The Essence of Calculus
Contents:
1.
2.
3.
4.
5.
Roots of the Calculus.
Derivative paradox.
Derivative formulas through geometry.
Trig Derivatives through geometry
List of derivative formulas
Source:
Most of the materials are taken from a video lessons by Grant Sanderson.
Grant Sanderson - is a mathematician and the owner of the official website
“3blue1brown”. Link:( https://www.3blue1brown.com/)
Book Recommendations:
1. “Humble Pi: A Comedy of Maths Errors” - (by the author Matt Parker)
2. “Infinite Powers: How Calculus Reveals the Secrets of the Universe” - (by
the author Steven Strogatz)
3. “Change Is the Only Constant: The Wisdom of Calculus in a Madcap
World” – (by the author Ben Orlin)
1.Roots of the Calculus
Calculus has a lot of rules and formulas which are often presented as things
to be memorized. Lots of derivative formulas for example:
Power rule - is the most often seen and used rule in a
derivatives. It’s simply done by multiplying the
coefficient by a power and by subtracting 1 from the
power.
Chain rule - is one of the important rules
in calculus as you work through
complicated problems, especially in
trigonometric functions.
Product rule - another one of the
fundamental and important formulas in
derivatives.
Quotient rule – like the other rules this
one is one of the basics and important rule.
But, now don’t worry about if you don’t understand these rules as you read
further you will learn and understand why we use and when we use these rules. In
Calculus we learn: Derivatives, Integrals, Differentials, Tailor Series, Implicit
differentiation and etc...
Introduction
“The art of doing mathematics is finding that special case that contains all the
germs of generality” – David Hilbert
The Fathers of Calculus
Isaac Barrow (October 1630 – 4 May 1677) - was an
English Christian theologian and mathematician who is
generally given credit for his early role in the development
of infinitesimal calculus; in particular, for proof of
the fundamental theorem of calculus.
Isaac Newton (25 December 1642 – 20 March 1726/27) – was
an English mathematician, physicist, astronomer, alchemist,
theologian, and author (described in his time as a "natural
philosopher"), widely recognized as one of the greatest
mathematicians and physicists and among the most influential
scientists of all time.
Gottfried Wilhelm von Leibniz (1 July 1646 – 14 November
1716)
was
a
German polymath active
as
a mathematician, philosopher, scientist and diplomat. He is one
of the most prominent figures in both the history of
philosophy and the history of mathematics. He wrote works
on philosophy, theology, ethics, politics, law and philology.
People who made the Calculus rigorous
Augustin-Louis Cauchy (21 August 1789 – 23 May 1857) was a French mathematician, engineer, and physicist who
made pioneering contributions to several branches of
mathematics, including mathematical analysis and continuum
mechanics.
Karl Theodor Wilhelm Weierstrass (31 October 1815 – 19
February 1897) - was a German mathematician often cited as
the "father of modern analysis". Despite leaving university
without a degree, he studied mathematics and trained as a
school teacher, eventually teaching mathematics,
physics, botany and gymnastics.