In this video I go over the logarithm law ln(x/y) = ln(x) - ln(y) and prove it using the previous log law which I proved in my earlier video which is ln(x*y) = ln(x) = ln(y). Note that in this video I prove this law strictly using integrals and derivatives and not on the old definition of logarithms as the inverse of exponential functions like I showed in my properties of logarithms video.
In this video I go over an example on shifting conic sections and this time shift the parabola y = 2x^2 – 4x + 1. Since this function is not in “standard” form, we can make it thus by completing the square to remove the x^1 power. Factoring the 2 out and completing the square, see my earlier video for more on completing the square, we get the formula y = 2(x – 1)^2 – 1. And as shown in my earlier video on shifting conic sections, and in particular parabolas, we see that this parabola is simply the parabola y = 2x^2 but shifted so that its vertex (originally at the origin) is now at the point (1 , -1). Besides just the shift, the function is exactly the same as the unshifted parabola. This is a great video in first performing algebra to complete the square and then using this new function to be able to better see how the function is just a simpler parabola but shifted vertically and horizontally; so make sure to watch this video!
Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIh5YgDSYZXX_ofHMq9g
View video notes on the Hive blockchain: https://peakd.com/mathematics/@mes/shifted-conics-example-1-parabola
Related Videos:
Shifted Conics: Hyperbolas: https://youtu.be/Evz6duQ2-U8
Shifted Conics: Parabolas: https://youtu.be/UlrAkAW3T8Y
Shifted Conics: Ellipses (and Circles): https://youtu.be/ZqtUfaQbj7U
Conic Sections: Hyperbola: Definition and Formula: https://youtu.be/UBIHovXNV9U
Conic Sections: Parabolas: Definition and Formula: https://youtu.be/kCJjXuuIqbE
Conic Sections: Ellipses: Definition and Derivation of Formula (Including Circles): https://youtu.be/9dETsJ2tz_M .
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In this video I go over an example on approximate integration and approximate the integral of the function 1/x from x = 1 to 2 using 5 subintervals, or n = 5, and using the Trapezoid and Midpoint Rules. This is an interesting example because we can easily check the accuracy of both approximation methods because the exact value of the integral is ln(2). Contrary to initial visual appearance of both methods, the Midpoint Rule is about two times more accurate than the Trapezoid Rule. I will explain the reason why in detail in my later videos so stay tuned!
Download the notes in my video: http://1drv.ms/1hk2NS3
View Video Notes on Steemit: https://steemit.com/mathematics/@mes/approximate-integration-example-1-1-x
Related Videos:
Approximate Integration: Left, Right, Midpoint, and Trapezoidal Rules: http://youtu.be/zWzmaLvQU6w
The Definite Integral - Brief Introduction: http://youtu.be/vhMP5SKbQjU
Evaluating Integrals - Examples Part 1 - Using Infinite Rectangles: http://youtu.be/cvqH43bRLoE
Evaluating Integrals - Examples Part 2 - Interpreting as Areas: http://youtu.be/yRP_7umJmIo
Evaluating Integrals - Midpoint vs Right Endpoint Approximations Comparison: http://youtu.be/3x3sF7P9xfY .
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...
https://www.youtube.com/watch?v=DTzZ1jz6OOg
In this video I go over a very long problem that involves first determining several arctan formulas and then using them to determine the value of the π up to 7 decimal places. One such formula is named after mathematician John Machin (1680 - 1751) whom used it to determine π correct to 100 decimal places well before the invention of computers. This method also involves using the Maclaurin series for arctan or inverse tan which I had derived in my earlier videos. With modern computers however, the value of π has been calculated to trillions of decimal places!
The timestamps of key parts of the video are listed below:
- Problem 7: 0:00
- Solution to Part (a): 2:10
- Solution to Part (b): 16:42
- Solution to Part (c): 24:24
- Solution to Part (d): 38:00
- Solution to Part (e): 50:06
- Solution to Part (f): Calculating π: 55:58
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=T20adTSxhC0
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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...
https://www.youtube.com/watch?v=mvxphs6j2M0
In this video I go over another Question in the Patterns in Integrals Discovery Project and this time go over the family of integrals with integrand x^n * e^x where n is a positive integer. Like in the other questions, I use a Computer Algebra System (CAS) to solve multiple integrals with that form and based on the pattern of the answers guess a formula for the general form of the integral. I also use a CAS to calculate the general form but that answer involves the Gamma function, Γ(x) = (x-1)!, but that topic is beyond what I have covered thus far so it is shown as reference only in the video. I also prove the guess made from the pattern of integral answers using the Principle of Mathematical Induction. This is an important video to understand the power of computers in determining integral formulas for entire families of integrals as well as understanding mathematical induction so make sure to watch the video!
Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIheRJ_xGwQn2_V5zjqA
View Video Notes on Steemit: https://steemit.com/mathematics/@mes/discovery-project-patterns-in-integrals-question-4-x-n-e-6
Related Videos:
Discovery Project: Patterns in Integrals: Question 3: x^n * ln(x): http://youtu.be/PA9-Me1ko10
Discovery Project: Patterns in Integrals: Question 2: sin(ax)cos(bx): http://youtu.be/O0p1DGMOcfM
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
Factorials - i.e. 4! = 4*3*2*1 = 24: http://youtu.be/SWnrhDOLQgA
Problems Plus Example 4 - Mathematical Induction: http://youtu.be/WdIr_onvUtE .
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...
https://www.youtube.com/watch?v=XgE75Pa0n-c
In this video I go over further into the Arc Length Formula and this time explain how it is sometimes useful to have a function that measures the arc length of a curve from a particular starting point point to any other point on the curve. From the arc length formula we determine this function, which is called the Arc Length Function. Also in this video, I write the integrand of the arc length formula in terms of differentials in order to develop a useful visual geometric interpretation of the rate of change of arc length. This is a very interesting video on arc length so make sure to watch this video!
Download the notes in my video: https://onedrive.live.com/redir?resid=88862EF47BCAF6CD!103234&authkey=!ACz4krW757H4JjE&ithint=file%2cpdf
View Video Notes on Steemit: https://steemit.com/mathematics/@mes/applications-of-integrals-arc-length-function
Related Videos:
Applications of Integrals: Arc Length: Example 3: Simpson's Rule Approximation: https://youtu.be/7x6-t0Nebxw
Applications of Integrals: Arc Length: Example 2: x = f(y): https://youtu.be/07Peo5ms848
Applications of Integrals: Arc Length: Example 1: https://youtu.be/Fqp2ai2RBEE
Applications of Integrals: Arc Length Proof: https://youtu.be/2rb4H_rmgxg
Differentials Notation in Linear Approximation: http://youtu.be/s0adatWiZg4
Fundamental Theorem of Calculus - Introduction and Part 1 of the Theorem: http://youtu.be/3o8Q6UJzJyk .
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...
https://www.youtube.com/watch?v=MWKK3qLvSwU
In #MESScience 4 I go over a thorough review of the main paper claiming isolation of the "virus" that causes COVID-19. I also go over an overview of the mainstream narrative on COVID-19 and the supposed cases and death figures. I ask the artificial intelligence (AI) chatbot ChatGPT to give me a link to the "main paper" on COVID-19 "virus" isolation, to which it gives out the paper titled "A Novel Coronavirus from Patients with Pneumonia in China, 2019" by Zhu et al published on January 24, 2020 in The New England Journal of Medicine: https://www.nejm.org/doi/full/10.1056/NEJMoa2001017
I go over every sentence of the above paper, provide context, and expand on technical terms where necessary. I also go over an overview of the mainstream explanation on nucleic acids, genomes, and cell theory to better grasp the claims in the paper. In the paper, a handful of patients from Wuhan, China on December 2019 reported pneumonia (or inflammation of the lungs) of "unknown cause", to which the China Center of Disease Control (China CDC) sent a rapid response team to investigate. The paper outlines the results of the investigation.
After examining the paper in detail, it is clear that there are more assumptions than actual common sense isolation of a "virus". The paper specifies genetic sequencing technology was used as the basis for their claim of a new "virus", and they do this by looking for common sequences of other "coronaviruses" in global databases. The physical laboratory experiments performed involved taking patient airway lung fluid, then mixing with chemicals, centrifuging, and assuming the supernatant has the "virus" inside. The supernatant and cell cultures were then heavily processed, stained with heavy metals, embedded in resin, cut in ultrathin sections, and then placed in high-powered electron microscopes. The results show blurry, dead, black and white particles, which are assumed to be the "virus". In my opinion, the paper was not convincing in the slightest that any actual particle was "isolated", and much less a "disease causing virus". Further study will be required to examine the genetic sequencing science that is used to claim the existence of these so-called "viruses".
The topics covered as well as their timestamps are listed below.
- Introduction: 0:00
- #MESScience Video Series: 1:25
- MES Research Note: 2:51
- Topics to Cover: 3:25
1. Mainstream Overview of COVID-19: 5:10
2. ChatGPT on the Main Paper on COVID Virus Isolation: 18:47
3. Paper: A Novel Coronavirus from Patients with Pneumonia in China, 2019: 21:37
4. Paper Abstract: 23:30
- Summary: 33:32
5. Paper Introduction: 34:40
- Summary: 46:31
6. Quick Overview of Nucleic Acids and Genomes: 48:26
7. Paper Methods
- Detecting "Viruses": 58:43
- Summary: 1:10:07
- Isolating the "Virus": 1:13:04
- Summary: 1:33:39
- Electron Microscope Preparation: 1:37:01
- Summary: 1:46:11
- Sequencing the "Virus": 1:48:11
- Summary: 1:55:43
- RNA Assumed to be from a "Virus": 1:56:48
- Summary: 2:00:09
8. Paper Results
- Patient Results: 2:01:34
- Summary: 2:09:16
- Detection and Isolation of a New "Virus": 2:10:57
- Summary: 2:27:33
- Genetic Characterization of the "Virus": 2:33:19
- Summary: 2:42:35
9. Paper Discussion: 2:44:08
- Summary: 2:55:01
10. MES Summary: 2:58:10
- MES Conclusions: 3:10:08
Stay tune for #MESScience Part 5...
Download Video Notes: https://1drv.ms/b/s!As32ynv0LoaIieFrmN8-j483bZv0OQ?e=MiN3gi
View video notes on the Hive blockchain: https://peakd.com/hive-128780/@mes/messcience-4-review-of-covid-19-virus-isolation-paper
View video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0E4aQ_cq4ZDD2WGiDU5vVgx
View the full #MESScience series: http://mes.fm/science-playlist
Related Videos:
Kary Mullis Testimony on Why He Began Questioning the ‘HIV Causes AIDS’ Theory https://youtu.be/y68ugCb2z60
PCR Test Founder Kary Mullis Speaks Out Against the Misinterpretation of the PCR Test https://youtu.be/hdR1dDdy0VI
RICHPLANET Show 280: Dr. Ryke Geerd Hamer and the Psychological Link of Cancer: https://youtu.be/Mz_oAnyPxxs
Presentation by Dr. Andrew Kaufman: Humanity is NOT a Virus: https://3speak.tv/watch?v=mestruth/ifuaesfv .
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In this video I go over further into the Steem/Steemit blockchain social media platform, and this time go over my understanding of the way that three main asset classes work that are the basis behind Steemit. These asset classes are Steem (STEEM), Steem Power (SP), and Steem Dollars (SMD). STEEM is the underlying cryptocurrency token underlying all of the Steem ecosystem, and Steem Power and Steem Dollars derive their value from STEEM. STEEM can be publicly traded and speculated upon just like other cryptocurrencies. Steem Power is STEEM locked into a long-term contract that has the added benefits of protection from dilution as STEEM is being created and gives holders the power to influence the trending exposure of blog posts and comments. Converting STEEM to SP can be done instantly and is referred to as “powering up”. Converting SP to STEEM takes over 2 years and is known as “powering down”. Steem Dollars can be viewed as the US Dollar equivalent of STEEM. In essence SMD is just USD but denominated in the STEEM cryptocurrency.
This cryptocurrency token system employed by Steemit is in my opinion truly revolutionary! Speculators can benefit by betting on the price fluctuations of STEEM, long term investors can benefit by owning SP which grows and increases their social influence, and all can benefit by storing their hard earned USD cash as STEEM, much like as storing money in a bank. I will be studying more about Steem, cryptocurrency, and blockchain technology, so stay tuned for more as I learn more!
Shoutout to @DeepSynergy for creating the amazing Steem Power and Steem Dollar designs which I used in my video thumbnail! https://steemit.com/steem/@deepsynergy/introducing-steem-power-and-steem-dollar-symbols
Note: @14:24 mark of the video, I made a typo: Should have written “Power-Down” and not “Power-Up”.
Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhvVWqli0g2LtX1cdQg
View Video Notes on Steemit: https://steemit.com/steemit/@mes/video-notes-steemit-tutorial-steem-steem-steem-power-sp-and-steem-dollars-smd-getonsteem
Related Videos:
Steemit: Overview: Social Media Platform on Steem Blockchain #GetOnSteem: https://youtu.be/1RBzUDRScyQ .
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Em
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https://www.youtube.com/watch?v=F5f1duDJG9Q
I use the definition of the Derivative to derive the derivative of exponential functions of the form f(x) = a^x. I also allude to the number e which is a very important number and greatly simplifies the derivative of exponential functions.
Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIioI5ltm9PU86OymIUw?e=cZxrwD
View video notes on the Hive blockchain: https://peakd.com/hive-128780/@mes/derivative-of-ax-exponential-functions-part-1-using-definition-of-derivative
Related Videos:
Definition of Derivative Simple Explanation: http://youtu.be/0rjGMpM06Eg
Power Functions Part 2: What is x^0 and 0^0???: http://youtu.be/VzFUDiLzRiE
Exponential Functions and Graphing : http://youtu.be/FFNwh8KR9-Q .
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