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
-
2:27:14
Math Easy Solutions
16 days ago $0.04 earnedMES Livestream 63: Tour of John Hutchison's Lab
2004 -
LIVE
Anvilight
6 hours agoWoW Classic US Servers | Paladin Level 18 | Based Scotsman Gives Opinions
131 watching -
6:05:54
NeoX5
10 hours agoIndiana Jones and the Great Circle - Part 3 [PC] | Rumble Gaming
13.6K3 -
4:05:22
barstoolsports
9 hours agoJon Gruden & Dave Portnoy Watch NFL Sunday With Potential Grinders
132K7 -
8:43
Scammer Payback
2 days agoHacking Scammers to Open Their Webcam
92.5K51 -
4:13:12
SilverFox
20 hours ago🔴LIVE - Path of Exile 2 - WORLD PREMIERE - Part 3
81.4K -
3:35:14
SOLTEKGG
9 hours agoNew Update | Epic Fortnite Fails & Wins!
53.5K1 -
58:52
Barstool Gambling
9 hours agoBarstool College Football Bracket Show with Brandon Walker, Big Cat, & Big T Presented By DraftKings
44K2 -
14:54
Degenerate Jay
1 day ago $29.41 earnedWhy Daniel Craig Almost Wasn't James Bond
153K40 -
24:25
MYLUNCHBREAK CHANNEL PAGE
2 days agoSecrets of the Giants
406K178