, 2004).
ISAAC
NEWTON
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A
German
polymath
active
as
a
mathematician, philosopher, scientist and
diplomat who invented calculus in addition to
many other branches of mathematics and
statistics. Leibniz has been called the "last
universal genius" due to his knowledge and
skills in different fields and because such
people became less common during the
Industrial Revolution and spread of specialized
labor after his lifetime. He is a prominent
figure in both the history of philosophy and the
history of mathematics. He wrote works on
philosophy, theology, ethics, politics, law,
history, philology, games, music, and other
studies. Leibniz also made major contributions
to physics and technology, and anticipated
notions that surfaced much later in probability
theory, biology, medicine, geology, psychology,
linguistics and computer science. In addition,
he contributed to the field of library science by
devising a cataloguing system whilst working
at the Herzog August Library in Wolfenbüttel,
Germany, that would have served as a guide
for many of Europe's largest libraries. Leibniz's
contributions to a wide range of subjects were
scattered in various learned journals, in tens of
thousands of letters and in unpublished
manuscripts. He wrote in several languages,
primarily in Latin, French and German.
GOTTFRIE
D WILHELM
LEIBNIZ
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Calculus
is
the
branch
of
mathematics
that
deals
with
continuous change. Calculus is also
called infinitesimal calculus or “the
calculus of infinitesimals”. The
meaning of classical calculus is the
study of continuous change of
functions. Most of these quantities
are the functions of time such as
velocity is equal to change in
distance with respect to time. The
two major concepts of calculus are:
Derivatives
Integrals
The derivative is the measure of the
rate of change of a function
whereas integral is the measure of
the area under the curve. The
derivative explains the function at a
specific point while the integral
accumulates the discrete values of a
function over a range of values.
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In calculus, differentiation is one of
the two important concepts apart
from integration. Differentiation is a
method of finding the derivative of a
function. Differentiation is a process,
in Maths, where we find the
instantaneous rate of change in
function based on one of its
variables.
The
most
common
example is the rate change of
displacement with respect to time,
called velocity. The opposite of
finding a derivative is antidifferentiation.
If x is a variable and y is another variable,
then the rate of change of x with respect to
y is given by dy/dx. This is the general
expression of derivative of a function and is
represented as f'(x) = dy/dx, where y = f(x)
is any function.
DERIVATIVES
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There is a number of methods
of calculations among which
are functions, differentiation,
and integration. Applications
of Integrals are applied in
various
fields
like
Mathematics,
Science,
Engineering. Further, for the
calculation
of
areas
or
irregular shapes in a twodimensional space, we use
majorly integrals formulas.
Given the derivative f’ of the function f, a question
that arises is, "Can we determine the function f?"
Here, the function f is called antiderivative or integral
of f’. The process of finding the antiderivative is
called integration. On the other hand, the value of
the function found by the process of integration is
called an Integral.
INTEGRALS
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Forensic science is an evergrowing field of science that
can be further subdivided
into: toxicology, anthropology,
odontology, mathematics, and
many others. Applications of
calculus to forensic science
can most clearly be seen in
the fields of forensic biology
and pathology. For calculus in
forensic
biology,
DNA
sequences use power series
as a powerful tool to compare
DNA from crime scenes, for
example. To put it in simpler
terms, power series are to
functions what DNA molecules
are to people. Specifically for
pathologists,
calculus
is
needed to estimate the time
of death for victims. Overall,
calculus
has
many
applications to many of the
subfields and forensics and is
often a useful tool in crime
scene investigation.
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THE USE OF
DIFFERENTIAL
EQUATIONS IN
FORENSIC
PATHOLOGY
vol. 1
A different kind of
calculus is used my
medical examiners and
forensic
technicians
everyday to estimate
time of death of a victim.
When a victim dies, they
experience three stages
of death, where the body
starts to decompose.
The first, livor mortis,
occurs twenty minutes to
three hours after death.
In this stage, the blood
settles to the lower part
of the body, creating a
purplish red discoloration
of the skin.
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ALGOR
MORTIS
Algor mortis is the rate at which the body cools after death.
Determining algor mortis is used
to estimate time of death.
Notably, if the victim has been
dead for more than several
hours, the change in body
temperature may be so large
which
could
sacrifice
the
accuracy
of
the
time,temperature is proportional
to the difference between the
temperature of the object and
that
of
the
surrounding
environment.
With
both
temperatures, it is possible to
figure out the constant and the
rate by means of integration and
the use of the properties of
exponential
functions.
The
following problem shows how
this
method
works
by
determining both constants and,
notably, by deriving a clear
function
between
the
temperature of a murdered body
and time to estimate time of
death
based
on
initial
conditions.
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vol. 1
A CALCULUS CAROLBy Denis Gannon (1940-1991)
(sung to the tune of "Oh, Christmas Tree")
Oh, Calculus; Oh, Calculus,
How tough are both your branches.
Oh, Calculus; Oh, Calculus,
To pass, what are my chances@
Derivatives I cannot take,
At integrals my fingers shake.
Oh, Calculus; Oh, Calculus,
How tough are both your branches.
Oh, Calculus; Oh, Calculus,
Your theorems I can't master.
Oh, Calculus; Oh, Calculus,
My proofs are a disaster.
You pull a trick out of the air,
Or find a reason, God knows where.
Oh, Calculus; Oh, Calculus,
Your theorems I can't master.
Oh, Calculus; Oh, Calculus,
Your problems do distress me.
Oh, Calculus; Oh, Calculus,
Related rates depress me.
I walk toward lampposts in my sleep,
And running water makes me weep.
Oh, Calculus; Oh, Calculus,
Your problems do distress me.
Oh, Calculus; Oh, Calculus,
My limit I am reaching.
Oh, Calculus; Oh, Calculus,
For mercy I'm beseeching.
my grades do not approach a B,
They're just an epsilon from D.
Oh, Calculus; Oh, Calculus,
My limit I am reaching.
Aenean imperdiet purus in sapien semper congue.