In this video I go over how to make captions for figures, tables, equations, etc which are located in the appendix of a report. It is very simple to change it and the table of figures automatically includes the appendix captions. What I mean by appendix captions is that instead of, for example, Figure 3.4: stuff, you can make it appear like Figure B.4, which uses the appendix header letter in the caption. If you are writing a report of any kind and need an appendix this video is a must watch!
In this video I go over Question 2 of the Discovery Project: Patterns in Integrals section of my calculus book. In this question I go over the family of integrals of the form with integrand sin(ax)cos(bx) and show how we can derive the general integral formula by finding the pattern that arises from using a computer to quickly solve different examples within that integral family.
Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIheQwjuYUOlKh5_pw-g
View Video Notes on Steemit: https://steemit.com/mathematics/@mes/discovery-project-patterns-in-integrals-question-2-sin-ax-cos-bx
Related Videos:
Discovery Project: Patterns in Integrals: Question 1: http://youtu.be/uQUu0XFMw8I
Integration using Tables of Integrals: Example 1: http://youtu.be/AOToFP-4Mfg
Can We Integrate All Continuous Functions?: http://youtu.be/OFEDLJYqYps
Integration by Partial Fractions: http://youtu.be/r07NnKf76og
Trigonometry Identities: sin(-x) = - sin(x) and cos(-x) = cos(x): http://youtu.be/tD5EA2SXyFQ
Trigonometry: Product Identities: http://youtu.be/os8XKWAj9P8 .
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...
https://www.youtube.com/watch?v=O0p1DGMOcfM
In this video I go over an example on finding the volume by using the method of cylindrical shells. The example involves solving the volume of the solid formed by rotating the region bounded by the functions y = 2x^2 - x^3 and y = 0.
Download the notes in my video: http://1drv.ms/1IKEi9H
View Video Notes on Steemit: https://steemit.com/mathematics/@mes/integrals-and-volumes-by-cylindrical-shells-example-1
Related Videos:
Integrals and Volumes by Cylindrical Shells: http://youtu.be/LbywV9X154E
Integrals and Volumes: http://youtu.be/-evdvkDwBuQ
Integrals and Areas Between Curves: http://youtu.be/2F03KMLIzbk
Area Under a Curve: Introduction to Integral Calculus: http://youtu.be/JbEbhv8ybmE
The Definite Integral - Brief Introduction: http://youtu.be/vhMP5SKbQjU
Fundamental Theorem of Calculus - Introduction and Part 1 of the Theorem: http://youtu.be/3o8Q6UJzJyk
Fundamental Theorem of Calculus - Proof of Part 1 of the Theorem: http://youtu.be/CAqTwiPxYwU .
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https://www.youtube.com/watch?v=3n6xQqNzN74
In this video I go over another law of exponent and prove that (e^x)^r = e^(rx) where r is a rational number. In this proof I use a similar method as in my previous videos on the laws of exponents and utilize the natural logarithm function, ln(x), in simplifying and breaking down the function to obtain the exponent law.
Download the notes in my video: http://mes.ph/notes/540
Related Videos:
Laws of Exponents: e^(x+y) = e^x*e^y: http://youtu.be/8z4zpIjsVjk
Laws of Exponents: e^(x-y) = e^x/e^y: http://youtu.be/DpGjtkyQVPI
Laws of Logarithms: ln(x*y) = ln(x) + ln(y): http://youtu.be/2SCZzFy2b2s
Laws of Logarithms: ln(x/y) = ln(x) - ln(y): http://youtu.be/GXkyY9EmDGM
Laws of Logarithms: ln(x^r) = r*ln(x): http://youtu.be/mvJK8lQcdTY
Logarithms and their Properties - An Introduction: http://youtu.be/AZ6KKym19gI
Natural Logarithmns Defined as Integrals: Introduction: http://youtu.be/M-N2PQ5UZns
Inverse Functions Part 2: One to One Functions and the Horizontal Line Test: http://youtu.be/iSNuplUWrbA .
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https://www.youtube.com/watch?v=0pIdZdg3YTg
In this video I go over Part 3 of Example 1 on using calculus to determine tangents to a parametric curve. In this part I solve for the intervals on the curve that are concave upwards, or concave downwards. This is done by using the second derivative test which looks at concavity. Basically if the second derivative is positive then it is concave upwards, i.e. accelerating upwards; if it is negative then it is concave downwards, i.e. decelerating or moving downwards at an increasing rate. After determining the intervals of concavity, I combine what we learned from Parts 1 and 2 to finally sketch the entire curve. Also, as a check of our curve, I use the amazing Desmos online calculator to plot out our parametric equations to confirm that indeed our sketch was correct. This is a great example on using calculus to sketch parametric curves so make sure to watch this video!
Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhuJFEJm40b2DF7Wo4g
View Video Notes on Steemit: https://steemit.com/mathematics/@mes/parametric-calculus-tangents-example-1-part-3
Related Videos:
Parametric Calculus: Tangents: Example 1 Part 2: https://youtu.be/IYfBPigvzNc
Parametric Calculus: Tangents: Example 1 Part 1: https://youtu.be/QBD_TvcJuTo
Parametric Calculus: Tangents: https://youtu.be/deQwD2o0Sas
Parametric Equations and Curves: https://youtu.be/Kd3XF4LZoFE
Second Derivative Test - A brief Introduction: http://youtu.be/lOwK5rQh0Kk .
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https://www.youtube.com/watch?v=G4RAm1POWoU
In this video I further into Polar Coordinates and this time look at Example 10 which involves graphing the function r = sin(8ϴ/5) using the amazing Desmos graphing calculator. Similar to my last video on graphing polar curves, I show how we can use the Desmos calculator to graph polar curves directly or by converting them to Parametric curves. Also in this video I show to determine the domain of the angle ϴ in which the polar curve repeats itself. I do this both visually using the graphing calculator, as well as analytically by using the periodic rotations of a typical sine wave. Note that this is just a quick and simple illustration of determining the domain for the simple case that the function does in fact have an exact whole number of rotations before it starts repeating itself. The curve graphed in this video is an amazing circular spiral flower shape and shows just how amazing the types of curves that can be plotted in polar coordinates (or as parametric equations)! Try it out yourself and let me know of any crazy shapes you can create!!
You can use my graph as a starting point: https://www.desmos.com/calculator/raiwkuult1
Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhvRDgaCbbcSUjWAFlA
View Video Notes on Steemit: https://steemit.com/mathematics/@mes/video-notes-polar-coordinates-example-10-graphing-r-sin-8-5
Related Videos:
Polar Coordinates: Graphing With Polar Curves with Desmos Calculator: https://youtu.be/xY9Be9HHRsk
Polar Coordinates: Example 9: Cardioid: Part 4: https://youtu.be/R6UtQD8tUF0
Polar Coordinates: Example 9: Cardioid: Part 3: Question B: https://youtu.be/-TZHaTjHfb8
Polar Coordinates: Example 9: Cardioid: Part 2: Question A: https://youtu.be/gUYmzZ8Cfhg
Polar Coordinates: Example 9: Cardioid: Part 1: Slope Formula & Trigonometric Algebra: https://youtu.be/MlIhueP36EE
Polar Coordinates: Tangents to Polar Curves: https://youtu.be/DJso0gmxCBY
Polar Coordinates: Symmetry: https://youtu.be/TWxforTOvxM
Polar Coordinates: Example 8: Four-Leaved Rose: https://youtu.be/mTk5j0jD3dE
Polar Coordinates: Example 7: Cardioid: https://youtu.be/rPErcaqNUIY
Polar Coordinates: Example 6: Part 2: Polar Circle to Cartesian: https://youtu.be/biUHN-BphkE
Polar Coordinates: Example 5: Straight Lines: https://youtu.be/AGSz3EVi05A
Polar Coordinates: Example 4: Circle: https://youtu.be/ebsaIlXaZxs
Polar Coordinates: Example 3: Cartesian to Polar
Polar Coordinates: Example 2: Polar to Cartesian: https://youtu.be/mvpb9QshNNU
Polar Coordinates: Cartesian Connection: https://youtu.be/HcaTYrpmGaU
Polar Coordinates: Example 1: https://youtu.be/q_kpqPpoLqE
Polar Coordinates: https://youtu.be/-KAdZL-N4ok
Parametric Equations and Polar Coordinates: https://youtu.be/usSors49Gdw .
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https://www.youtube.com/watch?v=m-A35NDX7b0
In this video I go over further into proving the parametric equations for the Cycloid curve and this time show that these equations do in fact work for all angles that the circle rotates to. In my earlier videos I derived the proof for the cases where θ is between 0 and π/2, as well as between π/2 and π. In this video I first show that the equations still work for the values θ = 0, π/2, and pi. From there I show that it still works for all other values of θ because of the cyclical nature of the trigonometric functions in the cycloid equations. Thus as the values of θ change, the derivation for the parametric equations will mirror all our previous derivations and thus give the exact same result. This is a great example to see how we can spot patterns in the derivation of parametric equations that involve trig functions, so make sure to watch this video!
Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhuAu4o8BZJsHTf-FQg
View Video Notes on Steemit: https://steemit.com/mathematics/@mes/parametric-curves-example-9-the-cycloid-proof-part-3
Related Videos:
Parametric Curves: Example 8: The Cycloid: Proof Part 2: https://youtu.be/_LAmOMbXXts
Parametric Curves: Example 7: The Cycloid: Proof Part 1: https://youtu.be/XmHpIZqeRKk
Parametric Curves: Example 6: Graphing Devices: https://youtu.be/cwpEasc9mhQ
Parametric Curves: Example 5: Lissajous Figure: https://youtu.be/0OT1OnnAQ9I
Parametric Curves: Example 4: https://youtu.be/WZYIS1My-g4
Parametric Curves: Example 3: https://youtu.be/VpiJdEviBbk
Parametric Curves: Example 2: https://youtu.be/SBkzZDlqTTE
Parametric Curves: Example 1: https://youtu.be/0k7QyWa9-HA
Parametric Equations and Curves: https://youtu.be/Kd3XF4LZoFE
Parametric Equations and Polar Coordinates: https://youtu.be/usSors49Gdw
Trigonometry: Sine, Cosine and Tan Functions: http://youtu.be/WKTIlF2oWw8
Angles - Degrees vs Radians: What are Radians??: http://youtu.be/bOdrVvQWRdE
Trigonometry Identities: cos(x +/- y) = cos(x)cos(y) -/+ sin(x)sin(y) : http://youtu.be/VuQczhk7HOs
Trigonometry Identities: sin(x +/- y) = sin(x)cos(y) +/- cos(x)sin(y): http://youtu.be/edtk9thfwbM .
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...
https://www.youtube.com/watch?v=4VuYJRFAI_g
In this video I go further into the Malaysian Airlines Flight MH370 teleportation video fakery, and this time go over the discovery of the clouds stock images background used for the "satellite" plane footage. The clouds stock footage was found by Reddit user DI370DPX3709DDYB2I6L and the person that took the photos was Jonas De Ro while he was visiting Japan on January 25, 2012. The alleged "satellite" footage, which was actually just a 2D to 3D conversion by YouTube's then experimental feature, had clouds that match exactly to those taken by Jonas. Not just a few clouds, but the entire sky background! Kim Dotcom accepted the debunk and will pay both Jonas and DI370DPX3709DDYB2I6L a payment, although not the original $100,000+ bounty since they didn't claim to be the hoaxers themselves. Even disinfo agent Ashton Forbes accepted the debunk and has now shifted his goal to becoming an electrical engineer LOL This alternate reality game was quite the joy ride!
Links shown in the video are listed below:
- MES Links: https://mes.fm/links
- Cloud stock footage found: https://t.me/meslinks/21840
- Video 1: https://www.reddit.com/r/AirlinerAbduction2014/comments/18dkpwb/video_of_entire_sky_matching_11_with_stock_footage/
- Video 2: https://twitter.com/TJPofTexas/status/1733037105020879295
- Cloud photo taker Jonas De Ro speaks out: https://twitter.com/JonasDeRo/status/1733055672747741412
- Video explanation: https://www.youtube.com/watch?v=o5BNiduJwnM
- RAW cloud images: https://drive.google.com/file/d/1JT0KOI1yJEtZVzdQtVBHWzyKujFDlBrb/view
- MES local download: https://1drv.ms/f/s!As32ynv0LoaIir0USutwZB-igTBO8w
- Kim Dotcom accepts debunk and promises to pay Jonas De Ro and the original Redditor a payment (but not the original $100,000 since they weren't the original hoaxers): https://twitter.com/KimDotcom/status/1733198949522293158
- Ashton Forbes accepts debunk but will continue investigating MH370: https://twitter.com/JustXAshton/status/1733214296463544660
- Ashton's next goal is becoming an electrical engineer LOL ?https://twitter.com/JustXAshton/status/1733221117819486361
- Ashton Forbes is a debunker now LOL ?https://twitter.com/JustXAshton/status/1733306006535348245
- GIMP Photoshop file: https://1drv.ms/u/s!As32ynv0LoaIir09m_bG1m4N1LxIgw
- May 19, 2014: Satellite Video: Airliner and UFOs by RegicideAnon: http://web.archive.org/web/20170606182854/https://youtube.com/watch?v=5Ok1A1fSzxY
- Download link: https://web.archive.org/web/20140526071334oe_...
- MES local download: https://1drv.ms/v/s!As32ynv0LoaIirhd1lFnID1lbw0Yzw
- Used the WayBack Machine YouTube downloader: https://www.waybackyt.download/
The timestamps of the video are shown below:
- Links to cover: 0:00
- MES Link: 1:36
- Reddit user DI370DPX3709DDYB2I6L discovers cloud images: 1:57
- Entire sky matches stock footage: 2:28
- Jonas De Ro took the photos in Japan: 4:49
- Kim Dotcom accepts debunk: 5:58
- Ashton Forbes accepts debunk: 7:10
- Ashton's next goal is to become an electrical engineer LOL: 9:11
- MES photoshop matching "satellite" footage with cloud stock footage: 10:24
- Live correcting the stock clouds images: 13:30
- Link to MES MH370 playlist: 16:50
Related Videos:
MES MH370 video playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0EJGgDKXr-wW8z1jd7pZ069 .
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In this video I determine the volume of an infinite string of beads formed by rotating an exponential and trigonometric function about the x-axis. The presence of the sine trig function means that the resulting 3D solid shape has nodes with a value of 0, hence forms what appears to be beads on a string. I first use the formula for disks to determine the volume of one bead, and then use an online integral calculator to solve the resulting volume integral. To calculate the total volume of the infinite number of beads, I do so using 2 methods. The first is simply expanding out the series and realizing it has a telescoping sum, which obtains our answer. The second method involves rewriting the volume of the n-th bead in the form of a Geometric Series, and I show that it is convergent and hence we can plug in our geometric series sum formula to obtain the total volume. I also play around with the amazing GeoGebra graphing calculator and discuss how to graph in 3D using the formula of a circle and our given function as the radius. Epic stuff!
The timestamps of key parts of the video are listed below:
- Problem 13: Rotating a curve to form a 3D string of beads: 0:00
- Solution to Part (a): Volume of the n-th bead: 1:01
- Graphing in 3D with GeoGebra Graphing Calculator: 1:49
- Formula for disks: 6:27
- Using an online integral calculator: 11:19
- Solution to Part (b): Total Volume of Beads: Method 1: Telescoping Sum: 17:36
- Method 2: Geometric Series: 23:48
This video was taken from my earlier video listed below:
- Infinite Sequences and Series: Problems Plus: https://youtu.be/zjdkQIIdTbg
- HIVE video notes: https://peakd.com/hive-128780/@mes/infinite-sequences-and-series-problems-plus
- Video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FQ96Egr5R7fZGeDTIUKz8P
Related Videos:
Sequences and Series playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0EXHAJ3vRg0T_kKEyPah1Lz .
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...
https://www.youtube.com/watch?v=6V6BIjxuQcs
In this video I go over the results section on the main COVID-19 "virus" isolation paper and look at the section that supposedly provides the genome and phylogenetic tree of this "new virus". De novo sequencing was performed on airway fluid samples and cell culture supernatants from the three Wuhan patients, and supposedly a "novel coronavirus" was identified in all three patients. These sequences were sent to the GISAID global flu "virus" database and compared with previous "virus" genomes. The 3 "virus" genomes had 86.9% similarity with previous "bat coronaviruses", but had less than 90% similarity of supposed specific genes involved in "viral" replication. Since they were less than 90% similar, this "new virus" was given its own clade on the phylogenetic tree.
Interestingly, the paper refers to the cell culture supernatants as "virus isolates", even though no common sense isolation was performed. It is clear that no actual "virus" is being observed, but it still raises the question of what these "genomes" refer to, how they are obtained, and what is the reasoning for grouping them in their respective clades.
The paper is listed below:
- A Novel Coronavirus from Patients with Pneumonia in China, 2019
- Authors: Na Zhu et al
- Published on January 24, 2020 in The New England Journal of Medicine (NEJM)
- https://www.nejm.org/doi/full/10.1056/NEJMoa2001017
The timestamps of key parts of the video are listed below:
- Genetic Characterization of the "Virus": 0:00
- De Novo Sequencing: 0:48
- Complete Genome Sequences Somehow Obtained: 1:19
- Global Initiative on Sharing All Influenza Data (GISAID), Influenza: 4:34
- 2019-nCoV Supposedly forms a Distinct Clade: 5:24
- Replicase Domains (ORF 1ab): 7:00
- New BetaCoV Alleged Genome and Phylogenetic Tree: 7:12
- Summary of the Genetic Characterization of the "Virus": 9:16
This video is taken from my earlier video listed below:
- ?#MESScience 4: Review of COVID-19 "Virus" Isolation Paper: https://youtu.be/cvDO85Rw4d8
- Video notes: https://peakd.com/hive-128780/@mes/messcience-4-review-of-covid-19-virus-isolation-paper
- Playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0E4aQ_cq4ZDD2WGiDU5vVgx
Related Videos:
?#MESScience: MES Science Tutorials: https://mes.fm/science-playlist .
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...
https://www.youtube.com/watch?v=qDY2fZdAdpA