Integration using Computer Algebra Systems (CAS): Example 1
In this video I go over an example on using computer algebra systems (CAS) and use an online CAS to solve the integral of the function x(x^2+2x+4)^(1/2). This was the same example I had solved earlier using tables of integrals and that video can be seen in the video links below. The resulting answer from both the tables of integrals and the online CAS appear different at first but I show that this is common and both can be rewritten so that the answers are identical in form. Also in this example I show that sometimes when rewriting the answer to another, there may be an additional constant appearing in the answer but since it is just a constant it can be absorbed into the all-encompassing constant of integration. This is a very important video to watch for those that may have questions about why a computer produces different answers than if they were to integrate by hand!
In this video I go over an example on Ellipses that looks at the amazing reflective property of ellipses! This property is such that the angle between a line drawn from one focus to a point on the ellipse is equal to the angle from that same point to the other focus. This means that emitting light or sound from one focus gets reflected onto the other focus! This is an amazing property of ellipses and is used in many real world applications such as Lithotripsy to treat kidney stones, and in Whispering Galleries. I will go over these applications in a later video so stay tuned!
In proving this property, I use the formula I derived from my earlier video on the angle between two intersecting lines in terms of the slopes of the lines. Using that formula twice, one for each angle, and determining the slope of the tangent line at the point on the ellipse, I show how the tan value of both angles are equivalent, and thus the angles themselves. Although this is a very tedious and detailed example, the methodical steps I go through provide a great understanding of the algebra and equation manipulating behind the derivation, so make sure to watch this video!
Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhvlZADcp8Lq3bF-tUw
View Video Notes on Steemit: https://steemit.com/mathematics/@mes/video-notes-conic-sections-ellipses-example-3-amazing-reflective-property
Related Videos:
Conic Sections: Ellipses: Example 2: Vertical Ellipse: https://youtu.be/cK0z2ZMC1fU
Conic Sections: Ellipses: Example 1: https://youtu.be/m9FXGv3kMkk
Conic Sections: Ellipses: Definition and Derivation of Formula (Including Circles): https://youtu.be/9dETsJ2tz_M
Conic Sections: Parabolas: Definition and Formula: https://youtu.be/kCJjXuuIqbE
Angle Between Two Lines: Formula in terms of Slopes: https://youtu.be/O8M4ZErxE-M .
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https://www.youtube.com/watch?v=H5IPfg3HSRU
In this video I go over an example on graphing a circle and a cylinder in 3D coordinates. The circle that I graph has the equation x^2 + y^2 = 1 and z = 3. This means that the circle is centered about the xy-axis origin but at a height of z = 3. The cylinder that I graph just has the equation x^2 + y^2 = 1. In the context of 3D coordinates this means it is a vertical cylinder with an indefinite height. Note that in the context of 2D coordinates, this would just be a circle centered about the xy-axis origin.
The timestamps of key parts of the video are listed below:
- Example 2a: Circle: 0:00
- Example 2b: Cylinder: 2:05
This video was taken from my earlier video listed below:
- Vectors and the Geometry of Space: 3D Coordinate Systems: https://youtu.be/xJ-qPJFf2gE
- Video notes: https://peakd.com/hive-128780/@mes/vector-space-and-geometry-3d-coordinate-systems
- Playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0GiAJeLMzhOsrMliibfce5m
Related videos:
Vectors and Geometry of Space video series: https://www.youtube.com/playlist?list=PLai3U8-WIK0FjJpwnxwdrOR7L8Ul8VZoZ .
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https://www.youtube.com/watch?v=JfCmic70QmA
In this video I have uploaded a clip from the 9/11 Observable Evidence documentary which discusses why there is still a coverup for what happened on September 11, 2001. The coverup of 9/11 still persists in large part psychologically: from poor problem-solving skills, to group think, and fear of the ramifications. What happened on 9/11 was very obvious, which was the towers turned mainly to dust, but still so few see this; instead believing in the Osama bin Laden fantasy that was repeated in the news seconds after the 2nd "plane" impact. 9/11 shows that the world is run by evil and that the educational system is designed to facilitate this evil through a large scale assembly line of workers that avoid true individual thought and inquiry. Dr. Judy Wood said it best when she called 9/11 an attack on human consciousness, because that is just what it was...
The timestamps of key parts of the video are listed below:
- Part One: Why Do We Still Have a Coverup?: 0:00
- Ambulance undamaged, very little Rubble, WTC 7 still standing: 1:19
- Determine what happened before the how, who, and why: 2:28
- The Twin Towers were colossal structures: 3:53
- Ambulance is not crushed, buried, or incinerated: 4:23
- Core columns are not crushed, bent, melted, pulverized, or buried: 5:00
- The massive WTC 1 left a rubble pile no higher than the lobby: 5:55
- 9/11 was an attack on human consciousness: 6:20
- Fox News Blames Osama bin Laden in 45 seconds: 7:41
- We are leaving our thinking to someone else: 9:10
- 500,000 tons vanished mainly into dust: 10:36
- Destruction of the educational system: 11:05
- The buildings turned to dust in mid-air: 11:27
- WTC 1 Spire turning to dust: 12:08
This video was taken from the following video listed below:
- 9/11 Observable Evidence (MES Dubbed): Still Working On It...
- 9/11 Observable Evidence (Original): https://youtu.be/8Xw-00NbEE8
- Video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0G_HHWt33moIqEeUBP3cgCh
Related Videos:
- #911Truth video series: https://www.youtube.com/playlist?list=PLai3U8-WIK0EzqTamtIXtgX8QudQSxuxh and https://peakd.com/truth/@mes/911 .
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https://www.youtube.com/watch?v=oHbUBbfipNw
In this video I go over the main assumption in the main paper on COVID-19 "virus" isolation, and that is the RNA extracted from patient and cell culture supernatants is assumed to be "viral". It took me a long time before realizing this since the paper does not state this directly. Instead, I had to ask ChatGPT to clarify a paragraph from the paper, as well as double-checking with the mainstream science literature. And indeed this is a key assumption made in virology in general. Ribonucleic acid (RNA) is supposedly the genetic makeup of the new SARS-CoV 2 "virus" which supposedly causes "COVID", so when a "viral infection" is suspected, then typically the assumption is that RNA found is from this "virus".
ChatGPT also outlines several methods to "confirm" this assumption, such as using PCR to detect specific RNA sequences, comparing the sequences with known "viral sequences", and "immunological assays". These assays use "antibodies" (or immune system "defense proteins") that are supposedly specific to and bind to proteins (called antigens) on the "virus"; thus allowing for indirect identification of this "virus".
All of this is interesting, yet it still remains highly questionable that a bunch of nucleotide sequences (aka RNA) are somehow assumed to be "infectious disease causing particles that can infect and replicate through a host and spread to other individuals (and even shut down the entire world)"...
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:
- RNA Assumed to be from a "Virus": 0:00
- RNA extracted from Airway Fluid Samples and Culture Supernatants: 0:22
- Asking #ChatGPT to Explain Paragraph: 0:48
- #ChatGPT: Assumption is RNA is from a "Virus": 1:41
- Summary of RNA "Virus" Assumption: 3:21
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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In this video I show a simple proof that you can sort n distinct objects in n! ways. This is very useful and important to understand especially if you are interested in statistics or even poker.
Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIibxXE_25YrR9cknp-w?e=XtVe42
View video notes on the Hive blockchain: https://peakd.com/hive-128780/@mes/factorials-sorting-n-distinct-objects-proof
Related Videos:
Factorials - i.e. 4! = 4*3*2*1 = 24: http://youtu.be/SWnrhDOLQgA .
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In this video I show how we can treat vectors algebraically by introducing a coordinate system and the concept of a position vector. Since vectors are considered equivalent if they have the same magnitude and direction, then they can be placed anywhere in a coordinate system and still be equivalent. However, if we move that vector such that its tail starts from the origin, then we can consider the coordinates of it's arrow head as the "components" of that vector; which we can represent using triangle brackets and call the "position vector". We can calculate the position vector from any vector that is offset away from the origin by subtracting each of the x, y, and z components from each other from the tail to arrow head coordinates. I also illustrate this concept with an example at the end of the video.
The timestamps of key parts of the video are listed below:
- Components: 0:00
- Equivalent Vectors: 3:00
- Position Vector: 7:09
- Equation 1: 13:10
- Example 3: 13:44
This video was taken from my earlier video listed below:
- Vectors and the Geometry of Space: Vectors: https://youtu.be/0lJiVlKw4Kc
- Video notes: https://peakd.com/hive-128780/@mes/vectors-and-the-geometry-of-space-vectors
- Playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0EiRECLVkBCcFhSpbSz8XIw
Related videos:
Vectors and Geometry of Space video series: https://www.youtube.com/playlist?list=PLai3U8-WIK0FjJpwnxwdrOR7L8Ul8VZoZ .
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In this video I go over Problem 1 which asks us to determine the 15th derivative at x = 0 for the function sin(x^3). Instead of manually solving the derivatives one by one, we can instead use the Maclaurin series for sin(x), replace x with x^3, and then solve for the 15th derivative for the corresponding series coefficient.
The timestamps of key parts of the video are listed below:
- Problem 1: 15th Derivative of sin(x^3) at x = 0: 0:00
- Maclaurin Series for sin(x): 0:40
- Derivatives as Series Coefficients: 3:30
- Calculation Check: 5:06
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=3THuk0w8dY4
In this video I explain what the squeeze theorem is and illustrate its use through solving an example where determining the limit of a function is not straight forward. This is especially useful when computing the limits of trigonometric functions. Also, if you are taking first year calculus then you will most likely see this in an exam.
Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIieckVrtd6TDMpLcVrg?e=xPerlA
View video notes on the Hive blockchain: https://peakd.com/hive-128780/@mes/squeeze-theorem-a-brief-explanation
Related Videos:
The Limit of a Function: http://youtu.be/0RX1o7KeZ28
What are Limits? A Simple Explanation: http://youtu.be/FbV7TzlkTZk
One Sided Limits - Plus Examples: http://youtu.be/QA2v_NCej10
Limit Laws - Brief Overview: http://youtu.be/qfk5c-43dLg .
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In this video I go further into the main paper on COVID-19 "virus" isolation and this time review the paper's methods on transmission electron microscopy (TEM) preparation. TEM involves firing a beam of electrons through an ultrathin section and the resulting interactions with the sample forms an image that can then be made visible through fluorescent screens or other methods. But to get to this point, the sample is typically first mixed with many heavy metal chemicals and embedded into a resin block. This means that any biological samples will be dead and heavily processed.
For this paper, the first sample prepared was the supernatant of the "infected" human airway cell cultures that showed "cytopathic effects" (CTE), and was then "virus inactivated" with a chemical preservative and ultracentrifuge at around 100,000 RPM. The resulting sedimented "virus" particles was then heavy metal stained on film-coated metal grids.
The second sample was the "infected" airway cell cultures (that showed CTE) themselves, and they were "fixed" with heavy metal preservatives, dehydrated with alcohol, and then embedded in a resin block before being cut to tiny nanometer slices for TEM.
This is a very complex process to somehow see dead particles assumed to be "virions"...
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:
- Paper Methods: Electron Microscope Preparation: 0:00
- Virus Inactivation, Paraformaldehyde, Fixation: 0:49
- Ultracentrifuge, Transmission Electron Microscopy (TEM), Heavy Metals: 1:41
- Fluorescence, Electrons, Electromagnetic Radiation (EMR), Aether: 2:29
- TEM Schematic: 3:22
- Enriched Supernatant Was Negatively Stained: 4:18
- Negative Stain, Staining, Film-Coated Grids, Hydrophilic, Formvar Grid: 5:06
- Fixing Airways Cells Showing Cytopathic Effects: 6:22
- Glutaraldehyde, Osmium Tetroxide, Grade Ethanol: 6:54
- PON812 Resin, Viscosity, Embedding: 7:31
- Ultrathin Sections Cut from Resin Block: 8:27
- Nanometers, Uranyl Acetate, Lead Citrate: 8:51
- Summary of Electron Microscope Preparation: 9:10
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=jyEcAmLyY-s