Math Easy Solutions | Recap on Power Series, Taylor Polynomials, and Taylor's Inequality @mes | Uploaded August 2024 | Updated October 2024, 8 hours ago.
In this video I go over a quick recap on power series, which is a specific type of infinite series whose terms are powers of x multiplied by coefficients. A power series converges for only 3 possible cases: at x = a, at all values of x, or at an interval of convergence R while the endpoints are indeterminant. A Taylor series is a specific type of power series whose coefficients are determined from the coefficients of a function. Taylor polynomials refer to a specific number of terms of a Taylor series. If a function is equal to its corresponding representation as a Taylor series then the remainder approaches zero. Lastly, a Maclaurin series is a specific type of Taylor series that is centered about zero.
Timestamps:
- Power Series: 0:00
- Convergence of a power series at x = a, all x, or a radius of convergence R: 0:56
- Series may or may not converge at end points of R: 1:42
- Taylor series is a power series with coefficients obtained from the function's derivatives: 2:37
- Maclaurin series is a Taylor series centered at a = 0: 3:23
- A function is equal to its Taylor series if remainder approaches zero: 3:55
- Taylor's Inequality is used to evaluate the remainder: 4:24
- Table 1 of common functions and their Maclaurin series: 5:13
Full video, notes, and playlists:
- Full video and playlist: youtube.com/playlist?list=PLai3U8-WIK0F76sIU8xm09oqBTq1mlry3
- HIVE notes: peakd.com/hive-128780/@mes/infinite-sequences-and-series-applications-of-taylor-polynomials
- Infinite Sequences and Series: youtube.com/playlist?list=PLai3U8-WIK0EXHAJ3vRg0T_kKEyPah1Lz .
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In this video I go over a quick recap on power series, which is a specific type of infinite series whose terms are powers of x multiplied by coefficients. A power series converges for only 3 possible cases: at x = a, at all values of x, or at an interval of convergence R while the endpoints are indeterminant. A Taylor series is a specific type of power series whose coefficients are determined from the coefficients of a function. Taylor polynomials refer to a specific number of terms of a Taylor series. If a function is equal to its corresponding representation as a Taylor series then the remainder approaches zero. Lastly, a Maclaurin series is a specific type of Taylor series that is centered about zero.
Timestamps:
- Power Series: 0:00
- Convergence of a power series at x = a, all x, or a radius of convergence R: 0:56
- Series may or may not converge at end points of R: 1:42
- Taylor series is a power series with coefficients obtained from the function's derivatives: 2:37
- Maclaurin series is a Taylor series centered at a = 0: 3:23
- A function is equal to its Taylor series if remainder approaches zero: 3:55
- Taylor's Inequality is used to evaluate the remainder: 4:24
- Table 1 of common functions and their Maclaurin series: 5:13
Full video, notes, and playlists:
- Full video and playlist: youtube.com/playlist?list=PLai3U8-WIK0F76sIU8xm09oqBTq1mlry3
- HIVE notes: peakd.com/hive-128780/@mes/infinite-sequences-and-series-applications-of-taylor-polynomials
- Infinite Sequences and Series: youtube.com/playlist?list=PLai3U8-WIK0EXHAJ3vRg0T_kKEyPah1Lz .
------------------------------------------------------
Become a MES Super Fan! youtube.com/channel/UCUUBq1GPBvvGNz7dpgO14Ow/join
DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate
SUBSCRIBE via EMAIL: https://mes.fm/subscribe
MES Links: https://mes.fm/links
MES Truth: https://mes.fm/truth
Official Website: https://MES.fm
Hive: peakd.com/@mes
Email me: contact@mes.fm
Free Calculators: https://mes.fm/calculators
BMI Calculator: https://bmicalculator.mes.fm
Grade Calculator: https://gradecalculator.mes.fm
Mortgage Calculator: https://mortgagecalculator.mes.fm
Percentage Calculator: https://percentagecalculator.mes.fm
Free Online Tools: https://mes.fm/tools
iPhone and Android Apps: https://mes.fm/mobile-apps
