Infinite Sequences and Series: Applications of Taylor Polynomials
In this video I go over further into infinite sequences and series, and this time look at the many applications of Taylor polynomials. When I was still a student in university, it was this particular concept of Taylor polynomials and their applications to all aspects of physics that got me interested in creating my Math Easy Solutions channel. And in this video I explore Taylor polynomials in approximating functions which can then be extended to most functions in physics.
The accuracy of our approximations can be determined using the Alternating Series Estimation theorem, Taylor's Inequality, and through graphical or even brute force calculation methods. The particular science and physics applications that I cover in this video include optics, electromagnetism, water waves, pendulums, and surveying.
The topics covered in this video are listed below with their time stamps.
- @ 0:00 - Intro
- @ 1:04 - Topics to Cover
1. @ 2:18 - Introduction
- @ 2:48 - Recap on Power Series and Taylor Polynomials
2. @ 8:22 - Approximating Functions by Polynomials
- @ 30:37 - Example 1: f(x) = x^(1/3)
- Example 2: f(x) = sin x
- @ 53:48 - Using Alternating Series Estimation Theorem
- @ 1:14:22 - Using Taylor's Inequality
- @ 1:21:11 - Using Graphical Methods
3. @ 1:32:04 - Applications to Physics
- @ 1:32:38 - Example 3: Einstein's Theory of Special Relativity
- @ 2:02:16 - Optical Physics
4. @ 2:21:25 - Exercises
- @ 2:21:42 - Exercise 1: Taylor Derivatives
- @ 2:30:50 - Exercise 2: Optical Physics
- @ 3:19:35 - Exercise 3: Electric Dipoles
- @ 3:33:36 - Exercise 4: Water Waves
- @ 4:09:52 - Exercise 5: Pendulum Period
- @ 4:52:04 - Exercise 6: Surveying
Download Video Notes: https://1drv.ms/b/s!As32ynv0LoaIiMQFpSc5JN-fpBUyHw
Video notes and playlists:
- PDF notes: https://1drv.ms/b/s!As32ynv0LoaIiMQFpSc5JN-fpBUyHw
- HIVE notes: https://peakd.com/hive-128780/@mes/infinite-sequences-and-series-applications-of-taylor-polynomials
- Video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0F76sIU8xm09oqBTq1mlry3
- Vectors and the Geometry of Space playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FjJpwnxwdrOR7L8Ul8VZoZ .
------------------------------------------------------
Become a MES Super Fan! https://www.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: https://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
-
3:48:02
Math Easy Solutions
10 days ago $0.06 earnedMES Livestream 53: Summary of Evidence of What Did (and Didn't) Happen on 9/11
2731 -
25:34
Stephen Gardner
14 hours ago🔥Trump MUST BE KEPT ALIVE at all costs! | Exclusive RFK JR Interview!!
143K258 -
53:31
Standpoint with Gabe Groisman
20 hours agoEp 50. God is Real! with Academy Award-winning actor John Voight
142K57 -
35:04
Power Slap
7 days agoPower Slap: Road to the Title - Season 3 Episode 9 - Bring Out That Monster
852K122 -
15:52
Scammer Payback
1 month agoScammers Located in this Apartment
197K71 -
10:41
Breaking Points
3 days agoARSON, 'FREAK OFFS', LUBE: Diddy Indictment SHOCKING DETAILS
179K72 -
45:44
hickok45
23 hours agoSunday Shoot-a-Round # 247
126K71 -
3:34
Cooking with Gruel
1 day agoBrown Butter Deviled Eggs
109K19 -
11:06
Bearing
19 hours agoThe Office 2024 Australian Reboot Looks GARBAGE
92.9K37 -
28:21
Lloyd And Mandy
23 hours ago $4.56 earnedThe INCREDIBLE Hack Every Online Business Owner MUST KNOW In 2024..
90.9K18