In this video I shift more conic sections and this time shift Hyperbolas. Once again this procedure is the same as in my earlier videos on shifting ellipses (and circles) and parabolas. Nonetheless it is important to see the same procedure applied to different functions. Shifting a parabola with the center at the origin so that the center is now at the point (h , k) requires switching every (x , y) point on the original hyperbola with (x – h, y – k). Thus to obtain the new (x , y) values we need to add h to every x – h value, and k to every y – k value. In other words, we shift every point horizontally by h and vertically by k. This is a great video to reiterate the concept of shifting functions in general so make sure to watch this video!
In this video I go over another troubleshooting video and this time look at using custom browser user scripts to augment or change the way any particular website appears. And in this particular instance, I show how to unblock the Brave browser from the Archive.is (and mirror sites Archive.vn and Archive.today) archiving webpage website tool.
The Brave browser is similar to Google Chrome in that they both use the same Chromium browser architecture but Brave allows users and publishers to earn cryptocurrency in the form of Basic Attention Token (BAT). I had switched from Google Chrome to Brave about 6 months ago and everything was working fine until all of a sudden the Archive.is webpage archiving tool which I had been using for years no longer supported the Brave browser. I did some digging and found that the owner of Archive.is has an issue with retrieving the BAT tokens that his website earned and as a result decided to not allow Brave browser users to access Archive.is. I include the email conversation the owner had with Brave so feel free to read through the back-and-forth communications at your leisure.
If you want to download Brave, please use my referral link: https://brave.com/tmx306
Although this particular video was in regard to unblocking Brave from Archive.is, the general tutorial on using custom browser user scripts with the Violentmonkey script manager and Greasy Fork script sharing service can be applied to many different scenarios of changing how a website is rendered on a browser. Let me know if you have some cool user scripts that you are using!
The topics covered in this video are listed below with their time stamps.
- @ 0:00 - Intro
- @ 1:06 - Topics to Cover
1. @ 1:26 - Introduction to Archive.is and the Brave Browser
2. @ 3:36 - Archive.is Website No Longer Supports the Brave Browser
- @ 8:24 - Solution: Custom Browser User Script
- @ 13:13 - MES Custom User Script Modification
Download Video Notes: https://1drv.ms/b/s!As32ynv0LoaIiLdxG36jNltAbDhg0w?e=VLl2a6
View video notes on the Hive blockchain: https://peakd.com/general/@mes/custom-browser-user-scripts-unblock-brave-browser-from-archive-is
Related Videos:
Blockchain Tutorials Playlist: https://mes.fm/blockchain-playlist
Computer Tutorials Playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0HVPZB2HtwnLHKOl4xDUTB_ .
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In this video I go over a pretty interesting example on Newton's Law of Cooling and model the change in temperature of a bottle of soda pop that is placed into a refrigerator. This is a great example to illustrate how an object cools when there is a temperature difference between it and its surrounding environment. Also in this example, I illustrate how the soda pop bottle's temperature eventually cools until it is the exact same as the refrigerator temperature, which makes physical sense. This is a pretty extensive example, but nonetheless very helpful in understanding how to apply differential equations to model real world applications, and in this specific case you can actually easily do an experiment by placing your own bottle inside the fridge and measuring the temperature change with time. Try that out for yourself and see if it fits your model!
Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhtFz4wBbbTyrejmMGg
View Video Notes on Steemit: https://steemit.com/mathematics/@mes/differential-equations-newton-s-law-of-cooling-example-1
Related Videos:
Differential Equations: Newton's Law of Cooling: https://youtu.be/9jw9xvM3krg
Differential Equations: Radioactive Decay: Example 1: https://youtu.be/O7XHjBYuscA
Differential Equations: Radioactive Decay: https://youtu.be/JWVC6cIyasw
Differential Equations: Population Growth: Proportionality Constant: https://youtu.be/y4cJX0rcXqw
Differential Equations: Exponential Growth and Decay: https://youtu.be/DZtDUIZuxcg
Power Functions and their Properties Part 1 - A Simple Explanation: http://youtu.be/2MKko4ZkSf0
Logarithms and their Properties - An Introduction: http://youtu.be/AZ6KKym19gI .
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https://www.youtube.com/watch?v=Kuegjx4WCPM
In this video I provide an introduction to 3D or Three-Dimensional Coordinate Systems. This section is the first part of the chapter on Vectors and the Geometry of Space from my calculus book. A 3D coordinate system is typically defined with the x-, y-, and z-axes in which the direction of the z-axis is determined by the Right-Hand Rule. Visualizing 3D geometry is often easy to use by considering the analogy of a house with 8 rooms (4 on top and 4 on the bottom) and all being in contact with the center point. In the context of 3D- coordinate systems, the 8 rooms are called octants, and the center point is the origin. I illustrate this by plotting several points in 3D. And finally I describe mathematical terms for all real numbers in a rectangular 3D coordinate system, and which is referred to as a Dimensional Rectangular Coordinate System.
The timestamps of key parts of the video are listed below:
- Introduction to Vectors and the Geometry of Space: 0:00
- Three-Dimensional Coordinate Systems: 1:30
- Right-Hand Rule: 3:08
- Octants: 5:00
- Point P in 3D Space: 7:16
- Plotting Points Examples: 13:22
- Dimensional Rectangular Coordinate System: 17:57
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=pQzNm5HOGaM
In this video I go over another model for population growth and this time it is the Gompertz Function. This function is the solution to the differential equation dP/dt = c*ln(K/P)*P, which is another model for a limiting population. The resulting solution, the Gompertz Function, is nonetheless very similar to the Logistic Model that I have covered in my earlier videos. In this video I went over parts a), b), and c) of this example, but will go over part d) as well as a brief history of Benjamin Gompertz in the next video, so stay tuned for that!
Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhtlAJ3_sp9gYnTbaCg
View Video Notes on Steemit: https://steemit.com/mathematics/@mes/population-growth-other-models-gompertz-example-1-part-1
Related Videos:
Population Growth: Other Models: Example 3: Extinction: https://youtu.be/Pa6UTdh2r9M
Population Growth: Other Models: Harvesting: Example 2: https://youtu.be/jNAYTNhpZzk
Population Growth: Other Models: Harvesting: Example 1 Part 2: https://youtu.be/l1n6WUOxYCs
Population Growth: Other Models: Harvesting: Example 1 Part 1: https://youtu.be/ZLQEJwViIw0
Population Growth: Introduction to Other Models: https://youtu.be/-l5Anv9VA3M
Differential Equations: Population Growth: https://youtu.be/Td8C_cTEGkA
Differential Equations: Logistic Equation: Analytic Solution: https://youtu.be/BlvLWTSYDDk
Differential Equations: Population Growth: Logistic Equation: https://youtu.be/yE8aoY8Bks4
Differential Equations: Population Growth: Proportionality Constant: https://youtu.be/y4cJX0rcXqw
Differential Equations: Exponential Growth and Decay: https://youtu.be/DZtDUIZuxcg
Differential Equations: Separable Equations: https://youtu.be/pBV-xT9ty94
Differential Equations: Euler's Method: https://youtu.be/VlwVl-3oPDM
Differential Equations: Direction Fields: https://youtu.be/zWv1y8Xp1ac
Power Functions and their Properties Part 1 - A Simple Explanation: http://youtu.be/2MKko4ZkSf0
Logarithms and their Properties - An Introduction: http://youtu.be/AZ6KKym19gI
Differential Equations: Population Growth: Logistic Equation: Example 4: https://youtu.be/vS2qba4ucQY
Differential Equations: Population Growth: Logistic Equation: Example 2: https://youtu.be/vvL1STfPRkY .
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https://www.youtube.com/watch?v=K6jUVW-xrh8
In this video I continue on my video series of daily water intake requirements and look at the effect of alcohol on hydration. Although alcohol has a diuretic effect it is not as significant as is usually perceived especially when diluted and when consumed when already dehydrated. If you drink, this is a very useful video to watch to make sure you are properly hydrated! Note though that in this video I deal strictly with hydration and not with the other possible effects of alcohol consumption such as added calories, blood-alcohol levels, and effects on the liver.
Download the notes in my video: https://www.dropbox.com/s/979td9sfs0fivpi/380%20-%20Does%20Alcohol%20count%20towards%20water%20intake.pdf
References:
Hobson, R. M. & Maughan, R. J. 2010. Clinical Aspects: Hydration Status and the Diuretic Action of a Small Does of Alcohol. Alcohol & Alcoholism. Volume 45, No. 4. Pages 366-373.
https://www.dropbox.com/s/7g4hz1vg1otm6gz/380%20-%20Hobson%20%26%20Maughan%202010%20Alcohol%20Diuretic.pdf
Shirreffs, SM. & Maughan R. J. 1997. Restoration of fluid balance after exercise-induced dehydration: effects of alcohol consumption. Journal of Applied Physiology. Volume 83. Pages 1152-1158.
https://www.dropbox.com/s/pya2usvfst5s5hf/380%20-%20Shirreffs%20%26%20Maughan%201997%20Alcohol%20Dehydration.pdf
Related Videos:
Does Coffee and Tea Count Towards Water Intake?: http://youtu.be/WMVpJatcktg
Water from Food and 8 Cups of Water Myth: http://youtu.be/uvxU09XmQNU
Complete Proteins - Vegetarian Diet and Myths about Plant Proteins: http://youtu.be/LHzzutoupY0
Food and Nutrition: What are Calories? and How much in Carbs, Fat, Protein, and Alcohol?: http://youtu.be/RaKutEJc64g .
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https://www.youtube.com/watch?v=5N_HR4JBmvo
In this video I go over further into infinite sequences and series and this time look at the Power Series which is a series in which a power function is being summed up. The power series has many useful applications such as the vibrations of a drum as in the Bessel function and has to do with the particular behavior of the power series to oscillate in large amplitudes initially and dissipate with distance and/or time. I go over many examples, exercises, and proofs in yet another epic long math video, so follow along to learn more!
The topics and their timestamps in the video are listed below:
- @ 0:00 - Intro
1. @ 1:54 - Power Series
- @ 9:41 - Note on Trigonometric Series and the Fourier Series
- @ 10:40 - Example 1
- @ 14:33 – Note on Factorials
- @ 15:23 - Example 2
2. @ 24:31 - Note on Bessel Functions
- @ 25:49 - Example 3: Bessel Function of Order 0
3. @ 49:41 - Theorem 1
- @ 55:54 - Summary of Previous Examples
- @ 58:35 - Example 4
- @ 1:07:22 - Example 5
4. Exercises
- @ 1:17:18 - Exercise 1: Bessel Function of Order 1
- @ 1:34:44 - Exercise 2: Proof of Theorem 1
- @ 1:35:53 - Theorem 2
- @ 1:49:24 - Theorem 3
- @ 1:53:48 - Completeness Axiom
Download Video Notes: https://1drv.ms/b/s!As32ynv0LoaIh_ZL0WExNvIL4J0s2Q?e=GkZR2u
View video notes on the Hive blockchain: https://peakd.com/mathematics/@mes/infinite-sequences-and-series-power-series
Related Videos:
Sequences and Series Playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0EXHAJ3vRg0T_kKEyPah1Lz
Infinite Sequences: Limits, Squeeze Theorem, Fibonacci Sequence & Golden Ratio + MORE: https://peakd.com/mathematics/@mes/infinite-sequences-limits-squeeze-theorem-fibonacci-sequence-and-golden-ratio-more
Infinite Series: Definition, Examples, Geometric Series, Harmonics Series, Telescoping Sum + MORE: https://peakd.com/mathematics/@mes/infinite-series-definition-examples-geometric-series-harmonics-series-telescoping-sum-more
Infinite Sequences and Series: The Integral Test and Estimate of Sums: https://peakd.com/mathematics/@mes/infinite-sequences-and-series-the-integral-test-and-estimate-of-sums
Infinite Sequences and Series: The Comparison Tests: https://peakd.com/mathematics/@mes/infinite-sequences-and-series-the-comparison-tests
Infinite Sequences and Series: Alternating Tests: https://peakd.com/mathematics/@mes/infinite-sequences-and-series-alternating-tests
Infinite Sequences and Series: Absolute Convergence and the Ratio/Root Tests: https://peakd.com/mathematics/@mes/infinite-sequences-and-series-absolute-convergence-and-the-ratio-root-tests
Infinite Sequences and Series: Strategy for Testing Series: https://peakd.com/mathematics/@mes/infinite-sequences-and-series-strategy-for-testing-series .
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In this video I go over the general exponent law with base a: (a*b) = (a^x)(b^x). In proving it I use the laws of exponents with base e as well as the definition a^x = e^(x*ln(a)) which I covered earlier. Also I use the logarithm law ln(a*b) = ln(a) + ln(b).
Download the notes in my video: http://mes.ph/notes/549
Related Videos:
Law of Exponents: (a^x)^y = a^(xy): http://youtu.be/342UkaWFUzQ
Law of Exponents a^(x-y) = (a^x)/(a^y): http://youtu.be/djwpuNtmYJY
Laws of Exponents: a^(x+y) = (a^x)(a^y): http://youtu.be/qgDPsFD_vSA
General Exponential Functions: http://youtu.be/c4R2urO1GCU
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 Exponents: (e^x)^r = e^(rx): http://youtu.be/0pIdZdg3YTg
Laws of Logarithms: ln(x*y) = ln(x) + ln(y): http://youtu.be/2SCZzFy2b2s .
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https://www.youtube.com/watch?v=kwr4nmuMEEQ
In this video I go over another example on improper integrals and this time solve the integral of the function sec(x) from x = 0 to x = π/2. This function has a vertical asymptote at x = π/2 because sec(x) approaches infinite as x approaches π/2, thus making it a Type 2 improper integral. Solving this by first writing it as a limit of a definite integral yields a divergent integral because the limit approaches infinite. In this particular integral, the divergent limit represents an infinite area under the curve.
Download the notes in my video: http://1drv.ms/1OXRMOD
View Video Notes on Steemit: https://steemit.com/mathematics/@mes/improper-integrals-example-6-sec-x
Related Videos:
Improper Integrals Example 5: 1/sqrt(x-2): https://youtu.be/C8X_TUdTo-A
Improper Integrals: Type 2: Discontinuous Integrands: https://youtu.be/livlGUBuM54
Improper Integrals: Introduction: https://youtu.be/ud44W-0jC-c
The Definite Integral - Brief Introduction: http://youtu.be/vhMP5SKbQjU
Integrals and Areas Between Curves: http://youtu.be/2F03KMLIzbk
Infinite Limits - Precise Definition: http://youtu.be/QyVTgSzn7dE
Infinite Limits - Vertical Asymptotes: http://youtu.be/H-5Txa8SOwQ
Trigonometric Identity: Integral of sec(x): http://youtu.be/s-AyOdd9kuc
Trigonometry: Sine, Cosine and Tan Functions: http://youtu.be/WKTIlF2oWw8 .
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https://www.youtube.com/watch?v=yHnv2w9OVWk