The discovery of infinite products byWallis and infinite series by Newton marked the
beginning of the modern mathematical era. The use of series allowed Newton to find
the area under a curve defined by any algebraic equation, an achievement completely
beyond the earlier methods ofTorricelli, Fermat, and Pascal. The work of Newton and
his contemporaries, including Leibniz and the Bernoullis, was concentrated in mathematical
analysis and physics.
The art of teaching, Mark Van Doren said, is the art of assisting discovery. I have tried to
write a book that assists students in discovering calculus—both for its practical power and
its surprising beauty. In this edition, as in the first five editions, I aim to convey to the student
a sense of the utility of calculus and develop technical competence, but I also strive
to give some appreciation for the intrinsic beauty of the subject. Newton undoubtedly
experienced a sense of triumph when he made his great discoveries. I want students to
share some of that excitement.
Ato Z of Mathematicians contains the fascinating
biographies of 150 mathematicians:
men and women from a variety of cultures, time
periods, and socioeconomic backgrounds, all of
whom have substantially influenced the history
of mathematics. Some made numerous discoveries
during a lifetime of creative work; others
made a single contribution. The great Carl
Gauss (1777–1855) developed the statistical
method of least squares and discovered countless
theorems in algebra, geometry, and analysis.
At the time of Isaac Newton’s invention of the calculus in the 17th century, the mechanical clock was the most
sophisticated machine known. The simplicity of the clock allowed its movements to be completely described with
mathematics. Newton not only described the clock’s movements with mathematics, but also the movements of the
planets and other astronomical bodies. Because of the success of the Newtonian method, a mathematics-based
model of reality resulted.
Important breakthroughs in the foundations of mechanical engineering occurred in England during the 17th century when Sir Isaac Newton both formulated the three Newton's Laws of Motion and developed Calculus, the mathematical basis of physics. Newton was reluctant to publish his methods and laws for years, but he was finally persuaded to do so by his colleagues, such as Sir Edmund Halley, much to the benefit of all mankind.
IT HAS BEEN SAID THAT SIR ISAAC NEWTON was the last person to know everything. He was an
accomplished physicist (his three laws of motion were the basis of classical mechanics, which defi ned
astrophysics for three centuries), mathematician (he was one of the inventors of calculus and
developed Newton’s Method for fi nding roots of equations), astronomer, natural philosopher,
and alchemist (okay, maybe the last one was a mistake). He invented the refl ecting telescope, a theory
of color, and a law of cooling, and he studied the speed of sound.