Premium Only Content
Partial Fraction Decomposition: Proof of the Simplest Case: REVISITED
In this video I revisit my earlier video on “Partial Fraction Decomposition: Proof of the Simplest Case”, https://youtu.be/Eq5yLJmC6pw, because a person by the username Heliocentric brought to my attention that I had not fully completed the proof. After a few back and forth exchanges I quickly realized that indeed Heliocentric was right and I had still some part of the proof yet to be explained. The issue at hand is in the Lemma 1 part of the proof which required proving that a polynomial exists with some given characteristics. In that video though, I simply assumed that the polynomial existed and worked to prove the characteristics. This is not fully complete because I still had yet to prove that it could have been in fact a polynomial. But as Heliocentric stated, and as I promised him 6 months ago that I would complete the proof of this video “later” (i.e. finally today!), I show how the proof that the function is in fact a polynomial can be shown by the Factor Theorem. Now recall in my earlier videos that the Factor Theorem is just a special case of the Polynomial Remainder Theorem, in which the division of an univariant polynomial by (x – a) has a remainder that equals zero. This in fact is the case with the formulation in the Lemma 1, and hence the factor theorem proves that in fact there does exist a polynomial P(x) with the given characteristics. This is a very important video illustrating now only the importance of thoroughly proving each step of a derivation, but also the importance to learn from constructive feedback and always make sure to correct yourself, so make sure to watch this video!
Video notes and playlist:
- PDF notes: https://1drv.ms/b/s!As32ynv0LoaIh44BB2VefNaDHI-HDQ
- HIVE notes: https://peakd.com/mathematics/@mes/partial-fraction-decomposition-proof-of-the-simplest-case-revisited
- Partial Fractions playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0HrJh8AbOkh3oYxSnthP997
Related Videos:
Partial Fraction Decomposition: Proof of the Simplest Case: http://youtu.be/Eq5yLJmC6pw
Polynomial Remainder Theorem: Factor Theorem & Factorization: https://youtu.be/ThX3uSXCD14
Euclidean Division of Integers: Theorem and Proof: https://youtu.be/66juubotzi0
Euclidean Division of Polynomials: Theorem and Proof: https://youtu.be/ONxn17okl5c
Polynomial Remainder Theorem: Proof + Factor Theorem: https://youtu.be/q4lwSBObkXc
Polynomial Remainder Theorem: Elementary Proof: https://youtu.be/Im0c25WbZBg .
------------------------------------------------------
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
-
3:36
Math Easy Solutions
8 days ago $0.03 earned🔬#MESExperiments 45: Rotating Cylinders in Water Behave Like Magnets
1104 -
11:08:56
SpartakusLIVE
13 hours agoPUBG w/ StoneMountain64 || WZ Challenge CHAMPION after
85.6K4 -
4:43:48
Drew Hernandez
11 hours agoOBIDEN REGIME MOVES TO SABOTAGE TRUMP'S DEEP STATE PURGE & GLOBALISTS DECLARE 2ND PLANDEMIC UNDER TRUMP
24.5K18 -
10:04:21
hambinooo
14 hours agohambinooo's rumble debut
105K8 -
1:07:22
barstoolsports
11 hours agoNo One is Safe With Survival at Stake | Surviving Barstool S4 Ep. 2
125K7 -
1:46:50
Laura Loomer
7 hours agoEP90: Biden's Bail Out: Hunter Pardoned By The Big Guy
59.6K23 -
1:32:19
Fresh and Fit
8 hours agoPamela Anderson Is PROOF That All Women Will HIT The Wall!
71.3K47 -
1:14:27
Kim Iversen
10 hours agoVaccine Mandates & Hidden Data: The Truth They Don’t Want You to Hear | Dr. Michael J. Schwartz
71.2K48 -
1:36:05
Glenn Greenwald
10 hours agoAmericans Rail Against Health Insurance Industry After CEO’s Murder; Syria Expert On New Outbreak Of War | SYSTEM UPDATE #375
136K136 -
6:08:03
Dr Disrespect
16 hours ago🔴LIVE - DR DISRESPECT - SOLO TRIPLE THREAT CHALLENGE
434K347