this is a research project for AAM high school

1. History of calculus
Altamimi, yasser N.

2. The Ancients
Pythagoras
(c. 580 - 500 B.C.)
Though not much is known of
this mysterious man, it is
almost certain that
mathematics began with him.
Pythagoras led a half-
religious, half-mathematical
group. The Pythagoreans
credited all their work to their
leader and their mottos
became "Everything is
number“.

3. Archimedes
(c.287-212 B.C.)
Archimedes was one of the
three greatest
mathematicians of all time.
Though he became famous
for many of his inventions,
inlcuding the "Screw of
Archimedes" and many war
machines he designed for
the King of Greece, his true
passion was for pure
mathematics.

4. The Early Moderns
Sir Isaac Newton
(1642-1727)
Newton actually discovered
calculus between 1665 and
1667 after his university
closed due to an outbreak
of the Plague. Newton was
only 22 at the time.
Newton is best known for
his work in physics, and
especially his three laws of
motion.

5. Fourier
(1768-1830)
Fourier was torn between his
father's desire for him to enter
the priesthood and his real
interest in mathematics. By the
age of 14 mathematics won out.
He became involved in the
aftermath of the French
Revolution. He also expanded
the definition of a function.
Riemann used the Fourier
series to define a definite
integral, and the series has
also been used for many other
applications to physics.

6. The Later Moderns
Johann Carl Friedrich Gauss
(1777-1885)
Perhaps the greatest
mathematician that ever
lived, Gauss made contributions
to many areas including number
theory, differential equations,
conics, and differential geometry.
He is said to have discovered non-
Euclidean geometry although he
never published anything on the
matter because he did not want
to ruin his reputation.

7. Lord Kelvin (William Thomson)
(1824-1907)
Lord Kelvin gained fame and
fortune when he invented the
mirror galvanometer, a
mechanism that could be used to
translate morse code sent over
the Atlantic Ocean. He applied
math to heat flow using
Fourier analysis (which
involves trigonometric
integrals) and this eventually
led him to his most famous
(and lucrative) discovery. Lord
Kelvin also devised the
absolute temperature scale
that bears his name.

8. RIGORIZATION
• various mathematicians used the concept of the limit
to give concrete meaning to the principles developed
my Leibniz and Newton. Enter Augustin
Louis Cauchy (1789 – 1857).
He succeeded in providing an algebraic foundation for
derivative, integral, and other fundamental ideas of cal
culus His two most important insights were: 1.)
Limits could be given a rigorous definition based on in
equalities 2.)
The derivative, integral, continuity, and infinite series c
ould all be given a rigorous foundation based on limits.

9. ANTICIPATION
• various mathematicians provided the stepping
stones to build the concepts of calculus. The
Anticipation of calculus started way back in the
time of ancient Greece, when, at around 450BC,
the philosopher Zeno of Elea made this
conjecture: If a body moves from A to B then
before it reaches B it passes through the mid-
point, say B1 of AB. Now to move to B1 it must
first reach the mid-point B2 of AB1. Continue this
argument to see that A must move through an
infinite number of distances and so cannot
move. Zeno of Elea

10. DEVELOPMENT
• During the Development, Newton and Liebniz developed
the main concepts and prinicples used today Isaac Newton
Gottfried Wilhelm von Leibniz created the foundations of
Calculus and brought all of these techniques together
under the umbrella of the derivative and integral. However,
their methods were not always logically sound, and it took
mathematicians a long time during the Rigorization stage to
justify them and put Calculus on a sound mathematical
foundation. In their development of the calculus both
Newton and Leibniz used "infinitesimals", quantities that
are infinitely small and yet nonzero. Of course, such
infinitesimals do not really exist, but Newton and Leibniz
found it convenient to use these quantities in their
computations and their derivations of results.