Math Easy Solutions

MES

In this video I go over another example on probability and this time look at determining the average or mean value of the exponential decreasing probability density function, which was determined in my earlier "Probability Example 2" video. This example involves using integration by parts as well as using L'Hospital's Rule to determine an indeterminate limit when solving for the average value. This is a very interesting video on probability and integration in general so make sure to watch it!

Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhr9JQcs4TGUEDtGZfw

View Video Notes on Steemit: https://steemit.com/mathematics/@mes/probability-average-value-example-1

Related Videos:

Probability: Average Value (or Mean Value): https://youtu.be/gF-zRmdTUWw
Probability: Example 2: Exponentially Decreasing Probability Density Function: https://youtu.be/QeU_9NDCXoA
Probability: Example 1: https://youtu.be/SDJPja8GJ1Q
Probability: Introduction: https://youtu.be/H_sfVMH0VpQ
Probability that my friend Dmitry Scores Goals: http://youtu.be/zbAN04Kj3D8
Three Prisoners Problem: http://youtu.be/8vY66MD7nsM
Odds of Having a Perfect NCAA March Madness Bracket: http://youtu.be/It1sCq9cAFM
Odds of Winning the Lottery: http://youtu.be/dVNFhu6tMQc
Blood Flow: Poiseuille's Law: https://youtu.be/X6aU0p7wJzI
Applications of Integrals: Hydrostatic Pressure and Force: https://youtu.be/fesMt6vmXIo
Applications of Integrals: Surface Area: https://youtu.be/JkDPmAD37qk
Applications of Integrals: Arc Length Function: https://youtu.be/MWKK3qLvSwU
Applications of Integrals: Arc Length Proof: https://youtu.be/2rb4H_rmgxg
Moments and Centers of Mass: Constant Density: https://youtu.be/3bglr1sRWUc
L'Hospital's Rule and Indeterminate Forms - Intro: http://youtu.be/x-djc6wrY5w
Integration by Parts: Proof: http://youtu.be/TZhEOct5u_M .

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In this video I go over another example on probability and average values and this time look at the probability of waiting longer than the average time we expect to wait when calling a company representative. What's interesting is that the average wait time does not necessarily mean that 50% of people wait at least this long. This is rather the median wait time and I will look at this further in my next video so stay tuned for that. The reason why the average wait time differs from the median wait time is because people with very long wait times skew the average value to be higher than when we base it strictly on finding the median value. This is a good example illustrating this concept so make sure to watch this video!

Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhr9tBUO-GsP8-NHkSQ

View Video Notes on Steemit: https://steemit.com/mathematics/@mes/probability-average-value-example-2

Related Videos:

Probability: Average Value: Example 2: https://youtu.be/1q_yYIoQ7no
Probability: Average Value (or Mean Value): https://youtu.be/gF-zRmdTUWw
Probability: Example 2: Exponentially Decreasing Probability Density Function: https://youtu.be/QeU_9NDCXoA
Probability: Example 1: https://youtu.be/SDJPja8GJ1Q
Probability: Introduction: https://youtu.be/H_sfVMH0VpQ
Probability that my friend Dmitry Scores Goals: http://youtu.be/zbAN04Kj3D8
Three Prisoners Problem: http://youtu.be/8vY66MD7nsM
Odds of Having a Perfect NCAA March Madness Bracket: http://youtu.be/It1sCq9cAFM
Odds of Winning the Lottery: http://youtu.be/dVNFhu6tMQc
Blood Flow: Poiseuille's Law: https://youtu.be/X6aU0p7wJzI
Applications of Integrals: Hydrostatic Pressure and Force: https://youtu.be/fesMt6vmXIo
Applications of Integrals: Surface Area: https://youtu.be/JkDPmAD37qk
Applications of Integrals: Arc Length Function: https://youtu.be/MWKK3qLvSwU
Applications of Integrals: Arc Length Proof: https://youtu.be/2rb4H_rmgxg
Moments and Centers of Mass: Constant Density: https://youtu.be/3bglr1sRWUc
Limits at Infinity: Horizontal Asymptotes: http://youtu.be/6pdgb09wRvI .

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In #MESExperiments Part 8, I have uploaded the late Francis J. McCabe’s amazing Gyro Wheel Torque “Over-Unity” demonstration, which he had up on his YouTube Channel in June 27, 2012. Francis showed that a large 50 pound, 32 inch diameter gyro, precessing from about 25 inches from the pivot point, can still be “torqued-up” by a very small and visibly weak 6 volt battery with a “Torque Rating” of 2.5 inch-pounds at 12 volts.

Crunching in the numbers, we get roughly:

- Output Torque = 50 pounds * 25 inches = 50 * 25 = 1,250 inch-pounds
- Input Torque = 2.5 inch-pounds * (6 volts input) / (12 volts rating) = 1.25 inch-pounds.
- Output Torque / Input Torque = 1250/1.25 = 1000 TIMES OVER-UNITY!

Recall that the mainstream definition of “Torque” is essentially force multiplied by the distance perpendicular from the fulcrum or point of rotation. For a fixed horizontal wheel, the torque would be the “Moment of Inertia” multiplied by the Acceleration. But while precessing, this torque is also equal to the weight multiplied by the distance to the pivot. More on this *mainstream* torque and precession can be found here: http://hyperphysics.phy-astr.gsu.edu/hbase/rotv2.html

Essentially what this means is that although a very weak motor won’t be able to spin a fixed horizontal heavy wheel, but if spun initially through the vertical near zero torque position and then allowed to precess, the motor magically is able to increase spin speed and maintain precession!

This is literally as if the very magical act of precession is causing the gyroscope to be “lifted” in a horizontal spiral plane. Later Francis turns off the power and the gyro-wheel begins precessing in a downwards spiral.

This is an absolutely mind-boggling demonstration by Francis J. McCabe, and just adds to amazing properties of gyroscopes shown in my earlier experiments.

To see the original video on Francis’ YouTube Channel, you can watch here:

https://youtu.be/QmqIg00xSFo

To learn more about Francis J. McCabe, such as his previous work for both NASA and Boeing as a Rocket Scientist before realizing that Gyro Science is where the real science is at, then make sure to read up his life on the following links:
- https://en.wikipedia.org/wiki/Francis_J._McCabe
- https://www.chestnuthilllocal.com/2013/01/08/mt-airy-inventor-finds-new-uses-for-the-gyroscope/
- https://www.chestnuthilllocal.com/2014/03/26/francis-j-mccabe-inventor-business-owner/
- http://www.franmccabe.com/
- https://www.youtube.com/user/Mccabefj/videos

Of note is that Francis viewed the Earth and in fact everything as a gyroscope; which I tend to agree with him on this! And it is no surprise that in his lecture, he mentioned he worked with THE Eric Laithwaite:

https://youtu.be/TVoXdgkSOfY?t=54

The world is definitely a small place, and nothing smaller than the number of people awakened to the magical and game-changing secrets (in plain sight) of gyroscopes….

Stay Tuned for #MESExperiments Number 9!

Related Videos:

#MESExperiments Video Series: https://mes.fm/experiments-playlist
#AntiGravity Video Series: https://mes.fm/antigravity-playlist
#FreeEnergy Video Series: https://mes.fm/freeenergy-playlist .

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In this video I go over an example on determining the median of a probability density function, which in this example is from my earlier video on Probability: Average Value: Example 2. The median is shown to be 3.5 minutes which is less than the average or mean value of 5 minutes solved previously. This is a reasonable result, which as explained in my last video on Median, the large values can skew the average more so than the median.

Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhsAhO0k15l5pvAWuNA

View Video Notes on Steemit: https://steemit.com/mathematics/@mes/probability-median-example-1

Related Videos:

Probability: Median: https://youtu.be/C8ZU8BjHIqQ
Probability: Average Value: Example 2: https://youtu.be/1q_yYIoQ7no
Probability: Average Value: Example 2: https://youtu.be/1q_yYIoQ7no
Probability: Average Value (or Mean Value): https://youtu.be/gF-zRmdTUWw
Probability: Example 2: Exponentially Decreasing Probability Density Function: https://youtu.be/QeU_9NDCXoA
Probability: Example 1: https://youtu.be/SDJPja8GJ1Q
Probability: Introduction: https://youtu.be/H_sfVMH0VpQ
Probability that my friend Dmitry Scores Goals: http://youtu.be/zbAN04Kj3D8
Three Prisoners Problem: http://youtu.be/8vY66MD7nsM
Odds of Having a Perfect NCAA March Madness Bracket: http://youtu.be/It1sCq9cAFM
Odds of Winning the Lottery: http://youtu.be/dVNFhu6tMQc
Blood Flow: Poiseuille's Law: https://youtu.be/X6aU0p7wJzI
Applications of Integrals: Hydrostatic Pressure and Force: https://youtu.be/fesMt6vmXIo
Applications of Integrals: Surface Area: https://youtu.be/JkDPmAD37qk
Applications of Integrals: Arc Length Function: https://youtu.be/MWKK3qLvSwU
Applications of Integrals: Arc Length Proof: https://youtu.be/2rb4H_rmgxg
Moments and Centers of Mass: Constant Density: https://youtu.be/3bglr1sRWUc
Limits at Infinity: Horizontal Asymptotes: http://youtu.be/6pdgb09wRvI .

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In this video, I go over an extremely extensive tutorial on Sequences as part of my new video series on Sequences and Series. Sequences are ordered lists of numbers where each term is categorized by its value and the integer corresponding to its place or order in the list. Series are summations of sequences; which I have shown in my earlier videos in finding areas and hence integrals of functions.

The topics I cover in this video include: Sequences and Notation, Definition and Precise Definition, Infinite Limits, Monotonic and Bounded Sequences, as well as the famous Fibonacci Sequence and its relationship with the also very famous Golden Ratio. And at the end of this video I go over a brief mainstream history overview of Leonardo Fibonacci. The Fibonacci sequence is the sequence in which the initial 2 terms are 1 and 1 (or 0 and 1 in modern computing) and then the terms that follow are just the summation of the previous two terms. The limit of the ratio of consecutive Fibonacci terms approach the Golden Ratio (φ) (which is the ratio of any two numbers such that it is the same as the ratio of their summation to the larger number). Fibonacci and Golden numbers/sequences/ratios/spirals/angles/etc. appear very often in all aspect of life from art, nature, design, finance, and even advertising! #AmazingStuff

Here is a list of the topics covered and their start times in the video:

1. @ 55:54 - Introduction to Sequences and Series
2. @ 9:25 – Sequences and Notation
3. @ 11:06 - Examples 1 to 3
3. @ 27:30 – Limit of a Sequence
4. @ 33:59 – Definition 1: Limit of a Sequence
5. @ 37:38 – Definition 2: Precise Definition of a Sequence
6. @ 47:33 – Theorem 1
7. @ 52:26 – Definition 3: Infinite Limits of Sequences at Infinity
8. @ 58:17 – Limit Laws for Sequences
9. @ 1:01:39 – Squeeze Theorem for Sequences
10. @ 1:08:10 – Theorem 2
11. @ 1:08:51 - Examples 4 to 7
12. @ 1:18:51 – Theorem 3
13. @ 1:19:48 – Examples 8 to 9
14. @ 1:26:46 – Creating Graphs of Sequences
15. @ 1:29:33 – Example 10
16. @ 1:41:46 – Definition 4: Monotonic Sequences
17. @ 1:43:42 – Examples 11 and 12
18. @ 1:54:08 – Definition 5: Bounded Sequences
19. @ 1:59:31 – Completeness Axiom
20. @ 2:03:43 - Monotonic Sequence Theorem
21. @ 2:09:27 – Example 13: Recursion and Mathematical Induction
22. @ 2:22:27 – Exercise 1: Convergence
23. @ 2:33:20 - Exercise 2: Proof of Theorem 2
24. @ 2:39:41 - Exercise 3: Proof of Theorem 3
25. @ 2:48:23 - Exercise 4: Fibonacci Sequence
26. @ 3:04:17 – Mainstream History of Fibonacci
27. @ 3:12:04 – Overview of Fibonacci Numbers
28. @ 3:17:33 – Overview of the Golden Ratio
29. @ 3:21:53 – Relationship Between Fibonacci Sequence and Golden Ratio
30. @ 3:27:06 – Golden Angle/Spiral and Approximations with Fibonacci Spiral
31. @ 3:31:30 – Fibonacci Numbers and Golden Ratio in Nature, Art, Design, & MORE! #Amazing

Stay tuned for my next super long math video!

Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIh68vMw9e1A75d63O3w

Related Videos:

Limits: https://www.youtube.com/playlist?list=PLFE39AF0D7E0651AC
Areas and Summation: https://www.youtube.com/playlist?list=PLai3U8-WIK0E6biFIz0glhAnUwE1qaviI
Parametric Equations and Curves: https://www.youtube.com/playlist?list=PLai3U8-WIK0H0AMIZV8HU3LVxSSf_Y9pi .

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In this video I go over a brief introduction on the most commonly used probability density function, the normal distribution. This function is represented by a bell-shaped curve, often referred to as the Bell Curve, and models many natural phenomena well, such as test scores, rainfall, heights, weights, etc. Although I go over the basics of the normal distribution function and its properties in terms of the standard deviation, I leave the actual derivation of the formula to later videos, as it is more advanced. So stay tuned for those videos!

Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhsBSj6EePdgyR-ZAAg

View Video Notes on Steemit: https://steemit.com/mathematics/@mes/probability-normal-distribution

Related Videos:

Probability: Median: Example 1: https://youtu.be/nDAfJfCa4Fc
Probability: Median: https://youtu.be/C8ZU8BjHIqQ
Probability: Average Value: Example 2: https://youtu.be/1q_yYIoQ7no
Probability: Average Value: Example 2: https://youtu.be/1q_yYIoQ7no
Probability: Average Value (or Mean Value): https://youtu.be/gF-zRmdTUWw
Probability: Example 2: Exponentially Decreasing Probability Density Function: https://youtu.be/QeU_9NDCXoA
Probability: Example 1: https://youtu.be/SDJPja8GJ1Q
Probability: Introduction: https://youtu.be/H_sfVMH0VpQ
Probability that my friend Dmitry Scores Goals: http://youtu.be/zbAN04Kj3D8
Three Prisoners Problem: http://youtu.be/8vY66MD7nsM
Odds of Having a Perfect NCAA March Madness Bracket: http://youtu.be/It1sCq9cAFM
Odds of Winning the Lottery: http://youtu.be/dVNFhu6tMQc
Blood Flow: Poiseuille's Law: https://youtu.be/X6aU0p7wJzI
Applications of Integrals: Hydrostatic Pressure and Force: https://youtu.be/fesMt6vmXIo
Applications of Integrals: Surface Area: https://youtu.be/JkDPmAD37qk
Applications of Integrals: Arc Length Function: https://youtu.be/MWKK3qLvSwU
Applications of Integrals: Arc Length Proof: https://youtu.be/2rb4H_rmgxg
Moments and Centers of Mass: Constant Density: https://youtu.be/3bglr1sRWUc .

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In this video I go over an example on normal distributions and this time look at the very well known application that follows a normal distribution probability density function, the Intelligence Quotient (IQ) scores. IQ tests have been widely used for about a century now and they, like many phenomena, are normally distributed. In the example I show that about 2/3rd of people (or 68%) have an IQ between 85 and 115 while less than 0.4% have an IQ higher than 140.

I also go over a brief history of the IQ tests as well its uses and drawbacks. IQ tests focus mainly on cognitive abilities such as memory, attention, speed, and pattern recognition. This is a very useful video if you are interested in learning more about the popular IQ testing concept so make sure to watch this video!

Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhsBg8srx4qaRfYXtnQ

View Video Notes on Steemit: https://steemit.com/mathematics/@mes/probability-normal-distribution-example-1-iq-scores

Related Videos:

Probability: Normal Distribution: https://youtu.be/b17gJ4F_v54
Probability: Median: Example 1: https://youtu.be/nDAfJfCa4Fc
Probability: Median: https://youtu.be/C8ZU8BjHIqQ
Probability: Average Value: Example 2: https://youtu.be/1q_yYIoQ7no
Probability: Average Value: Example 2: https://youtu.be/1q_yYIoQ7no
Probability: Average Value (or Mean Value): https://youtu.be/gF-zRmdTUWw
Probability: Example 2: Exponentially Decreasing Probability Density Function: https://youtu.be/QeU_9NDCXoA
Probability: Example 1: https://youtu.be/SDJPja8GJ1Q
Probability: Introduction: https://youtu.be/H_sfVMH0VpQ
Probability that my friend Dmitry Scores Goals: http://youtu.be/zbAN04Kj3D8
Three Prisoners Problem: http://youtu.be/8vY66MD7nsM
Odds of Having a Perfect NCAA March Madness Bracket: http://youtu.be/It1sCq9cAFM
Odds of Winning the Lottery: http://youtu.be/dVNFhu6tMQc
Blood Flow: Poiseuille's Law: https://youtu.be/X6aU0p7wJzI
Applications of Integrals: Hydrostatic Pressure and Force: https://youtu.be/fesMt6vmXIo
Applications of Integrals: Surface Area: https://youtu.be/JkDPmAD37qk
Applications of Integrals: Arc Length Function: https://youtu.be/MWKK3qLvSwU
Applications of Integrals: Arc Length Proof: https://youtu.be/2rb4H_rmgxg
Moments and Centers of Mass: Constant Density: https://youtu.be/3bglr1sRWUc
Can We Integrate All Continuous Functions?: http://youtu.be/OFEDLJYqYps .

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In this video I go over an introduction to differential equations and explain a bit about how they are the most important applications of calculus to the real-world. Differential equations are simply equations that consist of a function and some of its derivatives. These types of equations model real-world applications very well because often times physical concepts change at a rate that is proportional to its current state.

One such example is in population growth in which the rate of growth depends on what the current population is. In this video I use differential equations to model population growth. The first differential equation for population growth that I go over is for ideal conditions and is simply stated as the rate of growth is proportional to the current population. But a more accurate model assumes that there is a maximum carrying capacity in which the population levels off. This latter model is known as the Logistic Differential Equation and was first proposed by the Dutch mathematical biologist Pierre-François Verhulst in the 1840s. I also go over a brief history lesson on Verhulst.

This is an extremely important video as it lays the foundation for my later videos on one of the most powerful mathematical concepts, differential equations, so make sure to watch this video!

Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhsEMZvMcUkjvxzId8g

View Video Notes on Steemit: https://steemit.com/mathematics/@mes/differential-equations-population-growth

Related Videos:

Natural Exponential Function: y = e^x: http://youtu.be/vGsOA2eqkig .

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In this video I go over further into differential equations and this time use Hooke's Law to establish a relationship between the resistance force of a spring as being proportional to the length it stregths (or compresses). Since we are dealing with a force, we can apply Newton's Second Law of motion, which states that a force is equal to its mass times its acceleration. The acceleration of an object can also be considered as the second derivative of position of the spring. Thus we can model the motion of a spring through a second-order differential equation. It is called second-order because of it involves a function and its second derivatives.

Functions that fit this description are the sine and cosine functions, since the second derivatives both are themselves but with a negative sign. And similar to trigonometric functions, the motion of a spring oscillates which makes trig functions reasonable solutions to the motion of a spring differential equation.

Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhsEgtmClosN58R6igg

Related Videos:

Differential Equations: Population Growth: https://youtu.be/Td8C_cTEGkA
Integrals and Work: Example 2 - Hooke's Law: http://youtu.be/h8lwvB9rOng
Higher Derivatives Example on Acceleration: http://youtu.be/PVxUQjJ1vUA .

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In #911Truth Part 12 I have uploaded the infamous March 2, 2007 interview between Democracy Now’s Amy Goodman and Retired US General Wesley Clark regarding the United States PRE-PLANNED “7 countries in 5 years” invasion of the Middle East. Clark details how a mere 10 DAYS after 9/11, a general at the Pentagon told him that the decision to go war with Iraq was already made! And the reason given was “I don’t know”…. In other words, 10 days after 9/11, and before the media driven lie about “Iraq WMDs” the decision had already been made. Furthermore, Clark reveals that several weeks later, upon which the United States were already bombing Afghanistan, he went to see the unnamed general again to see if the Iraq War plan was still going to happen. But the General revealed that it was much worse and gave him a classified memo that listed “7 Countries in 5 Years” to be “take(n) out”: Iraq, Syria, Lebanon, Libya, Somalia, Sudan, and finally IRAN!

Now while the United States war machine has taken longer than “5 years” to carry out their plan, the first 6 countries have already been decimated resulting in mass genocide, a global immigration crisis, and the ballooning of fiat debt money across the globe that further increases the taxation upon ordinary hard working people. And even though Clark said he heard of the plan for the Middle East “War” aka Mass Ritual Sacrifice and Genocide "10 days after 9/11", it is clear the plan was made well in advance; and thus so too was the planned media brainwashing on a global scale planned as well.

There is now one country left on the list: IRAN. And from the current Puppet President, Donald Trump, and his “demented” tweets to the blatant government run Psychological Operation known as “Q Anon”, the level of outright threats towards Iran make it clear that the agenda for War will continue; but this time towards a more global war that includes Russia and China.

Since the war agenda continues regardless of who is president of ANY country, the inevitable realization comes to mind: we (as in the average ordinary citizen) are under global control. In fact, I would go so far as saying that the global power structure is not made up of “countries” but rather a two tier class: those that rule, and those that are ruled. But on an even deeper philosophical level, it is the very POSITION of power over others that will always lead to war; in other words, it doesn’t matter who is the president, even if it was yours truly, the result would be the same. Those that rule do so simply because they believe the global population are not fit to rule themselves, and everyday we prove them right by our very lifestyles, and ultimately by our very willingness to kill when asked to. Afterall, the “global elite” can only do so much in making us think that killing our fellow human being is EVER a viable decision. And ultimately the decision for peace, for self-governance, and saying no to war of ANY kind rests with us. #BoycottWar

Stay Tuned for #911Truth Part 13…

Full Amy Goodman and Wesley Clark Interview: [https://youtu.be/JOtbNC4oJ54](https://youtu.be/JOtbNC4oJ54)
“7 Countries in 5 Years” Transcript: https://genius.com/General-wesley-clark-seven-countries-in-five-years-annotated

View Video Notes on Steemit: https://steemit.com/war/@mes/911truth-part-12-gen-wesley-clark-reveals-middle-east-invasion-was-pre-planned-and-iran-is-next

Related Videos:

#911Truth Video Series: https://mes.fm/911truth-playlist
#FreeEnergy Video Series: https://mes.fm/freeenergy-playlist
#AntiGravity Video Series: https://mes.fm/antigravity-playlist
#MESExperiments Video Series: https://mes.fm/experiments-playlist
#Occult Video Series: https://mes.fm/occult-playlist
#PizzaGate Video Series: https://mes.fm/pizzagate-playlist .

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In this video I go over an example on differential equations and this time show that the solutions to the second-order differential equation y" + 9y = 0 are in the form of a combination of sine and cosine functions. This differential equation can be re-arranged to y" = -9y which is the same form as that in my last video on the motion of a spring. And thus as expected the solutions should be involving trigonometric functions because they model the oscillations of a spring very well.

Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhsE1Ms_uLy2M-31Bnw

View Video Notes on Steemit: https://steemit.com/mathematics/@mes/differential-equations-spring-motion-example-1

Related Videos:

Differential Equations: Motion of a Spring: https://youtu.be/mk2TiR5dwVs
Differential Equations: Population Growth: https://youtu.be/Td8C_cTEGkA
Integrals and Work: Example 2 - Hooke's Law: http://youtu.be/h8lwvB9rOng
Derivative of Trigonometry Functions: Derivative of sin(x): http://youtu.be/elEvQ4Wu7Pk
Derivative of Trigonometry Functions: Derivative of cos(x): http://youtu.be/LMjVp-GsrCw .

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In this video I go over a general overview on differential equations as well as a few of the definitions and terms associated with them. I discuss briefly about the order of a differential equation as well as what the solution to a differential equation is. I also allude to how most real-world models of differential equations are complex and thus don't usually have explicit solutions to them. Instead we often have to approximate the solutions and I will show how in later videos so stay tuned!

Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhsFhf69mv--wxTqDtQ

View Video Notes on Steemit: https://steemit.com/mathematics/@mes/differential-equations-general-overview

Related Videos:

Differential Equations: Spring Motion: Example 1: https://youtu.be/Twu30EJ93Wg
Differential Equations: Motion of a Spring: https://youtu.be/mk2TiR5dwVs
Differential Equations: Population Growth: https://youtu.be/Td8C_cTEGkA .

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In this video I go over an example on differential equations and show that the family of functions y = (1 + ce^t) / (1 - ce^t), where c is a constant, is a solution to the differential equation y' = 1/2(y^2 - 1). The process of proving that it is indeed a solution is to simply take the derivative of the family of functions and ensure that it satisfies the differential equation, which I show that it clearly does.

Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhsFwy6vbLODQ0spUnA

View Video Notes on Steemit: https://steemit.com/mathematics/@mes/differential-equations-example-1

Related Videos:

Differential Equations: General Overview: https://youtu.be/jit59tIY4UI
Differential Equations: Spring Motion: Example 1: https://youtu.be/Twu30EJ93Wg
Differential Equations: Motion of a Spring: https://youtu.be/mk2TiR5dwVs
Differential Equations: Population Growth: https://youtu.be/Td8C_cTEGkA
Derivative Rules - Proof of the Quotient Rule: http://youtu.be/fJcgnLKkISE
Foil Method - Simple Proof and Quick Alternative Method: http://youtu.be/tmj_r94D6wQ .

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In #MESExperiments number 7, I have repeated the same experiment as in the 5th experiment but this time removed the plastic and metal bases so that the gyroscope is directly in contact with the ice block. This means that the contact surface between the ice and the stem of the gyroscope has very little rotational friction and which can be see by the gyroscope outer casing spinning very rapidly; even though the gyroscope’s center disk is the only thing initially spun.

I positioned the gyroscope at about 35 degrees from the vertical and yet again the gyroscope magically rises upwards and with ZERO “centripetal force” as can be seen by the lack of horizontal movement as the gyroscope rises upwards. This experiment demonstrates that even if the gyroscope’s outer casing is free to rotate, the gyroscope still rises upwards. Thus the ability of the gyroscope to rise upwards is not due to horizontal friction (no centripetal force) and not due to rotational friction either. Then the question arises: how is the gyroscope precessing upwards? Stay tuned for my later experiments and my epic #AntiGravity Part 6 video which shows that “gravity” itself is being interacted with through the simple rotation of matter… #StayTuned

The gyroscope takes about 3.5 minutes to fully rise upwards and after which maintains its vertical position for about 1 minute. Then, as also shown in experiment number 5, the gyroscope magically “regains” its “centripetal force” as it precesses downwards and with the ice block moving in large horizontal circular movements. This upwards rising is even more impressive given the fact that the gyroscope stem has literally dug directly into the ice block. Thus the gyroscope rises upwards not only against gravity but against the surrounding ice wall. #AbsolutelyFascinating

Also, later in the video I show that as the gyroscope loses spin speed, it still has the ability to precess in a circular downwards spiral; albeit more chaotic as the spin speed lowers. But even at extremely low spin speeds, the gyroscope still has the magical ability to avoid falling directly downwards but instead still spiral downwards which also “cushions” the fall of the gyro. #AmazingStuff

Stay Tuned for #MESExperiments Number 8!

View Video on Steemit: https://steemit.com/mesexperiments/@mes/mesexperiments-7-gyroscopes-precess-upwards-on-ice-even-while-outer-casing-spins-magic

Related Videos:

#MESExperiments Video Series: https://mes.fm/experiments-playlist
#AntiGravity Video Series: https://mes.fm/antigravity-playlist
#FreeEnergy Video Series: https://mes.fm/freeenergy-playlist .

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In this video I go over another example on differential equations and this time discuss the more practical need for finding a particular solution to a differential equation as opposed to a general solution. One such solution involves satisfying the additional requirement that the solution has a specific initial value. Thus in solving such a problem, known as an initial value problem, we get one particular solution. In this example I look back at the same differential equation from Example 1 but this time apply the initial condition y(0) = 2.

Thus in the physical sense, the particular solution to an initial value problem means that we take our initial known or measured condition and then predict the future values from this starting point. This is a pretty interesting video on how to go about solving an initial value problem so make sure to watch this video!

Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhsIsflB-HCEIQkOQrQ

View Video Notes on Steemit: https://steemit.com/mathematics/@mes/differential-equations-example-2-initial-value-problem

Related Videos:

Differential Equations: Example 1: https://youtu.be/n575RKO48Ro
Differential Equations: General Overview: https://youtu.be/jit59tIY4UI
Differential Equations: Spring Motion: Example 1: https://youtu.be/Twu30EJ93Wg
Differential Equations: Motion of a Spring: https://youtu.be/mk2TiR5dwVs
Differential Equations: Population Growth: https://youtu.be/Td8C_cTEGkA .

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As explained in my earlier videos, most differential equations can't be solved explicitly which thus forces us to find different ways of estimating the solution; and one of those is in the concept of direction fields. For differential equations of the form y' = F(x, y), a direction field (or slope field) is any number of points in which the slope of the line segment near that point is plotted out. This allows us to get a general idea of the shape of the curve. Direction fields are very useful to visually see the solution of a differential equation without actually having to know the precise solution. This is a very important concept to understand so make sure to watch this video!

Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhsJtu3CqeI05b6SJkQ

View Video Notes on Steemit: https://steemit.com/mathematics/@mes/differential-equations-direction-fields

Related Videos:

Differential Equations: General Overview: https://youtu.be/jit59tIY4UI
Differential Equations: Spring Motion: Example 1: https://youtu.be/Twu30EJ93Wg
Differential Equations: Motion of a Spring: https://youtu.be/mk2TiR5dwVs
Differential Equations: Population Growth: https://youtu.be/Td8C_cTEGkA .

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In this video I go over an example on how to go about generating a direction field as well as using it to draw a particular solution. The differential equation used is y' = x^2 + y^2 - 1 and a particular solution is graphed that passes through the origin (0, 0). This is a pretty simple but useful video in showing how we can estimate a solution to the differential equation without knowing the actual formula for the solution.

Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhsMBfgeJ04US4Bitig

View Video Notes on Steemit: https://steemit.com/mathematics/@mes/differential-equations-direction-fields-example-1

Related Videos:

Differential Equations: Direction Fields: https://youtu.be/zWv1y8Xp1ac
Differential Equations: General Overview: https://youtu.be/jit59tIY4UI
Differential Equations: Spring Motion: Example 1: https://youtu.be/Twu30EJ93Wg
Differential Equations: Motion of a Spring: https://youtu.be/mk2TiR5dwVs
Differential Equations: Population Growth: https://youtu.be/Td8C_cTEGkA .

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In this video I go over a brief introduction to some of the definitions and concepts behind electric circuit such as resistors, voltage, inductors, current, and electromotive force. The current flowing through an electric circuit can be described as a first order differential equation, which is part of Kirchhoff's Laws and also uses Ohm's law for voltage drop due to a resistor. This video is to serve as a bit of a background in order to better understand the example in my next video, which will be on describing the solution to this differential equation by using differential fields.

If you haven't learned about electric circuits, this brief overview might be useful so make to watch this video!

Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhsMkadtGWg2f2U-ZPQ

View Video Notes on Steemit: https://steemit.com/mathematics/@mes/differential-equations-electric-circuit-introduction

Related Videos:

Differential Equations: Direction Fields: Example 1: https://youtu.be/mtbMQQZeMoQ
Differential Equations: Direction Fields: https://youtu.be/zWv1y8Xp1ac
Differential Equations: General Overview: https://youtu.be/jit59tIY4UI
Differential Equations: Spring Motion: Example 1: https://youtu.be/Twu30EJ93Wg
Differential Equations: Motion of a Spring: https://youtu.be/mk2TiR5dwVs
Differential Equations: Population Growth: https://youtu.be/Td8C_cTEGkA .

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In #MESExperiments number 6, I repeat my 5th experiment of a precessing gyroscope on ice but this time set the gyroscope at a near horizontal angle. And yet again the gyroscope demonstrates the (mainstream) physics-defying ability to magically precess with ZERO centripetal force, at sufficient gyro spin rate. In other words, the gyroscope precess as if it magically lost all its “mass” and thus generating ZERO “horizontal force” at the stem; and as explained in Experiment number 4, the gyroscope literally precesses without “angular momentum”. This is some truly mind-boggling properties of gyroscopes which, if viewed with the critical eye, requires a re-writing of centuries old (mainstream) physics textbooks and even science in general.

Once the gyroscope loses spin speed, the “centripetal force” gradually increases which can be seen by the stem of the gyroscope moving in a circular direction on the near frictionless ice surface. But even at these slower spin speeds, the amount of “centripetal force” is almost negligible. This is because, as shown in my earlier experiments, it just takes an incredibly small amount of “friction” to hold the gyroscope in place. And in fact it is this gyroscope’s magical property of seemingly behave “massless” that allows it to precess perfectly balanced even on the tip of your finger.

I can’t stress how monumental and game-changing these HIDDEN-IN-PLAIN-SITE properties of gyroscopes, because after all a gyroscope is essentially a constrained spinning top, and which a spinning top itself is just matter in rotation… Which begs the questions what is “matter” and why does rotation magically change its properties?

Stay Tuned for #MESExperiments Number 7!

View on Steemit: https://steemit.com/mesexperiments/@mes/mesexperiments-6-gyroscopes-precess-with-zero-centripetal-force-on-ice-even-at-horizontal-angle

Related Videos:

#MESExperiments Video Series: https://mes.fm/experiments-playlist
#AntiGravity Video Series: https://mes.fm/antigravity-playlist
#FreeEnergy Video Series: https://mes.fm/freeenergy-playlist .

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In this video I go over an example on drawing direction fields for the differential equation that I covered in my last video that relates the voltage drops due to an inductor and resistor with the voltage and current supplied of an electric circuit. The direction field in this example is very interesting in that, since the differential equation does not depend on the time variable but only on the current, this makes every line segment parallel to every other line segment to the left or the right of it, assuming they are at the same currents. This type of differential equation is called autonomous and thus if we know one solution to the differential equation, we can obtain infinitely many, simply by shifting the solution left or right.

This video relies heavily on the definitions and concepts involved in electric circuits so make sure to watch last video before watching this if you haven't covered electric circuits before.

Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhsNZFnoROicWKcXu3w

View Video Notes on Steemit: https://steemit.com/mathematics/@mes/differential-equations-direction-fields-example-2-electric-circuit

Related Videos:

Differential Equations: Electric Circuit: Introduction: https://youtu.be/E6vij-RzQ-o
Differential Equations: Direction Fields: Example 1: https://youtu.be/mtbMQQZeMoQ
Differential Equations: Direction Fields: https://youtu.be/zWv1y8Xp1ac
Differential Equations: General Overview: https://youtu.be/jit59tIY4UI
Differential Equations: Spring Motion: Example 1: https://youtu.be/Twu30EJ93Wg
Differential Equations: Motion of a Spring: https://youtu.be/mk2TiR5dwVs
Differential Equations: Population Growth: https://youtu.be/Td8C_cTEGkA .

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In my earlier videos I went over using direction fields to graphically approximate solutions to differential equations, but in this video I show how we can use direction fields to numerically approximate solutions as well. This process is called the Euler's Method and is quite simply approximating the solution to an initial-value problem by using straight line segments in which the slopes are determined at each point through the differential equation. I also show in the video that as we increase the number of line segments by shortening the step size between each point, then we effectively can get closer and closer to the exact solution. With computers, this is obviously very practical since they can solve many calculations at once, and in fact many super computers are used in numerically solving differential equations using similar methods as the Euler Method. This video gives a very important illustration of a very important concept, which is numerical approximation to differential equations, so make sure to watch this video!

Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhsQKa2zf5-ft8WNb3Q

View Video Notes on Steemit: https://steemit.com/mathematics/@mes/differential-equations-euler-s-method

Related Videos:

Differential Equations Direction Fields: Example 2: Electric Circuit: https://youtu.be/-bfPZG7-MTA

Differential Equations: Electric Circuit: Introduction: https://youtu.be/E6vij-RzQ-o
Differential Equations: Direction Fields: Example 1: https://youtu.be/mtbMQQZeMoQ
Differential Equations: Direction Fields: https://youtu.be/zWv1y8Xp1ac
Differential Equations: General Overview: https://youtu.be/jit59tIY4UI
Differential Equations: Spring Motion: Example 1: https://youtu.be/Twu30EJ93Wg
Differential Equations: Motion of a Spring: https://youtu.be/mk2TiR5dwVs
Differential Equations: Population Growth: https://youtu.be/Td8C_cTEGkA .

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This is a question that is usually brought up but not many actually take the time to find out the difference between deodorant and antiperspirant. In this video, my brother MFA goes over how deodorants and antiperspirants are both used to combat odors caused by sweat, mostly located in your armpits. Deodorants usually work to only mask the smell of bacteria from sweat, while antiperspirants actually try to block sweat glands from releasing moisture. But the choice to use is up to you, so make sure to watch this video to get a better idea of which one to use!

Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhsQsPoxR7zZmstmgdg

View Video Notes on Steemit: https://steemit.com/health/@mes/deodorant-vs-antiperspirant

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View Subscriber Count Without Unsubscribing: http://youtu.be/vxYw3ZRUdKo
Difference Between Expresso and Coffee: http://youtu.be/0zcRNLfOMIg
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Odds of Having a Perfect NCAA March Madness Bracket: http://youtu.be/It1sCq9cAFM
What is 20/20 Vision?: http://youtu.be/31kYnnIjugQ
NCAA vs. NBA 3 Point Line: http://youtu.be/1__25TpOdB0
Odds of Winning the Lottery: http://youtu.be/dVNFhu6tMQc
NBA Free Agency and Max Contracts: Introduction: http://youtu.be/osDN-bnPULY .

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In this video I go over an example on Euler's Method for numerically approximating solutions to a differential equation and this time look at the initial-value problem: y' = x + y with y(0) = 1. Initially I use the step size of 0.1 to roughly approximate the solution at x = 0.1, 0.2, ..., 1.0. But to get more accurate approximations we can decrease the step size even further. As shown in this video, when we decrease the step size further and further the solution approaches closer and closer to the exact value. This is a very useful video to understand Euler's method in detail, as well as how to develop spreadsheets to calculate it, so make sure to watch this video!

Download the notes in my video:

Notes: https://1drv.ms/b/s!As32ynv0LoaIhsQlsgrDZEb68Fl1LQ
Excel Notes: https://1drv.ms/x/s!As32ynv0LoaIhsQnSuqAQ7rhC3PsFg

View Video Notes on Steemit: https://steemit.com/mathematics/@mes/differential-equations-euler-s-method-example-1

Related Videos:

Differential Equations: Euler's Method: https://youtu.be/VlwVl-3oPDM

Differential Equations: Electric Circuit: Introduction: https://youtu.be/E6vij-RzQ-o
Differential Equations: Direction Fields: Example 1: https://youtu.be/mtbMQQZeMoQ
Differential Equations: Direction Fields: https://youtu.be/zWv1y8Xp1ac
Differential Equations: General Overview: https://youtu.be/jit59tIY4UI
Differential Equations: Spring Motion: Example 1: https://youtu.be/Twu30EJ93Wg
Differential Equations: Motion of a Spring: https://youtu.be/mk2TiR5dwVs
Differential Equations: Population Growth: https://youtu.be/Td8C_cTEGkA .

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In this video I go over another example on applying Euler's Method to numerically approximate a solution to an initial-value problem and this time look at the same Electric Circuit example that I covered in my earlier video. In this example, I take a look at the differential equation used for the current flowing through an electric circuit and use Euler's Method to approximate what the current is after half a second, when given that the current is initially 0 at time 0, i.e. when the circuit is turned off then suddenly turned on.

Although this example is pretty straight forward, I decided not to use a calculator but instead solve the multiplication, addition, and subtraction all by hand as an exercise in algebra. Sometimes it is a good brain workout to work out calculations by hand. This might also come in handy, say for example, your calculator's battery dies during a math exam, which happened to me!!

Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhskVmSVF0NgsMRrs2w

View Video Notes on Steemit: https://steemit.com/mathematics/@mes/differential-equations-euler-s-method-example-2

Related Videos:

Differential Equations: Euler's Method: Example 1: https://youtu.be/L_l5DLZsZLQ
Differential Equations: Electric Circuit: Introduction: https://youtu.be/E6vij-RzQ-o
Differential Equations: Direction Fields: Example 1: https://youtu.be/mtbMQQZeMoQ
Differential Equations: Direction Fields: https://youtu.be/zWv1y8Xp1ac
Differential Equations: General Overview: https://youtu.be/jit59tIY4UI
Differential Equations: Spring Motion: Example 1: https://youtu.be/Twu30EJ93Wg
Differential Equations: Motion of a Spring: https://youtu.be/mk2TiR5dwVs
Differential Equations: Population Growth: https://youtu.be/Td8C_cTEGkA
Addition and Subtraction by Hand - An in-depth look: http://youtu.be/Tkb7xU-lFWU
Multiplication by Hand - In depth look at the wonderful world of multiplication: http://youtu.be/bUKGh5R_0Sw
Long Division by Hand - An in depth look: http://youtu.be/giBZg5Vqryo .

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In this video I go over an extensive video on solving the very interesting and challenging “Problems Plus” examples at the end of my Stewart calculus chapter on Parametric Equations and Polar Coordinates. As explained in my #MESExperiments Introduction video, to free up time to work on my game-changing “alternative” research into free energy, anti-gravity, and all-around real science and real reality, I will be making more condensed and super long mathematics videos like these; instead of the usual short videos for each subsection. This way I will be able to cover more math topics while I upload less videos.

In this Problems Plus Examples video, I solve 7 very worth-while problems and they are listed below with their time-stamps to help you navigate through this giant video. These problems combine much of what I covered in my earlier videos on Polar and Parametric Calculus; but also calculus in general as these examples tie in many different mathematical concepts together to solve very abstract and useful problems. I hope you enjoy my new longer and condensed format of mathematical videos, and if you follow along for the ride you may in fact be getting a mathematical education that few if any “Schools” would or can provide! #MESUniversity

Question 1: @ 1:21 – Arc Length of Parametric Curve
Question 2: @ 10:40 – Sketching a Symmetric Curve
Question 3: @ 55:41 – Determining Viewing Rectangle of a Family of Polar Curves
Question 4: @ 1:23:55 – Spiraling Bugs in Polar Coordinates
Question 5: @ 1:55:29 – Folium of Descartes
Question 6: @ 3:21:07 – Epitrochoid and the Wankel Rotary Engine
Question 7: @ 4:23:50 – Hyperbola Tangent Lines and Equidistant Asymptote Lines

Stay tuned for my next super long math video!

Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIh6oci2DcIvOPGSF3Sw

View Video Notes on Steemit: https://steemit.com/mathematics/@mes/parametric-equations-and-polar-coordinates-problems-plus-examples

Related Videos:

Problems Plus Examples: https://www.youtube.com/playlist?list=PLai3U8-WIK0EmBi_pTs2cBSqfE8oHGHqB
Parametric Equations and Curves: https://www.youtube.com/playlist?list=PLai3U8-WIK0H0AMIZV8HU3LVxSSf_Y9pi
Calculus with Parametric Curves: https://www.youtube.com/playlist?list=PLai3U8-WIK0H0AMIZV8HU3LVxSSf_Y9pi
Polar Coordinates: https://www.youtube.com/playlist?list=PLai3U8-WIK0HUFiPLsYw5_Ljd5riOUzjP
Area of Polar Curves: https://www.youtube.com/playlist?list=PLai3U8-WIK0HEsLZeseN9E9cCgZGYlbe7
Conics in Polar Coordinates: https://www.youtube.com/playlist?list=PLai3U8-WIK0H4OJpJ2gslXVLT8mP-SgJP .

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Created 1 year, 4 months ago.

337 videos

CategoryEducation

I mainly teach math, but also do controversial videos that are censored on YouTube, as well as creating #FreeEnergy technology!