For questions about the mathematical field studying functions, focusing on infinitesimals and rates of change.
Questions tagged [calculus]
194 questions
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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 far in school anyway) how likely was it that he…
releseabe
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Discovery of Sine and Cosine
Discovery of Sine and Cosine of an angle, the intuition behind it is always intriguing. Apart from "that is the way they were defined", could someone explain how the discovery happened? I have read "What is Mathematics?" by R. Courant and related…
RSH
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The exhausting Greek fear of infinity
Every serious source I consulted, be it Cajori, Struik, Edwards,... discusses the method of exhaustion as the means used by ancient Greeks to avoid “taking limits”, because they “disliked infinity”.
As far as my sources go, exhaustion is defined as…
Rodrigo A. Pérez
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How were vector quantities developed?
I'm very interested to know how the concept of vectors came in mathematics and physics. How were vector quantities discovered in physics, and how and by whom were they developed?
Shahed al mamun
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Who introduced cylindrical coordinates?
Cylindrical coordinates$ x=r\cos θ, y=r\sin θ, z=w$ seem to be a simple generalization of polar coordinates. When did they appear first? Also, who came up with the name?
J.Petrovic
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History of the Fundamental Theorem of Calculus
The Fundamental Theorem of Calculus links the concepts of differentiation and integration together.
How did mathematicians of the past see the link between these two concepts? Integration is used to compute areas while differentiation is used to…
Kyoma
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Who invented the gradient?
Who is responsible for coming up with the gradient and why did they do so? In which work was it first described?
I have Googled this extensively, to no avail, and Boyer's History of Calculus does not appear to contain the answer to this.
user124384
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When was the inverse relationship between tangents and quadrature/area first identified?
Problems concerning tangents and quadrature have a long history predating the Newton/Leibniz formulation of calculus; indeed, they are amongst the oldest problems in mathematics. It seems reasonable to assume that the relationship between the two…
nwr
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What did the typical German student know before reading/studying Courant's Calculus when it was published?
I've been reading Courant's Integral and Differential Calculus for a bit, at some sections, there are problems which do not seem to be answerable with previously given material in the book.
Several days ago, I made this question but although the…
Red Banana
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What is the origin of the distinction between assignable and inassignable number?
Leibniz described his infinitesimals as being inassignable numbers in a number of texts, e.g., in his Cum Prodiisset that was analyzed in detail by H. Bos in a seminal text dating from the 1970s. The distinction between assignable and inassignable…
Mikhail Katz
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Who invented differential calculus for rational functions?
Euler mentions in his preface of the book "Foundations of Differential Calculus" (Translated version of Blanton):
....Even now there is more that remains obscure than what we see clearly. As differential calculus is extended to all kinds of…
Sensebe
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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 to solve the integral of any function in $R[\sin…
user2554
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What is the name of the identity $\frac{1}{2}\mathbf{\nabla (u \cdot u) = u \times (\nabla \times u ) + (u \cdot \nabla)u}$ and who derived it?
What is the name of this indentity and which mathematician did derive this?
$$\frac{1}{2}\mathbf{\nabla (u \cdot u) = u \times (\nabla \times u ) + (u \cdot \nabla)u}$$
MrYouMath
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How was logarithm discovered?
How was the concept of $\ln(x)$ found before the man knows that it is the area under hyperbola or it is related to the power of $e$ (base of logarithm). How did Napier compute the value of $e$ or $\ln(x)$ before the concept of power of numbers was…
user359791
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How did newton APPROXIMATE THE AREA UNDER THESE PARTICULAR CURVES
To find - How did Newton derive the general binomial theorem.
I know he approximated the area under functions.
1) But how did he approximate the area under CURVES like ( 1/((1-x^2)^(1/2))) or ( 1/((1-x^2)^(n/2))) , where n is odd.
I know he moved…
Shashaank
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