Origin of Taylor Series
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- Опубліковано 26 чер 2024
- The history of Taylor Series and Maclaurin Series including the works of de Lagny, Halley, Gregory, and Madhava using primary sources whenever possible. Lesson also presents the Taylor Theorem along with visualizations of James Gregory's equations. Finally the video discusses the time period and context during the battle over calculus.
Chapters
00:00 Intro
00:20 Solving Cube Roots
00:53 de Lagny's Conditions
01:26 Halley's Equations
03:46 Taylor's Letter
04:04 Taylor's Treatise
04:25 Two Mathematical Camps
04:51 Quotes About Taylor
05:29 Methodus
06:34 Going Back in Time
06:47 James Gregory
07:13 Gregory's Letter
07:47 Gregory's Other Series
08:32 Certain Mathematical Achievements
08:59 Taylor Series
09:31 Taylor Series Example
10:27 Colin Maclaurin
11:10 Nilakantha and Madhava
11:28 Oscar's Notes
11:58 Thank You
*Corrections* The second value of b at 2:22 is actually negative. James Gregory was 36 years old, not 37, when he died. The numerator at 9:18 should be f^(k)(a)(x-a)^k not f^(k)(x-a)^k. See Video Mistakes II: The Sequel • Video Mistakes II: The...
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Halley's Method • Halley's Method
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Computing π: Machin-like formula • Computing π: Machin-li...
References:
Methodus archive.org/details/UFIE00345...
Methodus (english) www.17centurymaths.com/content...
An account of methodus royalsocietypublishing.org/do...
A Treatise of Fluxions books.google.com/books?id=NUw...
Halley's Method www.biodiversitylibrary.org/p...
Thomas Fantet de Lagny (French) nubis.univ-paris1.fr/ark%3A/1...
Brook Taylor and the method of increments link.springer.com/article/10....
Certain Mathematical Achievements of James Gregory www.tandfonline.com/doi/abs/1...
Colin Maclaurin www.tandfonline.com/doi/abs/1...
The Discovery of the Series Formula for π byLeibniz, Gregory and Nilakantha www.tandfonline.com/doi/pdf/1...
James Gregory Tercentenary Memorial Volume catalog.hathitrust.org/Record...
#TaylorSeries #NumericalAnalysis
The history of mathematics is so important if for no other reason that it demystifies the theorems. These things didn't come out of nowhere, fully formed in the mind of the people for which the theorems are named.
Great job with this presentation. I thoroughly enjoyed it.
Two words- thank you. Thank you for amazing content free
Thank you for the video, I'll share this with my students. Important historical context here
This is so beautiful
this was a fantastic video. We leared about taylor series in my calc 2 class today and i wanted to learn about the history. I am fortunate to have found such a great video. Thanks!
dude me too
Did you both pass cal2? Im about to take my final. This semester has really transitioned me from looking at things in a large way...to looking at things in a small way lol. Love this stuff. Math is trippy
This is really greaT. I understand it better.
permisision to learn sir. thanks
**Corrections** The second value of b at 2:22 is actually negative. James Gregory was 36 years old, not 37, when he died. The numerator at 9:18 should be f^(k)(a)(x-a)^k not f^(k)(x-a)^k.
All ist well
Amazing
yo thanks for this i wanted to know the history
I managed to derive the generalized Newton's method for systems of nonlinear equations via a multivariate Taylor series.
I think we should explore Padé approximants as well as a way to generalize it to multiple variables
good vid
In 2:22 how did you get the value for b(repeating calculus step)
That number should be negative. I put a note in the description of this and two other small mistakes.
Oscar, have you ever seen a "iterative" derivation of the Taylor Series representation of a function?
I'm not sure of the "iterative" context but I can hazard a guess. Imagine building a constant function T0 that goes through f at a. It would look like T0 = f(a). Then a linear version of T that goes through f(a) but also has the same slope at a. It would look like T1 = f(a) + f'(a)(x-a). Then a quadratic that goes through f(a), has the same slope, and has the same second derivative as f at a. T2 = f(a) + f'(a)(x-a) + (f''(a)/2)(x-a)^2 and so on to infinity. Generalize that approach and you have Taylor Series.
@5:00 the reality is that none of them discovered differential calculus. The person who discovered it was Madhava from India in 1300. It's well know that intelectual property was subtracted from Kerala and these dudes managed to understand it 200 or 300 years later. All credits go to India.
Go to 11:10