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Gottfried Wilhelm Leibniz:

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Kaliyan F

on 6 June 2014

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Transcript of Gottfried Wilhelm Leibniz:

The Last "Universal Genius"

Leibniz v. Newton
Leibniz's Calculus
born in Leipzig on July 1, 1646
family was Lutheran & elite
father (Friedrich) was a jurist and professor of Moral Philosophy at the University of Leipzig
mother (Catharina) was the daughter of a professor of Law

Education & Life
University of Leipzig (baccalaureate)
University of Altdorf (Doc. of Law)
spent 4 years in Paris & met many influential people (intellectuals, mathematicians, etc.)
tutored by Christiaan Huygens in physics, philosophy, and math
developed many of his ideas after exposure to Pascal's manuscripts
Mathematical Discoveries & Later Life
Origin of the Dispute
Newton wrote
Method of Fluxions
in 1671 but refused to publish (or even publicly discuss) his works.
Leibniz published his papers on differential and integral calculus in 1684 and 1686, respectively
Newton's works were finally published in 1736, almost ten years after his death
By this time, Leibniz's works were already very well-read
In 1715, the Royal Society credited Newton with the discovery of calculus & Leibniz was guilty of plagiarism
Leibniz died unhonored & poor
After the death of Leibniz, the accusations of plagiarism were proved false & both men now are accredited for the discovery.
Newton had an impressive, stately funeral, but it was too late for Leibniz.
Much of Leibniz's discoveries are used commonly in calculus today, while Newton's are not.
General Leibniz Rule (the Product Rule)
Leibniz is generally credited with finding and providing the proof for the product rule, in which (fg)'= f'g+fg'.

So thanks for that.
The Argument
Had Leibniz discovered calculus independently or had he just invented another notation for Newton's ideas?
Debate lasted from 1709 until Leibniz's death in 1716 and involved Newton's disciple John Keill, as well as many other mathematicians
No one doubted that Newton had already developed his method when Leibniz began work, but there was no proof of this.
He only explained his method a full 20 years later, when Leibniz's articles were already well-read.
His manuscripts came to light only in 1736, well after his death and Leibniz's.
Leibniz's Arguments
published a description of his method years before Newton printed anything;
always alluded to the discovery as being his own invention, a statement which went unchallenged for years;
demonstrated in his private papers his development of calculus independently of Newton's path.
Newton's Arguments
saw some of Newton's papers on the subject around 1676.
may have obtained the fundamental ideas of the calculus from those papers.
The fact that Leibniz's claim went unchallenged is immaterial, and no attempt was made to rebut the private demonstrations.
Leibniz's Disadvantages
Leibniz had less education than Newton and was generally regarded as not having as much mathematical skill.
Leibniz saw mathematics as a link to his other interests, especially philosophy, & didn't pursue it as intensely.
Newton was already well-known for other achievements
A method for finding the determinant was
rediscovered and applied by Leibniz.
Example: Find the Determinant
Leibniz's Integral Rule
The Derivative is equal to...
Used when a function is defined as an
integral. Can be used to analyze a mathematical model or to evaluate very challenging integrals.
Find the derivative, f'(x)
What do organic mathematicians throw into their fireplaces?

Natural Logs!
(cos(tx))/t (dt)
discovered differential calculus, integrals, & infinite series
designed a calculating machine capable of performing addition, subtraction, multiplication, and division
vast network of correspondents
sent letters to over 1100 people
died November 14th, 1716
yay calculus
A math professor in an unheated room is cold and calculating.
Around 1673, Leibniz found a series that was able to converge to the value of pi by using James Gregor's arctangent expansion.

It converges very slowly: 5 billion terms are needed to get 10 correct digits of pi.(Pattanayak)
Finding Pi
Deaf mathematicians communicate through sine language.
When the stats teacher wrote a cookbook, she called it 'Pi A La Mode.'
with puns!
Now try it yourself!
Find the derivative, f'(t)
Conrad, Keith. “Differentiating Under the Integral
Sign.” PDF file. Web. 3 June 2014.

“Generalized Product Rule: Leibniz’s formula”.
Physics pages. Wordpress, March 2011. Web. 27 May 2014.

Hand, Paul. “Problem on computing the
determinant of a 3x3 matrix.” Leading Lesson. 2014. Web. 3 June 2014

Look, Brandon. “Gottfried Wilhelm Leibniz.” The
Stanford Encyclopedia of Philosophy (Fall 2014 Edition). Stanford University, 22 Dec. 2007. Web. 20 May 2014.

O’Connor, John J., and Edmund F. Robertson.
“Gottfried Wilhelm von Leibniz.” The MacTutor History of Mathematics Archive. University of St. Andrews, April 2o14. Web. 20 May 2014.

Pattanayak, Ari. The Mathematical Leibniz.
Rutgers Department of Mathematics, May 2002. Web. 27 May 2014.

Thiel, Christopher. “Determinants.” Internet
Archive. Internet Archive, March 2013. Web. 1 June 2014.

Tisdale, Chris. “Differentiate under integral
signs: Leibniz rule.” Online Video Clip. Youtube. Youtube, 9 November 2011. Web. 2 June 2014.

Full transcript