Premium Only Content
Exercise 4: Approximating the Velocity of a Shallow Water Wave using Maclaurin Series
In this video I go over the water wave velocity equation and approximate it when the waves are deep and when the waves are shallow. For deep waves, the hyperbolic tan or tanh(x) term in the water wave velocity equation approaches zero, which greatly simplifies the equation. For shallow waves, we can use the Maclaurin series approximation for tanh(x) and show that 3rd order or higher terms approach zero for shallow waves. I also calculate the error of this shallow wave speed approximation by using the alternating series estimation theorem.
Timestamps:
- Exercise 4: Water waves speed: 0:00
- Solution to (a): Deep water wave speed approximation: 1:43
- Approximation using hyperbolic tanh(x) = 1: 3:38
- Deep wave speed approximation formula: 5:29
- Solution to (b): Shallow water wave speed approximation: 6:04
- Maclaurin series approximation for tanh(x): 7:05
- Determining derivatives of tanh(x) at a = 0: 8:44
- Writing out our Maclaurin series approximation of tanh(x): 17:18
- 3rd order terms approach zero when water is shallow: 20:07
- Shallow water speed approximation: 21:43
- Shallow water speed approximation formula: 23:22
- Solution to (c): Alternating Series Estimation Theorem for the error: 24:25
- Estimation for tanh(x) approximation: 26:53
- tanh(x) remainder approximation if L is greater than 10d: 30:00
- Estimating accuracy of shallow water wave speed: 32:33
- Error is less than 0.0132gL: 34:02
Full video, notes, and playlists:
- Full video and playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0F76sIU8xm09oqBTq1mlry3
- HIVE notes: https://peakd.com/hive-128780/@mes/infinite-sequences-and-series-applications-of-taylor-polynomials
- Infinite Sequences and Series: https://www.youtube.com/playlist?list=PLai3U8-WIK0EXHAJ3vRg0T_kKEyPah1Lz .
------------------------------------------------------
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
-
2:39
Math Easy Solutions
5 days ago $0.04 earned🔬#MESExperiments 44: Dr. Irwin Moon Sends a MILLION Volts of Electricity Through His Body!
2163 -
8:39
Guns & Gadgets 2nd Amendment News
6 hours agoWHAT?! Federal Court Rules Magazine Bans Are Constitutional?!?
2.36K7 -
1:22:31
Dr. Drew
7 hours agoSalty Cracker: Trump Wins, The Left Immediately Makes Election Rigging Conspiracy Theories Great Again – Ask Dr. Drew
87.2K81 -
1:04:13
In The Litter Box w/ Jewels & Catturd
22 hours agoDumbfounded Democrats | In the Litter Box w/ Jewels & Catturd – Ep. 686 – 11/7/2024
113K68 -
1:25:15
FULL SEND PODCAST
6 hours agoBen Shapiro Predicts the 2024 Election Winner and Goes IN on Andrew Tate!
138K43 -
1:47:49
The Quartering
8 hours agoTrump Victory MELTDOWN Goes Nuclear!
159K52 -
1:40:49
SLS - Street League Skateboarding
10 days ago2024 SLS Sydney: Women’s Knockout Round
87.7K1 -
1:08:33
Savanah Hernandez
5 hours agoAmerica’s Golden Era Has Begun: Trump's Day 1 Policies
57.6K53 -
56:02
Uncommon Sense In Current Times
6 hours ago $2.28 earned"Are You a House Negro Or a Field Negro? A Faith Perspective on Freedom with Kevin McGary"
47.8K9 -
17:53
DeVory Darkins
9 hours agoThe View SELF-DESTRUCTS as Kamala CONCEDES Election
72.2K204