Difference between revisions of "2605: Taylor Series"
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==Explanation== | ==Explanation== | ||
{{incomplete|Created by THE MACLAURIN SERIES EVALUATED AT NON-ZERO X - Please change this comment when editing this page. Do NOT delete this tag too soon.}} | {{incomplete|Created by THE MACLAURIN SERIES EVALUATED AT NON-ZERO X - Please change this comment when editing this page. Do NOT delete this tag too soon.}} | ||
| − | In mathematics, the {{w|Taylor series}} of a function is an infinite sum of terms that are expressed in terms of the function's derivatives at a single point. The expression continues indefinitely, and indeed never ends. It can be useful in approximating | + | In mathematics, the {{w|Taylor series}} of a function is an infinite sum of terms that are expressed in terms of the function's derivatives at a single point. The expression continues indefinitely, and indeed never ends. It can be useful in approximating algebraic values, {{w|Machin-like formula|such as π}}, to make them easier to integrate or perform calculus on.[https://www.mathsisfun.com/algebra/taylor-series.html] However, owing to the fact that it contains many difficult calculus tricks, and can be somewhat tedious to calculate by hand, it is often not loved by math students. |
Miss Lenhart appears to be teaching a class on how to use the Taylor series. She has just explained what it is, and how it is used. At this point, she assumes her students wish to keep learning about the Taylor series; that they "wish it would never end". She then says "Good news!" as indeed, the Taylor series never ends, as it is an infinite expression, with each term smaller than the last. The humour is derived from the double meaning of wishing the series would never end. Normally this is said about an enjoyable experience as a way of expressing the joy one gets from such an event. In reality, Miss Lenhart is using the expression as a way to say the Taylor series is infinite, which is almost certainly not what her students are thinking. | Miss Lenhart appears to be teaching a class on how to use the Taylor series. She has just explained what it is, and how it is used. At this point, she assumes her students wish to keep learning about the Taylor series; that they "wish it would never end". She then says "Good news!" as indeed, the Taylor series never ends, as it is an infinite expression, with each term smaller than the last. The humour is derived from the double meaning of wishing the series would never end. Normally this is said about an enjoyable experience as a way of expressing the joy one gets from such an event. In reality, Miss Lenhart is using the expression as a way to say the Taylor series is infinite, which is almost certainly not what her students are thinking. | ||
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. For example, it is widely known that sin(x) = x for all values of x, and the first term is all that is required.{{citation needed}} The title text is also a pun on the use of the word "series" to refer to a television program. It equates each term in the mathematical series to a television season, suggesting that only the first term is useful. It makes fun on the common sentiment on bad series by saying that "The series should have been cancelled after the first season", replacing "season" with "term". It could also reference the "term" of US President {{w|Zachary Taylor}}, who died after serving only fifteen months in office, or the political career of {{w|Charles_Taylor_(Liberian_politician)|Charles Taylor}}, whose first term ended in civil war and exile. | 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. For example, it is widely known that sin(x) = x for all values of x, and the first term is all that is required.{{citation needed}} The title text is also a pun on the use of the word "series" to refer to a television program. It equates each term in the mathematical series to a television season, suggesting that only the first term is useful. It makes fun on the common sentiment on bad series by saying that "The series should have been cancelled after the first season", replacing "season" with "term". It could also reference the "term" of US President {{w|Zachary Taylor}}, who died after serving only fifteen months in office, or the political career of {{w|Charles_Taylor_(Liberian_politician)|Charles Taylor}}, whose first term ended in civil war and exile. | ||
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Revision as of 05:07, 12 April 2022
Explanation
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This is one of 61 incomplete explanations: Created by THE MACLAURIN SERIES EVALUATED AT NON-ZERO X - Please change this comment when editing this page. Do NOT delete this tag too soon. If you can fix this issue, edit the page! |
In mathematics, the Taylor series of a function is an infinite sum of terms that are expressed in terms of the function's derivatives at a single point. The expression continues indefinitely, and indeed never ends. It can be useful in approximating algebraic values, such as π, to make them easier to integrate or perform calculus on.[1] However, owing to the fact that it contains many difficult calculus tricks, and can be somewhat tedious to calculate by hand, it is often not loved by math students.
Miss Lenhart appears to be teaching a class on how to use the Taylor series. She has just explained what it is, and how it is used. At this point, she assumes her students wish to keep learning about the Taylor series; that they "wish it would never end". She then says "Good news!" as indeed, the Taylor series never ends, as it is an infinite expression, with each term smaller than the last. The humour is derived from the double meaning of wishing the series would never end. Normally this is said about an enjoyable experience as a way of expressing the joy one gets from such an event. In reality, Miss Lenhart is using the expression as a way to say the Taylor series is infinite, which is almost certainly not what her students are thinking.
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. For example, it is widely known that sin(x) = x for all values of x, and the first term is all that is required.[citation needed] The title text is also a pun on the use of the word "series" to refer to a television program. It equates each term in the mathematical series to a television season, suggesting that only the first term is useful. It makes fun on the common sentiment on bad series by saying that "The series should have been cancelled after the first season", replacing "season" with "term". It could also reference the "term" of US President Zachary Taylor, who died after serving only fifteen months in office, or the political career of Charles Taylor, whose first term ended in civil war and exile.
