Questions tagged [leibniz]

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8
votes
2answers
993 views

Where did Leibniz explore the product rule of differential calculus?

In what book/letter did Gottfried Wilhelm Leibniz explore the product rule as part of differential calculus?
5
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2answers
160 views

Why do we use Leibniz's “version” of calculus instead of Newton's?

I understand that they invented calculus independently at roughly the same time, but why do we use Leibniz's terminology/notation rather than Newton's? For example, why don't we use "fluxion"...
3
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1answer
270 views

Source of claim that Leibniz discovered separation of variables for ODEs in 1691?

Claims I'm evaluating I've read in multiple sources that Leibniz formulated separation of variables for ODEs in 1691. A couple example sources are below. Mathematical Thought from Ancient to Modern ...
17
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3answers
3k views

What does it mean by “d-ism of Leibniz” and “dotage of Newton” in simple English?

I am reading this article by Donald E. Knuth and get stuck by this sentence: Our mathematical language continues to improve, just as “the d-ism of Leibniz overtook the dotage of Newton” in past ...
7
votes
1answer
660 views

Why is differentiation under the integral sign named the Leibniz rule?

The question here asked why differentiation under the integral sign is named "Feynman's trick". That is a comparatively recent name for the method. Aside from the name "differentiation under the ...
11
votes
3answers
715 views

Was English mathematics behind Europe by many years because of Newton's notation?

Below are several quotes suggesting that Newton's notation had the effect of retarding English mathematics by 50 years, 100 years, or even centuries. Here is my simplistic two-sentence historical ...
1
vote
1answer
134 views

What was the mechanical principle of Leibniz's “integraph”?

For a very long time I've searched in the internet what was the actual integrating device which Leibniz designed in 1693. Yesterday I found the answer - the instrument which Leibniz devised is the ...
1
vote
1answer
102 views

Did Leibniz also design analog computers?

My question is based on the information that appears in several websites, according to which I found three examples of a kind of instrument that was probably an analog computer. The first one ...
2
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2answers
135 views

What navigation instrument did Leibniz develop?

My question refers to Gottfried Leibniz's "instrumentum longuitidimum" mentioned in some sites — a device that could record the course of a ship in sea and display its recent position directly on a ...
3
votes
0answers
208 views

How did Leibniz's prototypes of a yaw system and a braking mechanism (for windmills) work?

My question is concerned with two hardly mentioned yet very ingenious inventions of Leibniz. These two inventions represent technological inventiveness and visionary insight (about wind energy ...
15
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1answer
297 views

What kind of mathematical education did Leibniz have?

It doesn't seem that he began his life in mathematics. Does anyone know how it came to be ? What did he read ?
6
votes
2answers
237 views

Did Leibniz use infinite numbers?

Arthur's recent article Arthur, Richard T. W. Leibniz's actual infinite in relation to his analysis of matter. G. W. Leibniz, interrelations between mathematics and philosophy, 137–156, Archimedes,...
13
votes
2answers
640 views

Why is Leibniz less well regarded?

A well-known and specific example is that Leibniz is less well regarded than Newton for his calculus, the reason being notation, Leibniz notation lets you incorrectly work with derivatives as ...
37
votes
5answers
10k views

What is the difference between Calculus of Newton and that of Leibniz?

Are there any differences between the study of Calculus done by Newton as compared to that done by Leibniz? If yes, please mention point by point.