Premium Only Content

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
-
3:25:53
Math Easy Solutions
18 days ago $0.18 earnedMES Livestream 101: How Controlled Opposition Works
4611 -
LIVE
Barry Cunningham
3 hours agoREACTING TO STEPHEN MILLER | KASH PATEL | TULSI GABBARD INTERVIEWS AND MORE NEWS!
7,290 watching -
LIVE
Alex Zedra
59 minutes agoLIVE! Solo Scary Game night
164 watching -
58:01
MattMorseTV
3 hours ago $6.83 earnedđŸ”´The Dems. just lost 4.5 MILLION voters.đŸ”´
40.2K35 -
1:04:10
BonginoReport
5 hours agoCornhusker Clink & A Sizzling Border Wall Deter Illegals - Nightly Scroll w/ Hayley Caronia (Ep.116)
102K62 -
LIVE
ZWOGs
9 hours agođŸ”´LIVE IN 1440p! - SoT w/ Pudge & SBL, The Finals w/ The Brrrap Pack, Kingdome Come - Come Hang Out!
41 watching -
LIVE
VapinGamers
1 hour ago $0.01 earnedOff The Grid - Yes I Have a Problem but Winning Aint One! #1 Controller Scrub NA - !rumbot !music
59 watching -
LIVE
XxXAztecwarrior
2 hours agoThe Finals W/ The Tribe
10 watching -
2:01:05
Mally_Mouse
10 hours agoLet's Hang!!
17.2K -
LIVE
blackfox87
2 hours agoFoxyFam takes on Warzone! | PREMIUM CREATOR | #DisabledVeteran
93 watching