# Questions tagged [calculus]

For questions about the mathematical field studying functions, focusing on infinitesimals and rates of change.

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### What does an 100 year old calculus exam look like?

I wonder whether the questions on a calculus exam at university were easier or harder 100 years ago. Nowadays we have all these aids and different learning methods. I would love to see an old exam.
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### 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?
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### Where did the contour integral sign appear for the first time?

A simple question: Where did the contour integral sign appear for the first time? Wikipedia says that it was introduced by physicist Arnold Sommefield in 1917 ( Table of mathematical symbols by ...
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### What did Newton's teacher contribute to the Fundamental Theorem of Calculus?

Isaac Barrow was one of the professors who taught Isaac Newton at Cambridge. According to this page, he is said to have made contributions to the Fundamental Theorem of Calculus that was devised by ...
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### Why is the “universal trigonometric substitution” called “Weierstrass's substitution”?

The universal trigonometric substitution converts a rational function in $\sin(x), \cos(x)$ into a rational function of a new variable $t$ by the substitution $t = \tan(x/2)$. It therefore enables ...
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### Newton's evaluation of 1 + 1/3 - 1/5 - 1/7 + 1/9 + 1/11

I had asked the following question on MSE here, and I was directed to this exchange. There is a nice solution in the comments there, but perhaps someone here can add some additional insight? How ...
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### What steps did Richard Feynman take to devise his Integral Trick?

Richard Feynman is considered to be one of the greatest minds in physics, and has won many accolades as a result of his research in areas such as quantum mechanics and particle physics. However, I am ...
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### Who introduced the comma notation for partial derivatives?

In general relativity, it is common to use the comma notation for partial derivatives $$\frac{\partial g_{\mu\nu}}{\partial x_\rho} = g_{\mu\nu_,\rho}$$ Where did this notation first appear? Was it ...
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### 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"...
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### Did Benjamin Franklin know calculus?

My sense is that Franklin was a scientist more like Faraday than Maxwell. Given also that Calculus was fairly new when Franklin was in school (and as far as I know, Benjamin Franklin did not get very ...
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### What is the history of staircase or 𝜋=4 paradox?

The staircase 'paradox' has been discussed here and elsewhere a few times (search for staircase + paradox). My question is whether this puzzle has been discussed in the academic literature or ...
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### Before differential calculus was discovered, why were mathematicians interested in tangents?

I think it is often said that one great motivation for the invention of calculus was to have a tool allowing to calculate the slope of a tangent to a curve $C$ at a given point $P$, and even, to find ...
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### Were fluxions the only infinitesimals?

The Encyclopaedia Britannica in its history of Science article states that Newton integrals were made of infinitesimals, whereas Leibniz' were made of sticks and that the former's theory prevailed. ...
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### Two questions about Gauss's contributions to capillarity and the calculus of variations

In the last page of the abstract of Gauss's paper on capillarity "Principia generalia theoriae figurae fluidorum in statu aequilibrii" (1829), the author (who is he?) mentions (Gauss's werke, volume V,...
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### Who invented the gradient descent algorithm?

In connection to the question "Who invented the gradient?", I want to know who invented the gradient descent algorithm?
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### Was there a more intuitive early proof of the generalized mean value theorem?

I am interested in the early proofs of the theorem. It is often called Cauchy mean value theorem, so perhaps Cauchy proved it first. In all the proofs that I have seen we construct a contrived ...
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### What problem led to the discovery of Calculus?

As far as I remember, Calculus was invented/discovered/founded by Newton. What was he trying to achieve that made him find the limit of differences approaching zero? How far did he get into Calculus? ...