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In this video I go over further into the wonderful world of sequences and series, and this time go over Taylor and Maclaurin series. These series are precise and ingenious ways of approximating many functions by only knowing all of the function’s derivatives at a specific value; in the case of the Maclaurin series it is as x = 0. These series can also be used to integrate functions that don’t have elementary antiderivatives and thus are utilized in many computers and calculators as the basis behind many types of calculations.
Interestingly, it was this very concept of Taylor and Maclaurin series that first gave me the idea of creating a YouTube channel to better learn and organize my learning of mathematics and beyond. Taylor and Maclaurin series, as well as infinite series in general, require the coming together of many mathematical concepts and thus I had then realized while still in University that I need to fully refine my mathematical knowledge. And this particular video is the perfect illustration of such a culmination of so many various mathematical concepts.
The topics covered in this video are listed below with their time stamps.
@ 1:14 – MES Note on Taylor and Maclaurin Series
View video notes on the Hive blockchain: https://peakd.com/mathematics/@mes/infinite-sequences-and-series-taylor-and-maclaurin-series
Download Video Notes: https://1drv.ms/b/s!As32ynv0LoaIiIFz-mgCcPKh_6t2Sg?e=vhxEFP
Related Videos:
Sequences and Series Playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0EXHAJ3vRg0T_kKEyPah1Lz
Infinite Sequences and Series: Alternating Tests: https://peakd.com/mathematics/@mes/infinite-sequences-and-series-alternating-tests
Infinite Sequences and Series: Absolute Convergence and the Ratio/Root Tests: https://peakd.com/mathematics/@mes/infinite-sequences-and-series-absolute-convergence-and-the-ratio-root-tests
Infinite Sequences and Series: Strategy for Testing Series: https://peakd.com/mathematics/@mes/infinite-sequences-and-series-strategy-for-testing-series
Infinite Sequences and Series: Power Series: https://peakd.com/mathematics/@mes/infinite-sequences-and-series-power-series
Infinite Sequences and Series: Representations of Functions as Power Series: https://peakd.com/mathematics/@mes/infinite-sequences-and-series-representations-of-functions-as-power-series .
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