Math Easy Solutions

Math Easy Solutions

MES

subscribers

In #MESExperiments 11 I go over several gyro rising experiments comparing different gyros to various initial spin speeds in order to understand how the rate of rising is affected by initial spin speeds. I compare 3 different gyroscopes and 2 different initial spin speed types: full speed and a delayed start. The 3 gyroscopes include a small plastic gyro (29.10 grams), a UFO light-up plastic/metallic gyro (134.39 g), and a metallic precision gyro (150.68 g). For each gyro I have placed the experiments side-by-side to better compare their behavior. The delayed start time for the small gyro is 30 seconds, for the UFO gyro it is 1 minute, and for the precision gyro it is 3 minutes. All the experiments had angles very close to 45 degrees from the vertical but it should be noted that even a 1 degree difference can have a drastic impact on the rising rate or even the ability to rise.

The findings show that the small gyro and the UFO gyro rose faster when delayed indicating that slower spin rate helped increase rising rate. But the opposite happened with the precision gyro in that the faster spin speed with no delay rose faster. These are are very interesting findings and require further investigation. It is also important to note that the weight of the gyro spinning mass and non-spinning mass are key components in the gyro's magical ability to rise; and which can even allow the gyro to generate torque over-unity in lifting relatively heavy weight as demonstrated in my game-changing #AntiGravity Part 6 video, https://mes.fm/antigravity-playlist.

Note that the video thumbnail has the full speed rising time shown in the above vertical gyros while the bottom are the initial starting positions of the delayed start gyros.

The full results of each experiment are shown in the accompanying Steemit article and Excel File:

Steemit Video Notes: https://steemit.com/mesexperiments/@mes/mesexperiments-11-increasing-gyroscope-spin-speed-doesn-t-necessarily-increase-rising-rate
Excel File: https://1drv.ms/x/s!As32ynv0LoaIh-53X75dowZjPNboJA

Note that the rising rate increases for the small and UFO gyro but decreases for the precision gyro. Also interesting is the rising rate for the precision gyro is several times smaller than the other gyros. Furthermore the full speed gyros were in the "sleep" or vertical position for longer and as well as taking longer to fully fall down. This may be due to the minimal bearing friction in the vertical position.

Note that further, more detailed experiments are required to quantitatively measure the spin speeds as well as the relative weights of the spinning vs non-spinning mass. Also in the works is that I'm trying to obtain a gyro wheel with no outer casing at all to get a better understanding of how the gyro behaves with no non-spinning mass. I will also be looking to get a battery powered gyro wheel with variable and uniform spin speed control to further understand the magic of gyros; if you are able to make one or know of a place that sells it please get in contact with me at [email protected].

It is also worth noting that the according to the website I purchased the 150.68 g precision gyroscope from, the weight of the spinning brass disk including the rotating shaft is 112 g. Thus the ratio of the spinning mass to the total weight is 112/150.68 = 0.7433 = 74.33 %. I believe weighing the spinning rotors of the small toy gyro and UFO gyro and comparing the relative spinning mass ratio with the precision gyro may reveal further important information regarding the rising rates; which I will look to dissemble soon.

Stay Tuned for #MESExperiments 12…

Related Videos:

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

------------------------------------------------------

SUBSCRIBE via EMAIL: https://mes.fm/subscribe

DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate

Like, Subscribe, Favorite, and Comment Below!

Follow us on:

Official Website: https://MES.fm
Steemit: https://steemit.com/@mes
Gab: https://gab.ai/matheasysolutions
Minds: https://minds.com/matheasysolutions
Twitter: https://twitter.com/MathEasySolns
Facebook: https://fb.com/MathEasySolutions
LinkedIn: https://mes.fm/linkedin
Pinterest: https://pinterest.com/MathEasySolns
Instagram: https://instagram.com/MathEasySolutions
Email me: [email protected]

Try our Free Calculators: https://mes.fm/calculators

BMI Calculator: https://bmicalculator.mes.fm
Grade Calculator: https://gradecalculator.mes.fm
Mortgage Calculator: https://mortgagecalculator.mes.fm
Percentage Calculator: https://percentagecalculator.mes.fm

Try our Free Online Tools: https://mes.fm/tools

iPhone and Android Apps: https://mes.fm/mobile-apps

In this video I go over another example on approximate integration and this time use the Midpoint Rule with 10 sub-intervals to approximate the integral of the function e^(x^2) from x = 0 to x = 1. In fact there is no exact integral solution of this function and thus approximations are the only way to evaluate the integral. In this example I also go over the upper error bound for the approximation to see how accurate our approximation is with the midpoint rule.

Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhel1Um918VmwrnAE8Q

View Video Notes on Steemit: https://steemit.com/mathematics/@mes/approximate-integration-example-3-midpoint-rule

Related Videos:

Approximate Integration: Example 2: Accuracy: http://youtu.be/D9l2o-UiRLE
Approximate Integration: Midpoint Rule Error Bound: Proof: http://youtu.be/aKUFHXNeW7Y
Approximate Integration: Example 1: 1/x: http://youtu.be/DTzZ1jz6OOg
Approximate Integration: Accuracy and Error Bounds: http://youtu.be/WTdNktL_1Uc
Approximate Integration: Trapezoidal Rule Error Bound: Proof: http://youtu.be/_mrSHIin7Mw
Integration by Parts: Integration Constants: http://youtu.be/jJ-RJTNMy4s
Evaluating Integrals - Midpoint vs Right Endpoint Approximations Comparison: http://youtu.be/3x3sF7P9xfY .

------------------------------------------------------

SUBSCRIBE via EMAIL: https://mes.fm/subscribe

DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate

Like, Subscribe, Favorite, and Comment Below!

Follow us on:

Official Website: https://MES.fm
Steemit: https://steemit.com/@mes
Gab: https://gab.ai/matheasysolutions
Minds: https://minds.com/matheasysolutions
Twitter: https://twitter.com/MathEasySolns
Facebook: https://fb.com/MathEasySolutions
LinkedIn: https://mes.fm/linkedin
Pinterest: https://pinterest.com/MathEasySolns
Instagram: https://instagram.com/MathEasySolutions
Email me: [email protected]

Try our Free Calculators: https://mes.fm/calculators

BMI Calculator: https://bmicalculator.mes.fm
Grade Calculator: https://gradecalculator.mes.fm
Mortgage Calculator: https://mortgagecalculator.mes.fm
Percentage Calculator: https://percentagecalculator.mes.fm

Try our Free Online Tools: https://mes.fm/tools

iPhone and Android Apps: https://mes.fm/mobile-apps

In #MESExperiments 10, I compare two gyro setups when hung by a string: one without a counterweight and one with. The gyroscope without the counterweight is able to precess (magically) upwards from a very steep angle until it makes contact with the string. But adding the counterweight which should be providing some upwards lift/torque on the gyro instead makes it precess at a constant angle until it loses spin speed and starts to gradually drop downwards. This is as counterintuitive as it gets!

Note that the gyroscope weights 148.62 g and the counterweight is 120.43 g as per the weight readings at the bottom of my earlier video notes: https://steemit.com/mesexperiments/@mes/mesexperiments-9-gyroscope-with-counterweight-hung-on-a-string-rises-downwards-magicx1000.

The gyro without the counterweight, thus effectively there is nothing visible acting upon it as it floats and then rises upwards, is initially at an angle of about 55 degrees from the vertical. In about a minute and a half it rises and makes contact with the string.

The gyro setup with the counterweight was initially orientated at about 47 degrees from the vertical; thus about 8 degrees less steep than the other gyro setup yet it still couldn't rise! After precession at a relatively constantly angle close to the starting angle, the gyro gradually drops until just over 4 minutes in which it falls past the horizontal level.

Some further observations, which I covered in #AntiGravity Part 6, https://mes.fm/antigravity-playlist, are also seen for the gyro setup without the counterweight. As the gyro loses spin speed the precessional "centrifugal force" becomes apparent as it starts to precess in a widening spiral. As it slows even more, the precession circle is very wide. Even later, as the gyro spin speed slows down a lot so too does the precession speed and thus the precession circle becomes much smaller.

Later in the experiment, I conduct some forced precession experiments. When I apply a rotational force on the string in the opposite direction to the gyro spin speed, the gyro magically inertially propels itself upwards, and again as stated in #AntiGravity Part 6 so that the gyro spin and precession move towards alignment. Applying a rotational force to the string in the direction of the gyro spin direction generates no rising but instead the gyro becomes more rigid in alignment with the applied force.

As the string gets over wound-up, it begins applying an unwinding rotational force which although is relatively tiny compared to the weight of the gyro, it can still generate inertial lift of the gyro when the rotational force is opposite to the gyro spin direction. Thus, as also stated in #AntiGravity Part 6, this is alluding to the "torque over-unity" or force amplification ability of gyroscopes. And lastly, when the string gets wound-up again and this time unwinding in the direction of the gyro spin, the gyro once again becomes rigid in its orientation and exhibits no inertial lift. Fascinating stuff!

Stay Tuned for #MESExperiments 11…

View Video Notes on Steemit: https://steemit.com/mesexperiments/@mes/mesexperiments-10-gyroscopes-on-a-string-can-rise-but-not-if-sufficient-counterweight-is-added

Related Videos:

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

------------------------------------------------------

SUBSCRIBE via EMAIL: https://mes.fm/subscribe

DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate

Like, Subscribe, Favorite, and Comment Below!

Follow us on:

Official Website: https://MES.fm
Steemit: https://steemit.com/@mes
Gab: https://gab.ai/matheasysolutions
Minds: https://minds.com/matheasysolutions
Twitter: https://twitter.com/MathEasySolns
Facebook: https://fb.com/MathEasySolutions
LinkedIn: https://mes.fm/linkedin
Pinterest: https://pinterest.com/MathEasySolns
Instagram: https://instagram.com/MathEasySolutions
Email me: [email protected]

Try our Free Calculators: https://mes.fm/calculators

BMI Calculator: https://bmicalculator.mes.fm
Grade Calculator: https://gradecalculator.mes.fm
Mortgage Calculator: https://mortgagecalculator.mes.fm
Percentage Calculator: https://percentagecalculator.mes.fm

Try our Free Online Tools: https://mes.fm/tools

iPhone and Android Apps: https://mes.fm/mobile-apps

In this video I go over a very useful application on using Simpson's Rule to approximate a function that has no actual function given. Instead in this example, only a chart is given of the total megabits of data transferred from the United States to the Swiss academic and research network, SWITCH, on February 10, 1998. Since the chart contains data that is smooth without random bumps in the data, we can apply the Simpson's Rule by simply estimating data points for the summation. Also in this video I discuss a bit about the difference between megabits and megabytes so make sure to watch this video!

Download the notes in my video:

View Video Notes on Steemit: https://steemit.com/mathematics/@mes/approximate-integration-example-5-simpson-s-rule-application

PDF Notes: http://1drv.ms/1Lq0KqR
Excel Notes: http://1drv.ms/1CNJjfY

Related Videos:

Relating Simpson's Rule with Trapezoidal and Midpoint Rules: https://youtu.be/lX2UYAm7A90

Approximate Integration: Example 4: Simpson's Rule: https://youtu.be/7xpdZnT6IWU
Approximate Integration: Simpson's Rule: Proof: https://youtu.be/aDvSpOHQoLU
Approximate Integration: Midpoint Rule Error Bound: Proof: http://youtu.be/aKUFHXNeW7Y
Approximate Integration: Example 1: 1/x: http://youtu.be/DTzZ1jz6OOg
Approximate Integration: Accuracy and Error Bounds: http://youtu.be/WTdNktL_1Uc
Approximate Integration: Trapezoidal Rule Error Bound: Proof: http://youtu.be/_mrSHIin7Mw
Integration by Parts: Integration Constants: http://youtu.be/jJ-RJTNMy4s
Evaluating Integrals - Midpoint vs Right Endpoint Approximations Comparison: http://youtu.be/3x3sF7P9xfY .

------------------------------------------------------

SUBSCRIBE via EMAIL: https://mes.fm/subscribe

DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate

Like, Subscribe, Favorite, and Comment Below!

Follow us on:

Official Website: https://MES.fm
Steemit: https://steemit.com/@mes
Gab: https://gab.ai/matheasysolutions
Minds: https://minds.com/matheasysolutions
Twitter: https://twitter.com/MathEasySolns
Facebook: https://fb.com/MathEasySolutions
LinkedIn: https://mes.fm/linkedin
Pinterest: https://pinterest.com/MathEasySolns
Instagram: https://instagram.com/MathEasySolutions
Email me: [email protected]

Try our Free Calculators: https://mes.fm/calculators

BMI Calculator: https://bmicalculator.mes.fm
Grade Calculator: https://gradecalculator.mes.fm
Mortgage Calculator: https://mortgagecalculator.mes.fm
Percentage Calculator: https://percentagecalculator.mes.fm

Try our Free Online Tools: https://mes.fm/tools

iPhone and Android Apps: https://mes.fm/mobile-apps

In this video I go over another example on approximate integration and this time use the Simpson's Rule to approximate the integral of the function 1/x from x = 1 to x = 2. This was the same function that in my earlier video I approximated using the Trapezoidal and Midpoint Rules. In this video I show that the Simpson's Rule is much more accurate then either of the other two approximation methods. Not only that but it turns out the Simpson's Rule is a weight average of the Trapezoidal and Midpoint Rules. I will proof this fact in my next video so stay tuned for that!

Download the notes in my video: http://1drv.ms/1Vg5O7G

View Video Notes on Steemit: https://steemit.com/mathematics/@mes/approximate-integration-example-4-simpson-s-rule

Related Videos:

Approximate Integration: Simpson's Rule: Proof: https://youtu.be/aDvSpOHQoLU
Approximate Integration: Midpoint Rule Error Bound: Proof: http://youtu.be/aKUFHXNeW7Y
Approximate Integration: Example 1: 1/x: http://youtu.be/DTzZ1jz6OOg
Approximate Integration: Accuracy and Error Bounds: http://youtu.be/WTdNktL_1Uc
Approximate Integration: Trapezoidal Rule Error Bound: Proof: http://youtu.be/_mrSHIin7Mw
Integration by Parts: Integration Constants: http://youtu.be/jJ-RJTNMy4s
Evaluating Integrals - Midpoint vs Right Endpoint Approximations Comparison: http://youtu.be/3x3sF7P9xfY .

------------------------------------------------------

SUBSCRIBE via EMAIL: https://mes.fm/subscribe

DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate

Like, Subscribe, Favorite, and Comment Below!

Follow us on:

Official Website: https://MES.fm
Steemit: https://steemit.com/@mes
Gab: https://gab.ai/matheasysolutions
Minds: https://minds.com/matheasysolutions
Twitter: https://twitter.com/MathEasySolns
Facebook: https://fb.com/MathEasySolutions
LinkedIn: https://mes.fm/linkedin
Pinterest: https://pinterest.com/MathEasySolns
Instagram: https://instagram.com/MathEasySolutions
Email me: [email protected]

Try our Free Calculators: https://mes.fm/calculators

BMI Calculator: https://bmicalculator.mes.fm
Grade Calculator: https://gradecalculator.mes.fm
Mortgage Calculator: https://mortgagecalculator.mes.fm
Percentage Calculator: https://percentagecalculator.mes.fm

Try our Free Online Tools: https://mes.fm/tools

iPhone and Android Apps: https://mes.fm/mobile-apps

In this video I go over another integral approximation method and this time I derive the Simpson's Rule method which uses parabolas to estimate the area under a curve. This method moves away from the traditional straight lines segments used in the Left, Right, Midpoint, and Trapezoidal approximation methods and has curved segments in the shape of parabolas. This method is named after the English Mathematician Thomas Simpson (who lived from 1710 to 1761) who popularized this method in his best-selling calculus textbook: A New Treatise of Fluxions. Note that fluxions are what Isaac Newton used to refer to derivatives but eventually Leibnitz derivative notation won out. Also, even though the Simpson's Rule was actually known to Cavalieri and Gregory, Simpson greatly popularized it! The proof shown in this video is very clever and combined with the brief mathematical history lesson, makes this a very useful video to watch!

Download the notes in my video: https://onedrive.live.com/redir?resid=88862EF47BCAF6CD!95492&authkey=!AMKUSV7UbBmu_pU&ithint=file%2cpdf

View Video Notes on Steemit: https://steemit.com/mathematics/@mes/approximate-integration-simpson-s-rule-proof

Related Videos:

Approximate Integration: Example 3: Midpoint Rule: https://youtu.be/SxHfJ3MrkSk
Approximate Integration: Midpoint Rule Error Bound: Proof: http://youtu.be/aKUFHXNeW7Y
Approximate Integration: Example 1: 1/x: http://youtu.be/DTzZ1jz6OOg
Approximate Integration: Accuracy and Error Bounds: http://youtu.be/WTdNktL_1Uc
Approximate Integration: Trapezoidal Rule Error Bound: Proof: http://youtu.be/_mrSHIin7Mw
Integration by Parts: Integration Constants: http://youtu.be/jJ-RJTNMy4s
Evaluating Integrals - Midpoint vs Right Endpoint Approximations Comparison: http://youtu.be/3x3sF7P9xfY .

------------------------------------------------------

SUBSCRIBE via EMAIL: https://mes.fm/subscribe

DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate

Like, Subscribe, Favorite, and Comment Below!

Follow us on:

Official Website: https://MES.fm
Steemit: https://steemit.com/@mes
Gab: https://gab.ai/matheasysolutions
Minds: https://minds.com/matheasysolutions
Twitter: https://twitter.com/MathEasySolns
Facebook: https://fb.com/MathEasySolutions
LinkedIn: https://mes.fm/linkedin
Pinterest: https://pinterest.com/MathEasySolns
Instagram: https://instagram.com/MathEasySolutions
Email me: [email protected]

Try our Free Calculators: https://mes.fm/calculators

BMI Calculator: https://bmicalculator.mes.fm
Grade Calculator: https://gradecalculator.mes.fm
Mortgage Calculator: https://mortgagecalculator.mes.fm
Percentage Calculator: https://percentagecalculator.mes.fm

Try our Free Online Tools: https://mes.fm/tools

iPhone and Android Apps: https://mes.fm/mobile-apps

In #MESExperiments 9, I demonstrate one of the most fascinating experiments ever performed. This experiment came a whole year after discovering that gyroscopes rise magically all on their own (See Experiments 1, 2, 3, 5, 7 at https://mes.fm/experiments-playlist). Those earlier experiments shows that gyros rise upwards when they should instead fall down; effectively behaving lighter. And in this experiment, the opposite happens. Adding a counterweight such that the gyroscope is balanced horizontally instead makes the gyroscope behave heavier and magically drop downwards and lift the counterweight in the process! This is one of the most mind-boggling experiments of all time!

Note that from my epic #AntiGravity Part 6 video, https://mes.fm/antigravity-playlist, the gyro spin and precession directions tend to always want to align even if it means behaving heavier or lighter, i.e. magic. Note again that this demonstration is only possible when there is very little rotational or precessional friction, hence why it drops when hung by a string but with the conventional gimbal setup it would not even precess. Also from Part 6, this low friction requirement alludes to "torque over-unity" in that the gyroscope amplifies forces or torques.

As the gyro spin speed slows down the gyro is still upside down but now the precession spiral is larger, similar to Experiment 6 in which the centrifugal outwards precession "force" gets larger as the gyro slows down. Interestingly, at even slower gyro spin speeds the precession circle and precession speed gets smaller, again while the gyro is still upside down! After 7 minutes, the gyro starts to rise gradually upwards, but this is likely due to the string getting wound up and starts generating (over-unity) counter precessional force. Amazingly, just the mere unwinding of the string is enough to cause the gyro to precess in the reverse direction while this time rising upwards above the horizontal! And once again, as the gyro loses even more spin speed even in the now risen position the precession spiral/circle moves outwards further out. This time, the counterweight appears to be the new "center of mass".

Fascinating stuff!

View Video Notes on Steemit: https://steemit.com/mesexperiments/@mes/mesexperiments-9-gyroscope-with-counterweight-hung-on-a-string-rises-downwards-magicx1000

Related Videos:

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

------------------------------------------------------

SUBSCRIBE via EMAIL: https://mes.fm/subscribe

DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate

Like, Subscribe, Favorite, and Comment Below!

Follow us on:

Official Website: https://MES.fm
Steemit: https://steemit.com/@mes
Gab: https://gab.ai/matheasysolutions
Minds: https://minds.com/matheasysolutions
Twitter: https://twitter.com/MathEasySolns
Facebook: https://fb.com/MathEasySolutions
LinkedIn: https://mes.fm/linkedin
Pinterest: https://pinterest.com/MathEasySolns
Instagram: https://instagram.com/MathEasySolutions
Email me: [email protected]

Try our Free Calculators: https://mes.fm/calculators

BMI Calculator: https://bmicalculator.mes.fm
Grade Calculator: https://gradecalculator.mes.fm
Mortgage Calculator: https://mortgagecalculator.mes.fm
Percentage Calculator: https://percentagecalculator.mes.fm

Try our Free Online Tools: https://mes.fm/tools

iPhone and Android Apps: https://mes.fm/mobile-apps

In this video I go over a pretty extensive tutorial on infinite series, its definition, and many examples to elaborate in great detail. An infinite series is the summation of a sequence of terms as the terms approach an infinite number of terms and follow from my earlier video on infinite sequences; thus much of the previous video applies to this video. Several important series are covered such as the Geometric series and the Harmonic Series covered. Also, several interesting derivation techniques are utilized such as partial fraction decomposition and the amazing telescoping sum concept. I go over many examples and 2 important exercises from my calculus book (Early Transcendentals by James Stewart) to make the concept of infinite series, and their divergence or convergence, much more clear.

The topics and sections covered in this video are listed below with their timestamps:

1. @ 1:34 - Infinite Series and Notation
- @ 8:29 - Definition 1
2. @ 13:11 - Example 1: Geometric Series
- @ 27:43 - Example 2
- @ 32:49 - Example 3
- @ 39:49 - Example 4
- @ 48:28 - Example 5
3. @ 51:10 - Example 6: Telescoping Sum
4. @ 1:01:31 - Example 7: Harmonic Series
5. @ 1:10:30 - Theorem 1
- @ 1:16:02 - Test for Divergence
- @ 1:17:30 - Example 8
6. @ 1:20:35 - Theorem 2
- @ 1:28:15 - Example 9
7. End of Chapter Exercises
- @ 1:35:10 - Exercise 1
- @ 1:45:43 - Exercise 2

Download the notes in my video:

PDF Notes: https://1drv.ms/b/s!As32ynv0LoaIh8gxUmX71Fk9dZ5_wg
Excel File: https://1drv.ms/x/s!As32ynv0LoaIh8gwtUIvFFz4HKE0DA

Related Videos:

Infinite Sequences: Limits, Squeeze Theorem, Fibonacci Sequence & Golden Ratio + MORE: https://steemit.com/mathematics/@mes/infinite-sequences-limits-squeeze-theorem-fibonacci-sequence-and-golden-ratio-more

Sequences and Series Playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0EXHAJ3vRg0T_kKEyPah1Lz .

------------------------------------------------------

SUBSCRIBE via EMAIL: https://mes.fm/subscribe

DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate

Like, Subscribe, Favorite, and Comment Below!

Follow us on:

Official Website: https://MES.fm
Steemit: https://steemit.com/@mes
Gab: https://gab.ai/matheasysolutions
Minds: https://minds.com/matheasysolutions
Twitter: https://twitter.com/MathEasySolns
Facebook: https://fb.com/MathEasySolutions
LinkedIn: https://mes.fm/linkedin
Pinterest: https://pinterest.com/MathEasySolns
Instagram: https://instagram.com/MathEasySolutions
Email me: [email protected]

Try our Free Calculators: https://mes.fm/calculators

BMI Calculator: https://bmicalculator.mes.fm
Grade Calculator: https://gradecalculator.mes.fm
Mortgage Calculator: https://mortgagecalculator.mes.fm
Percentage Calculator: https://percentagecalculator.mes.fm

Try our Free Online Tools: https://mes.fm/tools

iPhone and Android Apps: https://mes.fm/mobile-apps

In this video I go over some mathematics for a change after going all year working on my game changing #AntiGravity Part 6 video. In this video I look at the “Laboratory Project” on Logistic Sequences; note that laboratory projects are very interesting math projects at the end of some sections in my calculus book titled Early Transcendentals by James Stewart. The logistic sequence is defined by the logistic difference equation:

Current population = (a constant k) * (previous population)*(1 – previous population)

Note that this equation is similar to the logistic differential equation which I covered earlier and is given by the following formula.

Population growth = (a constant k) * population (1 – population / carrying capacity K)

The logistic sequence involves individual discrete values for the population size and is often preferred for modeling insect populations where mating and death occur periodically. In this project I take a look at modeling the logistic equation using Microsoft Excel spreadsheet to compare how the populations change with changing initial populations and constant k. Interestingly for some values of k there appears to be a leveling off of the population into 1 or more branches. But for other larger values of k the model gives very chaotic and spread out values for the population. The link to the Excel sheet is listed below so make sure to download it and play around with the logistic sequence model!

Download the notes in my video:

PDF Notes: https://1drv.ms/b/s!As32ynv0LoaIh8N8XBPGW5vi1TjDKw
Excel File: https://1drv.ms/x/s!As32ynv0LoaIh8N-0itIkBrT5E2YMw

View Video Notes on Steemit: https://steemit.com/mathematics/@mes/laboratory-project-logistic-sequences

Related Videos:

Infinite Sequences: Limits, Squeeze Theorem, Fibonacci Sequence & Golden Ratio + MORE: https://steemit.com/mathematics/@mes/infinite-sequences-limits-squeeze-theorem-fibonacci-sequence-and-golden-ratio-more
Differential Equations: Population Growth: Logistic Equation: https://steemit.com/mathematics/@mes/differential-equations-population-growth-logistic-equation .

------------------------------------------------------

SUBSCRIBE via EMAIL: https://mes.fm/subscribe

DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate

Like, Subscribe, Favorite, and Comment Below!

Follow us on:

Official Website: https://MES.fm
Steemit: https://steemit.com/@mes
Gab: https://gab.ai/matheasysolutions
Minds: https://minds.com/matheasysolutions
Twitter: https://twitter.com/MathEasySolns
Facebook: https://fb.com/MathEasySolutions
LinkedIn: https://mes.fm/linkedin
Pinterest: https://pinterest.com/MathEasySolns
Instagram: https://instagram.com/MathEasySolutions
Email me: [email protected]

Try our Free Calculators: https://mes.fm/calculators

BMI Calculator: https://bmicalculator.mes.fm
Grade Calculator: https://gradecalculator.mes.fm
Mortgage Calculator: https://mortgagecalculator.mes.fm
Percentage Calculator: https://percentagecalculator.mes.fm

Try our Free Online Tools: https://mes.fm/tools

iPhone and Android Apps: https://mes.fm/mobile-apps

Part 6 is split into two videos.

See Video 1 for the first part of #AntiGravity Part 6: https://www.bitchute.com/video/IS6BL47ytHEI/

The sections in the second video are shown below with their accompanying times in the video.

17. @ 0:00 - Inertial Propulsion and Inertial Lift are Facts of Life
18. @ 52:58 - Tippy Tops and Phi Tops Demonstrate Rising with Spin Axis Change
19. @ 1:54:32 - The Amazing and Underappreciated Gyrocompass
20. @ 2:50:48 - The Concept of Inertia and Coherency
21. @ 3:03:39 - Overview of Mainstream Clueless Science Regarding Gyroscopes and Objects in Rotation
22. @ 3:45:51 - SUMMARY OF MY SELF-APPOINTED PHD
23. @ 5:10:57 - MES DUALITY BREAKTHROUGH CONCEPT
24. @ 5:53:35 - AREAS OF FURTHER RESEARCH
25. @ 7:37:52 - Exploring the True Nature of Gravity, Mass, Magnetism, Electricity, Light, and Reality
26. @ 7:48:05 - David LaPoint’s Primer Fields, the Ferrocell, and Ken Wheeler’s Magnetism
27. @ 10:29:19 - THE TO KEY GYROSCOPIC MAGIC IS ‘COUNTERSPACE’
28. @ 11:05:58- True Magnetism and the Interconnectedness of All Things

Stay tuned for #AntiGravity Part 7!

Download my PhD:

- Word: https://1drv.ms/w/s!As32ynv0LoaIh75UFj1Vekcq1656wA
- PDF: https://1drv.ms/b/s!As32ynv0LoaIh-xTV42m_NX2ZDQYIw

View PhD on Steemit:

- Part 1: https://steemit.com/antigravity/@mes/antigravity-part-6-video-1-objects-in-rotation-defy-mainstream-physics-mes-duality-concept
- Part 2: https://steemit.com/antigravity/@mes/antigravity-part-6-objects-in-rotation-defy-mainstream-physics-mes-duality-concept-notes-2
- Part 3: https://steemit.com/antigravity/@mes/antigravity-part-6-objects-in-rotation-defy-mainstream-physics-mes-duality-concept-notes-3
- Part 4: https://steemit.com/antigravity/@mes/antigravity-part-6-objects-in-rotation-defy-mainstream-physics-mes-duality-concept-notes-4
- Part 5: https://steemit.com/antigravity/@mes/antigravity-part-6-objects-in-rotation-defy-mainstream-physics-mes-duality-concept-notes-5
- Part 6: https://steemit.com/antigravity/@mes/antigravity-part-6-objects-in-rotation-defy-mainstream-physics-mes-duality-concept-notes-6
- Part 7: https://steemit.com/antigravity/@mes/antigravity-part-6-objects-in-rotation-defy-mainstream-physics-mes-duality-concept-notes-7

Related Videos:

#AntiGravity: https://mes.fm/antigravity-playlist
#MESExperiments: https://mes.fm/experiments-playlist
DRAFT #MESExperiments: https://mes.fm/experiments-draft
#FreeEnergy: https://mes.fm/freeenergy-playlist
#911Truth: https://mes.fm/911truth-playlist .

------------------------------------------------------

SUBSCRIBE via EMAIL: https://mes.fm/subscribe

DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate

Like, Subscribe, Favorite, and Comment Below!

Follow us on:

Official Website: https://MES.fm
Steemit: https://steemit.com/@mes
Gab: https://gab.ai/matheasysolutions
Minds: https://minds.com/matheasysolutions
Twitter: https://twitter.com/MathEasySolns
Facebook: https://fb.com/MathEasySolutions
LinkedIn: https://mes.fm/linkedin
Pinterest: https://pinterest.com/MathEasySolns
Instagram: https://instagram.com/MathEasySolutions
Email me: [email protected]

Try our Free Calculators: https://mes.fm/calculators

BMI Calculator: https://bmicalculator.mes.fm
Grade Calculator: https://gradecalculator.mes.fm
Mortgage Calculator: https://mortgagecalculator.mes.fm
Percentage Calculator: https://percentagecalculator.mes.fm

Try our Free Online Tools: https://mes.fm/tools

iPhone and Android Apps: https://mes.fm/mobile-apps

In #AntiGravity Part 6, I present the many findings and discoveries made during this past year and a half regarding gyroscopes and all things rotation in general. The discoveries made are on the face of them so simple yet shatter the most overly complicated notions of conventional mainstream physics and science in general. The simple act of rotation defies the very bedrock underneath all of conventional (public) physics. The concept of ‘inertia’ and how it is defined underlies both conventional Newtonian mechanics and Einsteinian Relativity. But the simple act of rotation allows objects to have the magical ability to ‘inertially’ lift upwards, forwards, and even downwards, all without losing additional spin speed and while generating incredible torque over unity yet also behaving ‘massless’. Objects in rotation prove ‘spin angular momentum’, ‘precessional angular momentum’, ‘mass’, ‘inertia’, and hence ‘gravity’ as separate entities are merely illusions; puppets in a puppet show where the puppet master always lay underneath: the Aether.

Understanding the true nature of such simple motions as ‘rotation’, which is nothing more than curved linear motion, requires exploring and firmly grasping the true nature of reality itself. From inertia and magnetism to even psychology, technology, and consciousness itself. This video and document, which I am self-appointing as my ‘Doctorate in Philosophy’ or PhD sets the precedent for true scientific exploration and the start of an investigation into the true nature of reality, which has been covered up both by those that rule this world and those that choose to be ruled. Hope you enjoy this epic journey!

Part 6 is split into two videos. The sections in the first video are shown below with their accompanying times in the video.

1. @ 1:34 - Important Links and Notes
2. @ 5:45 - Introduction
3. @ 8:37 - Table of Contents
4. @ 55:56 - #MESExperiments Science Experiments Video Series
5. @ 58:08 - General Notes on Scientific Exploration
6. @ 1:06:01 - Clearing Eric Laithwaite’s Name
7. @ 2:25:11 - Eric Laithwaite’s Unconventional Interpretation of Newtonian Mechanics
8. @ 3:06:30 - Cambridge University’s Bogus Fake Science and Coverup of Gyro Magic
9. @ 4:04:00 - TOP SECRET: The Movie Inception and Spinning Tops
10. @ 4:07:06 - Overview of Conventional Physics Regarding Spinning Tops, Gyroscopes, and Objects in Rotation
11. @ 4:52:03 - Overview of Newton’s Laws and Einstein’s Relativity
12. @ 5:28:39 - Owen Liang’s Gyro Space Top Proves Spin Angular Momentum is an Illusion
13. @ 7:06:33 - INCEPTION IS REAL: Are We Living in a Dream?
14. @ 7:07:36 - Exploring Owen Liang’s Many Unnecessary Accounts
15. @ 9:00:10 - Owen Liang’s Battle with Wikipedia
16. @ 9:19:47 - Francis McCabe and Gyro 1000X+ Torque Over Unity!

See Video 2 for the second part of #AntiGravity Part 6: https://www.bitchute.com/video/sUnLAlGpiL3a/

Stay tuned for #AntiGravity Part 7!

Download my PhD:

- Word: https://1drv.ms/w/s!As32ynv0LoaIh75UFj1Vekcq1656wA
- PDF: https://1drv.ms/b/s!As32ynv0LoaIh-xTV42m_NX2ZDQYIw

View PhD on Steemit:

- Part 1 of 7: https://steemit.com/antigravity/@mes/antigravity-part-6-video-1-objects-in-rotation-defy-mainstream-physics-mes-duality-concept

Related Videos:

#AntiGravity: https://mes.fm/antigravity-playlist
#MESExperiments: https://mes.fm/experiments-playlist
DRAFT #MESExperiments: https://mes.fm/experiments-draft
#FreeEnergy: https://mes.fm/freeenergy-playlist
#911Truth: https://mes.fm/911truth-playlist .

------------------------------------------------------

SUBSCRIBE via EMAIL: https://mes.fm/subscribe

DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate

Like, Subscribe, Favorite, and Comment Below!

Follow us on:

Official Website: https://MES.fm
Steemit: https://steemit.com/@mes
Gab: https://gab.ai/matheasysolutions
Minds: https://minds.com/matheasysolutions
Twitter: https://twitter.com/MathEasySolns
Facebook: https://fb.com/MathEasySolutions
LinkedIn: https://mes.fm/linkedin
Pinterest: https://pinterest.com/MathEasySolns
Instagram: https://instagram.com/MathEasySolutions
Email me: [email protected]

Try our Free Calculators: https://mes.fm/calculators

BMI Calculator: https://bmicalculator.mes.fm
Grade Calculator: https://gradecalculator.mes.fm
Mortgage Calculator: https://mortgagecalculator.mes.fm
Percentage Calculator: https://percentagecalculator.mes.fm

Try our Free Online Tools: https://mes.fm/tools

iPhone and Android Apps: https://mes.fm/mobile-apps

In this video I go further into the Simpson's Rule for approximating integrals and prove that it is in fact a weighted average of both the Trapezoidal and Midpoint Rules. As shown in my earlier videos that the Trapezoidal and Midpoint Rules have error values that are usually opposite in signs, a weighted average (and thus Simpson's Rule) is usually much more accurate than either two integration rules. In this video I go over the proof by a clever method of breaking a function into 2n sub-intervals for the Simpson's Rule while using only the even intervals in estimating the function using the Trapezoidal Rule and only the odd intervals for the Midpoint Rule approximation. This is a very interesting way of proving that it is a weighted average so make sure to watch this video!

Download the notes in my video: http://1drv.ms/1CNJjfY

View Video Notes on Steemit: https://steemit.com/mathematics/@mes/relating-simpson-s-rule-with-trapezoidal-and-midpoint-rules

Related Videos:

Approximate Integration: Example 4: Simpson's Rule: https://youtu.be/7xpdZnT6IWU
Approximate Integration: Simpson's Rule: Proof: https://youtu.be/aDvSpOHQoLU
Approximate Integration: Midpoint Rule Error Bound: Proof: http://youtu.be/aKUFHXNeW7Y
Approximate Integration: Example 1: 1/x: http://youtu.be/DTzZ1jz6OOg
Approximate Integration: Accuracy and Error Bounds: http://youtu.be/WTdNktL_1Uc
Approximate Integration: Trapezoidal Rule Error Bound: Proof: http://youtu.be/_mrSHIin7Mw
Integration by Parts: Integration Constants: http://youtu.be/jJ-RJTNMy4s
Evaluating Integrals - Midpoint vs Right Endpoint Approximations Comparison: http://youtu.be/3x3sF7P9xfY .

------------------------------------------------------

SUBSCRIBE via EMAIL: https://mes.fm/subscribe

DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate

Like, Subscribe, Favorite, and Comment Below!

Follow us on:

Official Website: https://MES.fm
Steemit: https://steemit.com/@mes
Gab: https://gab.ai/matheasysolutions
Minds: https://minds.com/matheasysolutions
Twitter: https://twitter.com/MathEasySolns
Facebook: https://fb.com/MathEasySolutions
LinkedIn: https://mes.fm/linkedin
Pinterest: https://pinterest.com/MathEasySolns
Instagram: https://instagram.com/MathEasySolutions
Email me: [email protected]

Try our Free Calculators: https://mes.fm/calculators

BMI Calculator: https://bmicalculator.mes.fm
Grade Calculator: https://gradecalculator.mes.fm
Mortgage Calculator: https://mortgagecalculator.mes.fm
Percentage Calculator: https://percentagecalculator.mes.fm

Try our Free Online Tools: https://mes.fm/tools

iPhone and Android Apps: https://mes.fm/mobile-apps

In this video I go over our newly updated Percentage Calculator (http://percentcalculator.com) and show how to use the calculator as well as showing how to derive the formulas for each calculation. In the new update to our calculator we have added more calculations as well as a very useful formula function that shows the formula used in each of the calculations. The formulas also automatically change with the input! And like before all the calculations are automatically calculated as you type! We hope you like our new percentage calculator and please let us know if you have any questions or recommendations by commenting either in the YouTube comments below or on the http://percentcalculator.com website!

Download the notes in my video: http://1drv.ms/1MQhzwd

View Video Notes on Steemit: https://steemit.com/calculator/@mes/percentage-calculator-percentcalculator-com-update

Related Videos:

Mortgage Calculator Tutorial: mc.mes.fm: http://youtu.be/IZkpH9bWgPU
Grade Calculator: gc.mes.fm (Update): https://youtu.be/KjAfCz-8e4w
GPA Calculator: finalexamcalculator.com/gpa: http://youtu.be/wEwOjGJmiDU
BMI (Body Mass Index) Introduction + History: http://youtu.be/4kuCuBjoXmE .

------------------------------------------------------

SUBSCRIBE via EMAIL: https://mes.fm/subscribe

DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate

Like, Subscribe, Favorite, and Comment Below!

Follow us on:

Official Website: https://MES.fm
Steemit: https://steemit.com/@mes
Gab: https://gab.ai/matheasysolutions
Minds: https://minds.com/matheasysolutions
Twitter: https://twitter.com/MathEasySolns
Facebook: https://fb.com/MathEasySolutions
LinkedIn: https://mes.fm/linkedin
Pinterest: https://pinterest.com/MathEasySolns
Instagram: https://instagram.com/MathEasySolutions
Email me: [email protected]

Try our Free Calculators: https://mes.fm/calculators

BMI Calculator: https://bmicalculator.mes.fm
Grade Calculator: https://gradecalculator.mes.fm
Mortgage Calculator: https://mortgagecalculator.mes.fm
Percentage Calculator: https://percentagecalculator.mes.fm

Try our Free Online Tools: https://mes.fm/tools

iPhone and Android Apps: https://mes.fm/mobile-apps

In this video I go over a tutorial on our Grade Calculator and go over how to use it as well as doing manually solving the calculations behind the calculator. The website for the Grade Calculator is http://gradecalculator.mes.fm as well as through the shortened URL http://gc.mes.fm.

The Grade Calculator calculates the final exam grade needed on a course to obtain a desired overall course grade, and is very helpful as a way to bring down the stress of students worrying about their final exams. Please let us know what you think of our Grade Calculator as well as if you have any recommendations on how to make it even better!

Download the notes in my video:

PDF Notes: http://1drv.ms/1P8IBPr
Excel Notes: http://1drv.ms/1LFaHiX

View Video Notes on Steemit: https://steemit.com/calculator/@mes/grade-calculator-gc-mes-fm-update

Related Videos:

Percentage Calculator: PercentCalculator.com (Update): https://youtu.be/wxbwPBve4sQ
Mortgage Calculator Tutorial: mc.mes.fm: http://youtu.be/IZkpH9bWgPU
GPA Calculator: finalexamcalculator.com/gpa: http://youtu.be/wEwOjGJmiDU
BMI (Body Mass Index) Introduction + History: http://youtu.be/4kuCuBjoXmE .

------------------------------------------------------

SUBSCRIBE via EMAIL: https://mes.fm/subscribe

DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate

Like, Subscribe, Favorite, and Comment Below!

Follow us on:

Official Website: https://MES.fm
Steemit: https://steemit.com/@mes
Gab: https://gab.ai/matheasysolutions
Minds: https://minds.com/matheasysolutions
Twitter: https://twitter.com/MathEasySolns
Facebook: https://fb.com/MathEasySolutions
LinkedIn: https://mes.fm/linkedin
Pinterest: https://pinterest.com/MathEasySolns
Instagram: https://instagram.com/MathEasySolutions
Email me: [email protected]

Try our Free Calculators: https://mes.fm/calculators

BMI Calculator: https://bmicalculator.mes.fm
Grade Calculator: https://gradecalculator.mes.fm
Mortgage Calculator: https://mortgagecalculator.mes.fm
Percentage Calculator: https://percentagecalculator.mes.fm

Try our Free Online Tools: https://mes.fm/tools

iPhone and Android Apps: https://mes.fm/mobile-apps

In this video I go over an incredibly long video proving the Error Bound formula for the Simpson's Rule Integration Approximation method. This is a very long and tedious proof which explains why you won't find this proof in any calculus textbook. But here at Math Easy Solutions we don't shy away from any mathematical concept, regardless of how challenging it may be. If you have the time to watch the entire one hour and 45 minute video, it will make you truly appreciate some of the great lengths that the pioneers in mathematics have taken in deriving and simplifying formulas which we often take for granted.

Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhqJXI9Ugs0GEe8855Q

View Video Notes on Steemit: https://steemit.com/mathematics/@mes/simpson-s-rule-approimation-error-bound-proof

Related Videos:

Relating Simpson's Rule with Trapezoidal and Midpoint Rules: https://youtu.be/lX2UYAm7A90
Approximate Integration: Example 4: Simpson's Rule: https://youtu.be/7xpdZnT6IWU
Approximate Integration: Simpson's Rule: Proof: https://youtu.be/aDvSpOHQoLU
Approximate Integration: Midpoint Rule Error Bound: Proof: http://youtu.be/aKUFHXNeW7Y
Approximate Integration: Example 1: 1/x: http://youtu.be/DTzZ1jz6OOg
Approximate Integration: Accuracy and Error Bounds: http://youtu.be/WTdNktL_1Uc
Approximate Integration: Trapezoidal Rule Error Bound: Proof: http://youtu.be/_mrSHIin7Mw
Integration by Parts: Integration Constants: http://youtu.be/jJ-RJTNMy4s
Evaluating Integrals - Midpoint vs Right Endpoint Approximations Comparison: http://youtu.be/3x3sF7P9xfY .

------------------------------------------------------

SUBSCRIBE via EMAIL: https://mes.fm/subscribe

DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate

Like, Subscribe, Favorite, and Comment Below!

Follow us on:

Official Website: https://MES.fm
Steemit: https://steemit.com/@mes
Gab: https://gab.ai/matheasysolutions
Minds: https://minds.com/matheasysolutions
Twitter: https://twitter.com/MathEasySolns
Facebook: https://fb.com/MathEasySolutions
LinkedIn: https://mes.fm/linkedin
Pinterest: https://pinterest.com/MathEasySolns
Instagram: https://instagram.com/MathEasySolutions
Email me: [email protected]

Try our Free Calculators: https://mes.fm/calculators

BMI Calculator: https://bmicalculator.mes.fm
Grade Calculator: https://gradecalculator.mes.fm
Mortgage Calculator: https://mortgagecalculator.mes.fm
Percentage Calculator: https://percentagecalculator.mes.fm

Try our Free Online Tools: https://mes.fm/tools

iPhone and Android Apps: https://mes.fm/mobile-apps

In this video I go over another example on approximate integration and this time use the Simpson's Rule to approximate the integral from x = 0 to x = 1 of the function e^(x^2). This particular function has no definite integral formula so approximating it is the only way of calculating its integral. In this video I show that the accuracy using the Simpson's Rule is an order of magnitude better than using the Midpoint Rule to approximate this same integral, as shown in example 2 of this video series.

Download the notes in my video: http://1drv.ms/1QmOOFa

View Video Notes on Steemit: https://steemit.com/mathematics/@mes/approximate-integration-example-7-simpson-s-rule-accuracy

Related Videos:

Approximate Integration: Example 6: Simpson's Rule Error: https://youtu.be/jgrdYT-9IGY
Simpson's Rule Approimation: Error Bound Proof: https://youtu.be/q8jD7U0_BSs
Relating Simpson's Rule with Trapezoidal and Midpoint Rules: https://youtu.be/lX2UYAm7A90
Approximate Integration: Example 4: Simpson's Rule: https://youtu.be/7xpdZnT6IWU
Approximate Integration: Simpson's Rule: Proof: https://youtu.be/aDvSpOHQoLU
Approximate Integration: Midpoint Rule Error Bound: Proof: http://youtu.be/aKUFHXNeW7Y
Approximate Integration: Example 2: Accuracy: http://youtu.be/D9l2o-UiRLE
Approximate Integration: Accuracy and Error Bounds: http://youtu.be/WTdNktL_1Uc
Approximate Integration: Trapezoidal Rule Error Bound: Proof: http://youtu.be/_mrSHIin7Mw
Integration by Parts: Integration Constants: http://youtu.be/jJ-RJTNMy4s
Evaluating Integrals - Midpoint vs Right Endpoint Approximations Comparison: http://youtu.be/3x3sF7P9xfY .

------------------------------------------------------

SUBSCRIBE via EMAIL: https://mes.fm/subscribe

DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate

Like, Subscribe, Favorite, and Comment Below!

Follow us on:

Official Website: https://MES.fm
Steemit: https://steemit.com/@mes
Gab: https://gab.ai/matheasysolutions
Minds: https://minds.com/matheasysolutions
Twitter: https://twitter.com/MathEasySolns
Facebook: https://fb.com/MathEasySolutions
LinkedIn: https://mes.fm/linkedin
Pinterest: https://pinterest.com/MathEasySolns
Instagram: https://instagram.com/MathEasySolutions
Email me: [email protected]

Try our Free Calculators: https://mes.fm/calculators

BMI Calculator: https://bmicalculator.mes.fm
Grade Calculator: https://gradecalculator.mes.fm
Mortgage Calculator: https://mortgagecalculator.mes.fm
Percentage Calculator: https://percentagecalculator.mes.fm

Try our Free Online Tools: https://mes.fm/tools

iPhone and Android Apps: https://mes.fm/mobile-apps

In this video I go over a short introduction on improper integrals and present 2 examples on the two types of improper integrals: Type 1: The interval is infinite. Type 2: There is an infinite discontinuity.

One of the most important applications of improper integrals is probability distribution, which will be discussed in later videos so stay tuned for those!

Download the notes in my video: http://1drv.ms/1CNJjfY

View Video Notes on Steemit: https://steemit.com/mathematics/@mes/improper-integrals-introduction

Related Videos:

The Definite Integral - Brief Introduction: http://youtu.be/vhMP5SKbQjU
Integrals and Areas Between Curves: http://youtu.be/2F03KMLIzbk .

------------------------------------------------------

SUBSCRIBE via EMAIL: https://mes.fm/subscribe

DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate

Like, Subscribe, Favorite, and Comment Below!

Follow us on:

Official Website: https://MES.fm
Steemit: https://steemit.com/@mes
Gab: https://gab.ai/matheasysolutions
Minds: https://minds.com/matheasysolutions
Twitter: https://twitter.com/MathEasySolns
Facebook: https://fb.com/MathEasySolutions
LinkedIn: https://mes.fm/linkedin
Pinterest: https://pinterest.com/MathEasySolns
Instagram: https://instagram.com/MathEasySolutions
Email me: [email protected]

Try our Free Calculators: https://mes.fm/calculators

BMI Calculator: https://bmicalculator.mes.fm
Grade Calculator: https://gradecalculator.mes.fm
Mortgage Calculator: https://mortgagecalculator.mes.fm
Percentage Calculator: https://percentagecalculator.mes.fm

Try our Free Online Tools: https://mes.fm/tools

iPhone and Android Apps: https://mes.fm/mobile-apps

In this video I go over further into improper integrals and this time discuss the type 1, Infinite Intervals, in great detail as well as outlining a definition for it. The first type of improper integrals is when the interval is infinite, such as the integral of a function from x = a to infinity. Even though the interval may be infinite the actual integral may approach a finite number if the limit of the function at positive or negative infinity exists.

Download the notes in my video: http://1drv.ms/1L0BkCr

View Video Notes on Steemit: https://steemit.com/mathematics/@mes/improper-integrals-type-1-infinite-intervals

Related Videos:

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 .

------------------------------------------------------

SUBSCRIBE via EMAIL: https://mes.fm/subscribe

DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate

Like, Subscribe, Favorite, and Comment Below!

Follow us on:

Official Website: https://MES.fm
Steemit: https://steemit.com/@mes
Gab: https://gab.ai/matheasysolutions
Minds: https://minds.com/matheasysolutions
Twitter: https://twitter.com/MathEasySolns
Facebook: https://fb.com/MathEasySolutions
LinkedIn: https://mes.fm/linkedin
Pinterest: https://pinterest.com/MathEasySolns
Instagram: https://instagram.com/MathEasySolutions
Email me: [email protected]

Try our Free Calculators: https://mes.fm/calculators

BMI Calculator: https://bmicalculator.mes.fm
Grade Calculator: https://gradecalculator.mes.fm
Mortgage Calculator: https://mortgagecalculator.mes.fm
Percentage Calculator: https://percentagecalculator.mes.fm

Try our Free Online Tools: https://mes.fm/tools

iPhone and Android Apps: https://mes.fm/mobile-apps

In this video I go over another example on improper integrals and this time solve the integral of the function 1/(1+x^2) from x approaches negative infinity to x approaches positive infinity. This integral can be simplified into two parts by integrating it from negative infinity until a number, chosen as zero in this example for convenience, and then from that number to positive infinity. This integral is very interesting as it converges at both positive and negative infinity resulting in the integral, and thus the area under the curve, to be equal to the number π.

Download the notes in my video: http://1drv.ms/1L6Ld1l

View Video Notes on Steemit: https://steemit.com/mathematics/@mes/improper-integrals-example-3-1-1-x-2

Related Videos:

Derivative of arctan(x) or Inverse tan(x): http://youtu.be/q9jdOiQ7pZY
Inverse Trigonometric Functions: Inverse cosine, sine, and tan Functions: http://youtu.be/Ifv1vkJZdrk
Improper Integrals: Example 2: x*e^x: https://youtu.be/w2FxwExbBac
Improper Integrals: Example 1: Divergent Sum: https://youtu.be/6b_zaerpudo
Improper Integrals: Introduction: https://youtu.be/ud44W-0jC-c
Improper Integrals: Type 1: Infinite Intervals: https://youtu.be/9ZlsCy3wdZU
Infinite Limits - Precise Definition: http://youtu.be/QyVTgSzn7dE
Infinite Limits - Vertical Asymptotes: http://youtu.be/H-5Txa8SOwQ .

------------------------------------------------------

SUBSCRIBE via EMAIL: https://mes.fm/subscribe

DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate

Like, Subscribe, Favorite, and Comment Below!

Follow us on:

Official Website: https://MES.fm
Steemit: https://steemit.com/@mes
Gab: https://gab.ai/matheasysolutions
Minds: https://minds.com/matheasysolutions
Twitter: https://twitter.com/MathEasySolns
Facebook: https://fb.com/MathEasySolutions
LinkedIn: https://mes.fm/linkedin
Pinterest: https://pinterest.com/MathEasySolns
Instagram: https://instagram.com/MathEasySolutions
Email me: [email protected]

Try our Free Calculators: https://mes.fm/calculators

BMI Calculator: https://bmicalculator.mes.fm
Grade Calculator: https://gradecalculator.mes.fm
Mortgage Calculator: https://mortgagecalculator.mes.fm
Percentage Calculator: https://percentagecalculator.mes.fm

Try our Free Online Tools: https://mes.fm/tools

iPhone and Android Apps: https://mes.fm/mobile-apps

In this video I go over another example on improper integrals and this time solve for the values of p in the integral 1/x^p from x = 1 to x approaches infinite, that make this integral convergent. Please note that in the Example 1 of the example video series, see video link below, I have already showed that for the case of p = 1, the integral diverges. In this example I show that the integral converges to 1/(p - 1) for p is greater than 1 but diverges for p is less than 1.

Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhqR3ELrTCNRJXvGfEQ

View Video Notes on Steemit: https://steemit.com/mathematics/@mes/improper-integrals-example-4-1-x-p

Related Videos:

Improper Integrals: Example 3: 1/(1+x^2): https://youtu.be/6KizcIQ6H_E
Improper Integrals: Example 2: x*e^x: https://youtu.be/w2FxwExbBac
Improper Integrals: Example 1: Divergent Sum: https://youtu.be/6b_zaerpudo
Improper Integrals: Introduction: https://youtu.be/ud44W-0jC-c
Improper Integrals: Type 1: Infinite Intervals: https://youtu.be/9ZlsCy3wdZU
Infinite Limits - Precise Definition: http://youtu.be/QyVTgSzn7dE
Infinite Limits - Vertical Asymptotes: http://youtu.be/H-5Txa8SOwQ
Derivative of y = x^n - Part 2: General Power Rule: http://youtu.be/Ibvu33oh49o .

------------------------------------------------------

SUBSCRIBE via EMAIL: https://mes.fm/subscribe

DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate

Like, Subscribe, Favorite, and Comment Below!

Follow us on:

Official Website: https://MES.fm
Steemit: https://steemit.com/@mes
Gab: https://gab.ai/matheasysolutions
Minds: https://minds.com/matheasysolutions
Twitter: https://twitter.com/MathEasySolns
Facebook: https://fb.com/MathEasySolutions
LinkedIn: https://mes.fm/linkedin
Pinterest: https://pinterest.com/MathEasySolns
Instagram: https://instagram.com/MathEasySolutions
Email me: [email protected]

Try our Free Calculators: https://mes.fm/calculators

BMI Calculator: https://bmicalculator.mes.fm
Grade Calculator: https://gradecalculator.mes.fm
Mortgage Calculator: https://mortgagecalculator.mes.fm
Percentage Calculator: https://percentagecalculator.mes.fm

Try our Free Online Tools: https://mes.fm/tools

iPhone and Android Apps: https://mes.fm/mobile-apps

In this video I go over the Type 2 Improper Integrals, which is the case when there are discontinuities in the integrand (i.e. the function being integrated). Basically, the only difference between the Type 1 and Type 2 improper integrals is that we are dealing with an infinite horizontal region in Type 1, and an infinite vertical region in Type 2. The discontinuities in Type 2 improper integrals arise from a vertical asymptote and like the Type 1 case, we can define the improper integral as a limit of a definite integral. If this definite integral converges to a number, then the integral is convergent otherwise it is said to be divergent and the limit does not exist.

Download the notes in my video: http://1drv.ms/1p7Duq1

View Video Notes on Steemit: https://steemit.com/mathematics/@mes/improper-integrals-type-2-discontinuous-integrands

Related Videos:

Improper Integrals: Type 1: Infinite Intervals: https://youtu.be/9ZlsCy3wdZU

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 .

------------------------------------------------------

SUBSCRIBE via EMAIL: https://mes.fm/subscribe

DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate

Like, Subscribe, Favorite, and Comment Below!

Follow us on:

Official Website: https://MES.fm
Steemit: https://steemit.com/@mes
Gab: https://gab.ai/matheasysolutions
Minds: https://minds.com/matheasysolutions
Twitter: https://twitter.com/MathEasySolns
Facebook: https://fb.com/MathEasySolutions
LinkedIn: https://mes.fm/linkedin
Pinterest: https://pinterest.com/MathEasySolns
Instagram: https://instagram.com/MathEasySolutions
Email me: [email protected]

Try our Free Calculators: https://mes.fm/calculators

BMI Calculator: https://bmicalculator.mes.fm
Grade Calculator: https://gradecalculator.mes.fm
Mortgage Calculator: https://mortgagecalculator.mes.fm
Percentage Calculator: https://percentagecalculator.mes.fm

Try our Free Online Tools: https://mes.fm/tools

iPhone and Android Apps: https://mes.fm/mobile-apps

In this video I go over another example on improper integrals and this time solve the integral of the function 1/sqrt(x-2) from x =2 to x = 5. This integral is a Type 2 improper integral because the integrand has an infinite discontinuity or vertical asymptote at x = 2. But when we write this integral as a limit of a definite integral, the limit ends up converging to the value 2*sqrt(3) and thus represents the area under the curve.

Download the notes in my video: http://1drv.ms/1QwqPpw

View Video Notes on Steemit: https://steemit.com/mathematics/@mes/improper-integrals-example-5-1-sqrt-x-2

Related Videos:

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 .

------------------------------------------------------

SUBSCRIBE via EMAIL: https://mes.fm/subscribe

DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate

Like, Subscribe, Favorite, and Comment Below!

Follow us on:

Official Website: https://MES.fm
Steemit: https://steemit.com/@mes
Gab: https://gab.ai/matheasysolutions
Minds: https://minds.com/matheasysolutions
Twitter: https://twitter.com/MathEasySolns
Facebook: https://fb.com/MathEasySolutions
LinkedIn: https://mes.fm/linkedin
Pinterest: https://pinterest.com/MathEasySolns
Instagram: https://instagram.com/MathEasySolutions
Email me: [email protected]

Try our Free Calculators: https://mes.fm/calculators

BMI Calculator: https://bmicalculator.mes.fm
Grade Calculator: https://gradecalculator.mes.fm
Mortgage Calculator: https://mortgagecalculator.mes.fm
Percentage Calculator: https://percentagecalculator.mes.fm

Try our Free Online Tools: https://mes.fm/tools

iPhone and Android Apps: https://mes.fm/mobile-apps

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

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 .

------------------------------------------------------

SUBSCRIBE via EMAIL: https://mes.fm/subscribe

DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate

Like, Subscribe, Favorite, and Comment Below!

Follow us on:

Official Website: https://MES.fm
Steemit: https://steemit.com/@mes
Gab: https://gab.ai/matheasysolutions
Minds: https://minds.com/matheasysolutions
Twitter: https://twitter.com/MathEasySolns
Facebook: https://fb.com/MathEasySolutions
LinkedIn: https://mes.fm/linkedin
Pinterest: https://pinterest.com/MathEasySolns
Instagram: https://instagram.com/MathEasySolutions
Email me: [email protected]

Try our Free Calculators: https://mes.fm/calculators

BMI Calculator: https://bmicalculator.mes.fm
Grade Calculator: https://gradecalculator.mes.fm
Mortgage Calculator: https://mortgagecalculator.mes.fm
Percentage Calculator: https://percentagecalculator.mes.fm

Try our Free Online Tools: https://mes.fm/tools

iPhone and Android Apps: https://mes.fm/mobile-apps

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 .

------------------------------------------------------

SUBSCRIBE via EMAIL: https://mes.fm/subscribe

DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate

Like, Subscribe, Favorite, and Comment Below!

Follow us on:

Official Website: https://MES.fm
Steemit: https://steemit.com/@mes
Gab: https://gab.ai/matheasysolutions
Minds: https://minds.com/matheasysolutions
Twitter: https://twitter.com/MathEasySolns
Facebook: https://fb.com/MathEasySolutions
LinkedIn: https://mes.fm/linkedin
Pinterest: https://pinterest.com/MathEasySolns
Instagram: https://instagram.com/MathEasySolutions
Email me: [email protected]

Try our Free Calculators: https://mes.fm/calculators

BMI Calculator: https://bmicalculator.mes.fm
Grade Calculator: https://gradecalculator.mes.fm
Mortgage Calculator: https://mortgagecalculator.mes.fm
Percentage Calculator: https://percentagecalculator.mes.fm

Try our Free Online Tools: https://mes.fm/tools

iPhone and Android Apps: https://mes.fm/mobile-apps

In this video I go over another example on improper integrals and this time evaluate the integral of the function 1/(x - 1) from x = 0 to x = 3. This is a very important example because it illustrates the need to always check the function being integrated to see if it is continuous or discontinuous in the interval being integrated. In this particular example there is a vertical asymptote at x = 1 so we must treat this as an improper integral of type 2 and evaluate it accordingly. In this example, I show how this integral diverges to negative infinite so the integral does not exist as a definite number. If I had not noticed that vertical asymptote and instead solved it like a regular integral the answer would have yielded the number ln(2) which is wrong! So make sure to always check if you are dealing with a proper or improper integral before you start evaluating the integral.

Download the notes in my video: http://1drv.ms/1U2vvqF

View Video Notes on Steemit: https://steemit.com/mathematics/@mes/improper-integrals-example-7-important-example

Related Videos:

Improper Integrals: Example 6: sec(x): https://youtu.be/yHnv2w9OVWk
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
Integration by Parts: Example 2: ln(x): http://youtu.be/wVjra6DCZzE .

------------------------------------------------------

SUBSCRIBE via EMAIL: https://mes.fm/subscribe

DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate

Like, Subscribe, Favorite, and Comment Below!

Follow us on:

Official Website: https://MES.fm
Steemit: https://steemit.com/@mes
Gab: https://gab.ai/matheasysolutions
Minds: https://minds.com/matheasysolutions
Twitter: https://twitter.com/MathEasySolns
Facebook: https://fb.com/MathEasySolutions
LinkedIn: https://mes.fm/linkedin
Pinterest: https://pinterest.com/MathEasySolns
Instagram: https://instagram.com/MathEasySolutions
Email me: [email protected]

Try our Free Calculators: https://mes.fm/calculators

BMI Calculator: https://bmicalculator.mes.fm
Grade Calculator: https://gradecalculator.mes.fm
Mortgage Calculator: https://mortgagecalculator.mes.fm
Percentage Calculator: https://percentagecalculator.mes.fm

Try our Free Online Tools: https://mes.fm/tools

iPhone and Android Apps: https://mes.fm/mobile-apps

SHOW MORE

Created 1 year, 10 months ago.

411 videos

CategoryEducation

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