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Daily tweets about real and complex analysis and related topics. From @JohnDCook.

https://t.co/FTK9GLfoPn
Joined December 2009
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@AnalysisFact
Analysis Fact
@AnalysisFact
3 years
Applied mathematics consulting https://t.co/AwpFbcBvIn
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@AnalysisFact
Analysis Fact
@AnalysisFact
11 hours
Integral representations of means
johndcook.com
Means of two numbers, a and b, may be written as f inverse of the average f over the interval [a, b]. Arithmetic, geometric, logarithmic, and identric means.
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@AnalysisFact
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17 hours
Γ(1/2) = √π
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1 day
A Cantor set is uncountable and yet can have Lebesgue measure zero (or positive measure).
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@mathladyhazel
Math Lady Hazel 🇦🇷
@mathladyhazel
2 days
Winter is here, and it is time to take derivative with respect to x.
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@AnalysisFact
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2 days
Relating tail thickness, Fourier transforms, and complex analysis.
en.wikipedia.org
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@AnalysisFact
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2 days
New post: Weak derivatives https://t.co/8LffnPAxGK
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2 days
The rational numbers have Lebesgue measure zero.
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@AnalysisFact
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3 days
To integrate the impossible integral
johndcook.com
An "impossible" integral creates an opportunity to discuss in what sense it is impossible and in what sense it is possible.
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@AnalysisFact
3 days
Explanation here: https://t.co/L5Cdnzb8Do
johndcook.com
What is the Fourier transform of a constant function? What does it even mean? Two hand-wavy derivations and a rigorous formulation.
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3 days
https://t.co/4ahroewqHC
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3 days
Analytic functions dilate and rotate tiny disks, but can't flip them over. Complex conjugate is not analytic because it flips disks over.
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4 days
Strange attractors and Imagery
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@AnalysisFact
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4 days
New post: Fourier transform of a Fourier series https://t.co/N3KINghlcs
johndcook.com
The previous post showed how we can take the Fourier transform of functions that don't have a Fourier transform in the classical sense. The classical definition of the Fourier transform of a function...
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@AnalysisFact
Analysis Fact
@AnalysisFact
4 days
Fourier transform of a constant function https://t.co/L5Cdnzb8Do
johndcook.com
What is the Fourier transform of a constant function? What does it even mean? Two hand-wavy derivations and a rigorous formulation.
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@AnalysisFact
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@AnalysisFact
6 days
Interpolation is generally more trustworthy than extrapolation.
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@AnalysisFact
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@AnalysisFact
7 days
How to start with a minimal math library and bootstrap it to compute the functions not included
johndcook.com
How to start with a minimal math library and compute functions that are not included. e.g. how to use arc tangent to compute the other inverse trig functions.
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@AnalysisFact
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@AnalysisFact
7 days
Kepler and the contraction mapping theorem https://t.co/Y2kqdHlMNC
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@AnalysisFact
7 days
1/Γ(z) is an entire function, i.e. it is analytic everywhere in the complex plane.
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8 days
Crinkle Crankle Calculus https://t.co/RC36vuI2Ax
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@AnalysisFact
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8 days
The Navigational Triangle Using spherical trig to calculate your position https://t.co/AlhvvjPXjc
johndcook.com
The navigational triangle has one vertex at your position, one at the North Pole, and one at the geographic position of a star. Solving this spherical triangle.
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