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.
- @ 1:04 - Topics to Cover
- @ 2:18 - Introduction
- @ 2:48 - Recap on Power Series and Taylor Polynomials
- @ 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
- @ 1:32:04 - Applications to Physics
- @ 1:32:38 - Example 3: Einstein's Theory of Special Relativity
- @ 2:02:16 - Optical Physics
- @ 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?e=sQWbWc
Related Videos:
Sequences and Series Playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0EXHAJ3vRg0T_kKEyPah1Lz
Infinite Sequences and Series: Taylor and Maclaurin Series: https://peakd.com/mathematics/@mes/infinite-sequences-and-series-taylor-and-maclaurin-series .
SUBSCRIBE via EMAIL: https://mes.fm/subscribe
DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate
Like, Subscribe, Favorite, and Comment Below!
Follow us on:
MES Truth: https://mes.fm/truth
Official Website: https://MES.fm
Hive: https://peakd.com/@mes
Gab: https://gab.ai/matheasysolutions
Minds: https://minds.com/matheasysolutions
Twitter: https://twitter.com/MathEasySolns
Facebook: https://fb.com/MathEasySolutions
LinkedIn: https://mes.fm/linkedin
Pinterest: https://pinterest.com/MathEasySolns
Instagram: https://instagram.com/MathEasySolutions
Email me: [email protected]
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
▶️ DTube
Get up to speed with this 5+ hour video on applying Taylor polynomial approximations to physics and more!
View video notes on the Hive blockchain: https://peakd.com/hive-128780/@mes/infinite-sequences-and-series-applications-of-taylor-polynomials