Oscar Veliz | Origin of Taylor Series @OscarVeliz | Uploaded 4 years ago | Updated 2 minutes ago
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 youtu.be/YEUbzqkJBf0
Suggested Videos:
Halley's Method youtu.be/3WiVGSy_084
Video Mistakes and How to Fix Them youtu.be/4jw0cjddmB8
Computing π: Machin-like formula youtu.be/M_fTdDx8IlY
References:
Methodus archive.org/details/UFIE003454_TO0324_PNI-2529_000000/page/6/mode/2up
Methodus (english) http://www.17centurymaths.com/contents/taylorscontents.html
An account of methodus royalsocietypublishing.org/doi/10.1098/rstl.1714.0039
A Treatise of Fluxions books.google.com/books?id=NUw7AQAAIAAJ&vq
Halley's Method biodiversitylibrary.org/page/23266907#page/660/mode/1up
Thomas Fantet de Lagny (French) https://nubis.univ-paris1.fr/ark%3A/15733/3415#?c=&m=&s=&cv=&xywh=-56%2C-26%2C1895%2C2570
Brook Taylor and the method of increments link.springer.com/article/10.1007/BF00329903
Certain Mathematical Achievements of James Gregory tandfonline.com/doi/abs/10.1080/00029890.1943.11991343
Colin Maclaurin tandfonline.com/doi/abs/10.1080/00029890.1947.11991846
The Discovery of the Series Formula for π byLeibniz, Gregory and Nilakantha tandfonline.com/doi/pdf/10.1080/0025570X.1990.11977541
James Gregory Tercentenary Memorial Volume catalog.hathitrust.org/Record/000438471
#TaylorSeries #NumericalAnalysis
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 youtu.be/YEUbzqkJBf0
Suggested Videos:
Halley's Method youtu.be/3WiVGSy_084
Video Mistakes and How to Fix Them youtu.be/4jw0cjddmB8
Computing π: Machin-like formula youtu.be/M_fTdDx8IlY
References:
Methodus archive.org/details/UFIE003454_TO0324_PNI-2529_000000/page/6/mode/2up
Methodus (english) http://www.17centurymaths.com/contents/taylorscontents.html
An account of methodus royalsocietypublishing.org/doi/10.1098/rstl.1714.0039
A Treatise of Fluxions books.google.com/books?id=NUw7AQAAIAAJ&vq
Halley's Method biodiversitylibrary.org/page/23266907#page/660/mode/1up
Thomas Fantet de Lagny (French) https://nubis.univ-paris1.fr/ark%3A/15733/3415#?c=&m=&s=&cv=&xywh=-56%2C-26%2C1895%2C2570
Brook Taylor and the method of increments link.springer.com/article/10.1007/BF00329903
Certain Mathematical Achievements of James Gregory tandfonline.com/doi/abs/10.1080/00029890.1943.11991343
Colin Maclaurin tandfonline.com/doi/abs/10.1080/00029890.1947.11991846
The Discovery of the Series Formula for π byLeibniz, Gregory and Nilakantha tandfonline.com/doi/pdf/10.1080/0025570X.1990.11977541
James Gregory Tercentenary Memorial Volume catalog.hathitrust.org/Record/000438471
#TaylorSeries #NumericalAnalysis
