# Questions tagged [calculus]

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

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### Where can I find the Royal Society report on the controversy over the invention of differential calculus?

Where can I find the report on the Leibniz–Newton calculus controversy mentioned in this article? In 1712 the Royal Society in England wrote a report purporting to settle the matter — except, the ... 1 vote
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### Can the so-called completeness of real numbers be understood as closure under limits in the real number system?

Someone suggested (please see the comments below) that I post this question on hsm.stackexchange. There is a connection to the history of mathematics in this, regarding the relationship between the ...
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### Did the Maclaurin series for sine and cosine unsettle Indian mathematicians?

As many of you may know, sometime around the 14/15th centuries an Indian mathematician by the name of Madhava of Sangamagrama derived the Maclaurin series for sine and cosine for the first time in ...
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### Who was the first person in history to calculate the limit $\lim\limits_{n\to\infty}\left(1+\dfrac{1}{n}\right)^n$?

At the beginning of a calculus course, we encounter two famous limits. They are $$\lim_{x\to0}\frac{\sin x}{x}\qquad\text{and}\qquad\lim\limits_{n\to\infty}\left(1+\dfrac{1}{n}\right)^n.$$ I'm not ...
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### Did any mathematicians of the time (the 17th Century) try out an intermediary between Bernoulli's and Nieuwentijdt’s infinitesimals?

In §4 of the Stanford Encyclopedia of Philosophy article on continuity and infinitesimals, the author (John L. Bell) mentions that: ... Johann Bernoulli (1667–1748) [in a] letter of his to Leibniz ...
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### Ab-initio method (First principle of Mathematics)

Who was the first one to give proof of 1st Principle of Mathematics in calculus (also known as ab-initio method) ,was he newton or someone else ??
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### When did derivative mean not only "slope of tangent" but also "instantaneous rate of change"?

When did derivative mean not only "slope of tangent" but also "instantaneous rate of change"? Fermat was interested in minima and maxima, and realized these occur when the tangent ...
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### How was the Fundamental Theorem of Calculus discovered?

How was the Fundamental Theorem of Calculus discovered? The FTC is at once simple enough that Math.SE is full of questions asking "why is it such a big deal" and yet avoided discovery for ...
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### What physical problems required the invention of the derivative?

I know that Fermat had a method of adequality in order to solve certain optimization. One such problem was: "Suppose that you have a rectangle of material and need to cut corners into it such ...
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### When were the foundations of vector calculus laid?

Upon some browsing I find from many online sources that vector calculus was created in the time of late 19th century by Gibbs and Heaviside, but Gauss, Green, Stokes, etc., who lived much before that, ...
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### Surface Integrals History

Can't find any information about who and when first used surface/surface area integrals. What was the original motivation? In it's modern form it depends on some relatively modern notations like ...
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### A result on convergence of series of positive terms

Just recently I learned from a highschooler I help in her Calculus class about a convergence test for series with positive terms, and and of which I was not aware. The test is a hybrid between the ...
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### How did Isaac Newton write the integral symbol?

Isaac Newton is known as the discoverer of the FTC (Fundamental Theorem of Calculus), so maybe he wrote the integral symbol and derivative symbol. I know he wrote the derivative symbol as $\dot y$ but ...
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### Origin of Riemann-Stieltjes Integral

What need (if there was any) created Riemann-Stieltjes integral? What did Riemann-Stieltjes integral want to attain?
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### What is the history of the Basel Problem before Euler and how did it inform him?

I am interested in the history of the Basel problem. More specifically, I'm interested in knowing the history of failed attempts before Euler's crack of it, so as to know what bits of evidence ...
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### What is Weierstrass' "simple diagram" in the calculus of variations?

In An essay on the psychology of invention in the mathematical field Hadamard said this about Weierstrass: The two German mathematicians whom Poincaré compares are Weierstrass and Riemann. That, as ...
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### What book did Maria Gaetana Agnesi write which contained both differential and integral calculus?

Wikipedia says the following about Maria Gaetana Agnesi: She is credited with writing the first book discussing both differential and integral calculus and was a member of the faculty at the ...
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### The term "constant" in "integration by parts" ("partielle Integration")

In Riemann's "Ueber die Darstellbarkeit einer Function durch eine trigonometrische Reihe", Riemann mentions taking a factor as "constant" in "partial integration", which ...
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### Did Newton know the chain rule?

I heard someone say recently that Newton didn't know the chain rule. Is that true? I know Newton didn't share our current conception of functions, the real line, limits, etc., so if he did use ...
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### What was the difference between Number and Magnitude in Ancient Greece [duplicate]

I've been reading Infinite Powers by Steven Strogatz and in it, he writes about how the greeks differentiated between numbers as being discrete and magnitudes as being continuous. However, all of ... 226 views

### Origin of the special Finnish notation for difference of antiderivative

Apologies for a question that is specific to one country (but perhaps others find it a curious example of how mathematical notation can vary between countries). In Finnish calculus texts, if $F$ is an ...
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### Did Berkeley's criticism of infinitesimals hobble calculus pedagogy?

I recently read an article that discussed--rather briefly--the issues of infinitesimals and the criticism of them by Berkeley. The author of the article (which, of course, I cannot find, as I read it ...
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### Where can I find a copy of Dieudonné's 'Infinitesimal Calculus'?

I found a copy of the French version 'Calcul infinitésimal' online but the English edition seems to only be available on Amazon for a very hefty price, or in American libraries which I do not have ...
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### Source of L’Hôpital’s 1696 Calculus textbook

A calculus textbook I’m using references a calculus book of L’Hôpital in which he illustrates his rule, which is taught in many calculus classes. Does anyone have a source as a scanned PDF? I’d love ...
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### Notations for Laplacian: $\nabla^2$ vs. $\Delta$

For a (sufficiently smooth) function $f\colon \Bbb R^n\to\Bbb R$, the Laplacian of $f$ is defined to be $\sum_{j=1}^n \frac{\partial^2 f}{\partial x_j^2}$. There are two notations for the Laplacian ...
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We know that Sir Isaac Newton thought about calculus when he tried to efficiently describe his physical laws but what made Sir Gottfried Leibniz think about something which we know today as calculus? 292 views

### History of interpolation methods - Newton

I'm interested in reading more about how Newton developed his method of interpolation and also the proofs he developed to this topic. I'm currently reading "Analysis by its history" which ...
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### Did anyone ever propose the distinction between "divergent to infinity" as opposed to "divergent but with finite average"?

There are different regularization methods that allow us to ascribe finite values to divergent integrals, series or sequences. Still, in my view there is fundamental difference between divergent ...
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### How did Euler obtain this formula from a paper/work in 1748?

I am reading this book on trigonometric series, "Тригонометрические ряды от Эйлера до Лебега" (Trigonometric series from Euler to Lebesgue) , it is in Russian, and my Russian is abysmal. But ...
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