2605: Taylor Series - Revision history

Elizium23: does not apply

2026-02-07T17:55:17Z

does not apply

Kynde: Category:News

2026-02-07T14:59:38Z

Category:News

172.71.214.107: A pair of words ("scholastic or television") were previously in the wrong order

2023-11-26T06:15:22Z

A pair of words ("scholastic or television") were previously in the wrong order

Account: /* Explanation */ Removing some stale incomplete tags

2022-07-02T21:24:48Z

‎Explanation: Removing some stale incomplete tags

172.70.126.87: Undo revision 271109 by Explain xkcd server admin (talk)

2022-05-21T01:06:23Z

Undo revision 271109 by Explain xkcd server admin (talk)

Show changes

Explain xkcd server admin at 21:39, 20 May 2022

2022-05-20T21:39:19Z

Show changes

172.70.230.63: Undo revision 265842 by 👖🔥 (talk)

2022-05-11T18:12:41Z

Undo revision 265842 by 👖🔥 (talk)

Show changes

👖🔥 at 17:28, 11 May 2022

2022-05-11T17:28:02Z

Show changes

Jacky720: rv

2022-05-04T23:42:56Z

Show changes

Ex Kay Cee Dee at 23:42, 4 May 2022

2022-05-04T23:42:51Z

Show changes

@@ Line 25: / Line 25: @@
 {{comic discussion}}
 [[Category:Comics featuring Miss Lenhart]]
 [[Category:Math]]

@@ Line 8: / Line 8: @@
 ==Explanation==
 In mathematics, a {{w|Taylor series}} {{w|Polynomial expansion|expansion}} is a {{w|polynomial}} {{w|power series}} approximation of a function[https://matheducators.stackexchange.com/a/10212] around a given point, composed of an infinite sum of the function's {{w|Derivative|derivatives}}, each both divided by successive {{w|Factorial|factorials}} and multiplied by the incrementally increasing {{w|Exponentiation|power}} of the distance from the given point. Such expansions usually continue without end. Beyond approximation of functions, Taylor series are also useful for deriving numerical approximations of {{w|Irrational number|irrational}} values, {{w|Machin-like formula|such as π}}, as well as {{w|Symbolic integration|symbolic}} forms to make functions easier to integrate or otherwise manipulate with calculus.[https://www.mathsisfun.com/algebra/taylor-series.html] However, because they involve difficult calculus operations, and can be annoyingly tedious to {{w|Numerical analysis|calculate by hand}}, they are often not loved by math students.[https://www.reddit.com/r/EngineeringStudents/comments/gbo8tm/taylor_series_can_fuck_off/]
@@ Line 26: / Line 25: @@
 {{comic discussion}}
 [[Category:Comics featuring Miss Lenhart]]
 [[Category:Math]]

@@ Line 13: / Line 13: @@
 [[Miss Lenhart]] appears to be teaching a class about how to use a Taylor series. She presumes her students want to keep learning about the series, in that they, "wish it would never end." She then says "Good news!" because the series does not end. The cartoon's humor is based on the contrast between wishing the series won't end, ordinarily desired of sequences of enjoyable events, and the infinite nature of the Taylor series, which is less likely appreciated by her students struggling to understand why the sums {{w|Convergent series|converge}} to their resulting value.
-The title text is a reference to the common practice among physicists and engineers of abbreviating the Taylor series to only the first few terms, typically one or two, in order to simplify the mathematics of their models. The title text is also a pun on the use of the word "series" to refer to a television program. It symbolizes the terms of the mathematical series as a {{w|metaphor}} with a television season, suggesting that only the first term is useful. It makes fun of the common sentiment against bad {{w|screenwriting}} of a series by saying that, "The series should have been cancelled after the first season," replacing "season" with "term." (Notably, both "term" and "season" are used to refer to a stretch of time during which a program is airing—generally, a television or scholastic program, respectively.) Also note that US President {{w|Zachary Taylor}} died during his first term. In a way, his presidency was cancelled during his first term.
+The title text is a reference to the common practice among physicists and engineers of abbreviating the Taylor series to only the first few terms, typically one or two, in order to simplify the mathematics of their models. The title text is also a pun on the use of the word "series" to refer to a television program. It symbolizes the terms of the mathematical series as a {{w|metaphor}} with a television season, suggesting that only the first term is useful. It makes fun of the common sentiment against bad {{w|screenwriting}} of a series by saying that, "The series should have been cancelled after the first season," replacing "season" with "term." (Notably, both "term" and "season" are used to refer to a stretch of time during which a program is airing—generally, a scholastic or television program, respectively.) Also note that US President {{w|Zachary Taylor}} died during his first term. In a way, his presidency was cancelled during his first term.
 ==Transcript==

← Older revision		Revision as of 21:24, 2 July 2022
Line 8:		Line 8:

	==Explanation==		==Explanation==
−	~~{{incomplete\|Created by THE MACLAURIN SERIES EVALUATED AT X PLUS EPSILON - Please change this comment when editing this page. Do NOT delete this tag too soon.}}~~

	In mathematics, a {{w\|Taylor series}} {{w\|Polynomial expansion\|expansion}} is a {{w\|polynomial}} {{w\|power series}} approximation of a function[https://matheducators.stackexchange.com/a/10212] around a given point, composed of an infinite sum of the function's {{w\|Derivative\|derivatives}}, each both divided by successive {{w\|Factorial\|factorials}} and multiplied by the incrementally increasing {{w\|Exponentiation\|power}} of the distance from the given point. Such expansions usually continue without end. Beyond approximation of functions, Taylor series are also useful for deriving numerical approximations of {{w\|Irrational number\|irrational}} values, {{w\|Machin-like formula\|such as π}}, as well as {{w\|Symbolic integration\|symbolic}} forms to make functions easier to integrate or otherwise manipulate with calculus.[https://www.mathsisfun.com/algebra/taylor-series.html] However, because they involve difficult calculus operations, and can be annoyingly tedious to {{w\|Numerical analysis\|calculate by hand}}, they are often not loved by math students.[https://www.reddit.com/r/EngineeringStudents/comments/gbo8tm/taylor_series_can_fuck_off/]		In mathematics, a {{w\|Taylor series}} {{w\|Polynomial expansion\|expansion}} is a {{w\|polynomial}} {{w\|power series}} approximation of a function[https://matheducators.stackexchange.com/a/10212] around a given point, composed of an infinite sum of the function's {{w\|Derivative\|derivatives}}, each both divided by successive {{w\|Factorial\|factorials}} and multiplied by the incrementally increasing {{w\|Exponentiation\|power}} of the distance from the given point. Such expansions usually continue without end. Beyond approximation of functions, Taylor series are also useful for deriving numerical approximations of {{w\|Irrational number\|irrational}} values, {{w\|Machin-like formula\|such as π}}, as well as {{w\|Symbolic integration\|symbolic}} forms to make functions easier to integrate or otherwise manipulate with calculus.[https://www.mathsisfun.com/algebra/taylor-series.html] However, because they involve difficult calculus operations, and can be annoyingly tedious to {{w\|Numerical analysis\|calculate by hand}}, they are often not loved by math students.[https://www.reddit.com/r/EngineeringStudents/comments/gbo8tm/taylor_series_can_fuck_off/]