I know this may be a scarry topic and even frighting to some. Also, being that Halloween is this coming weekend this was a perfect topic. *que evil laugh ....
So what is this thing called Calculus? How is this Calculus study the rate of change? Well the following is from thoughtco.com that may bring us some light on this subject:
"By Deb Russell
Updated January 21, 2020
Calculus is a branch of mathematics that involves the study of rates of change. Before calculus was invented, all math was static: It could only help calculate objects that were perfectly still. But the universe is constantly moving and changing. No objects—from the stars in space to subatomic particles or cells in the body—are always at rest. Indeed, just about everything in the universe is constantly moving. Calculus helped to determine how particles, stars, and matter actually move and change in real time.
Calculus is used in a multitude of fields that you wouldn't ordinarily think would make use of its concepts. Among them are physics, engineering, economics, statistics, and medicine. Calculus is also used in such disparate areas as space travel, as well as determining how medications interact with the body, and even how to build safer structures. You'll understand why calculus is useful in so many areas if you know a bit about its history as well as what it is designed to do and measure.
Key Takeaways: Fundamental Theorem of the Calculus
Calculus is the study of rates of change.
Gottfried Leibniz and Isaac Newton, 17th-century mathematicians, both invented calculus independently. Newton invented it first, but Leibniz created the notations that mathematicians use today.
There are two types of calculus: Differential calculus determines the rate of change of a quantity, while integral calculus finds the quantity where the rate of change is known.
Who Invented Calculus?
Calculus was developed in the latter half of the 17th century by two mathematicians, Gottfried Leibniz and Isaac Newton. Newton first developed calculus and applied it directly to the understanding of physical systems. Independently, Leibniz developed the notations used in calculus. Put simply, while basic math uses operations such as plus, minus, times, and division (+, -, x, and ÷), calculus uses operations that employ functions and integrals to calculate rates of change.
Those tools allowed Newton, Leibniz, and other mathematicians who followed to calculate things like the exact slope of a curve at any point. The Story of Mathematics explains the importance of Newton's fundamental theorem of the calculus:
"Unlike the static geometry of the Greeks, calculus allowed mathematicians and engineers to make sense of the motion and dynamic change in the changing world around us, such as the orbits of planets, the motion of fluids, etc."
Using calculus, scientists, astronomers, physicists, mathematicians, and chemists could now chart the orbit of the planets and stars, as well as the path of electrons and protons at the atomic level.
Differential vs. Integral Calculus
There are two branches of calculus: differential and integral calculus. "Differential calculus studies the derivative and integral calculus studies...the integral," notes the Massachusetts Institute of Technology. But there is more to it than that. Differential calculus determines the rate of change of a quantity. It examines the rates of change of slopes and curves.
This branch is concerned with the study of the rate of change of functions with respect to their variables, especially through the use of derivatives and differentials. The derivative is the slope of a line on a graph. You find the slope of a line by calculating the rise over the run.
Integral calculus, by contrast, seeks to find the quantity where the rate of change is known. This branch focuses on such concepts as slopes of tangent lines and velocities. While differential calculus focuses on the curve itself, integral calculus concerns itself with the space or area under the curve. Integral calculus is used to figure the total size or value, such as lengths, areas, and volumes.
Calculus played an integral role in the development of navigation in the 17th and 18th centuries because it allowed sailors to use the position of the moon to accurately determine the local time. To chart their position at sea, navigators needed to be able to measure both time and angles with accuracy. Before the development of calculus, ship navigators and captains could do neither.
Calculus — both derivative and integral — helped to improve the understanding of this important concept in terms of the curve of the Earth, the distance ships had to travel around a curve to get to a specific location, and even the alignment of the Earth, seas, and ships in relation to the stars.
Practical Applications
Calculus has many practical applications in real life. Some of the concepts that use calculus include motion, electricity, heat, light, harmonics, acoustics, and astronomy. Calculus is used in geography, computer vision (such as for autonomous driving of cars), photography, artificial intelligence, robotics, video games, and even movies. Calculus is also used to calculate the rates of radioactive decay in chemistry, and even to predict birth and death rates, as well as in the study of gravity and planetary motion, fluid flow, ship design, geometric curves, and bridge engineering.
In physics, for example, calculus is used to help define, explain, and calculate motion, electricity, heat, light, harmonics, acoustics, astronomy, and dynamics. Einstein's theory of relativity relies on calculus, a field of mathematics that also helps economists predict how much profit a company or industry can make. And in shipbuilding, calculus has been used for many years to determine both the curve of the hull of the ship (using differential calculus), as well as the area under the hull (using integral calculus), and even in the general design of ships.
In addition, calculus is used to check answers for different mathematical disciplines such as statistics, analytical geometry, and algebra.
Calculus in Economics
Economists use calculus to predict supply, demand, and maximum potential profits. Supply and demand are, after all, essentially charted on a curve—and an ever-changing curve at that.
Economists use calculus to determine the price elasticity of demand. They refer to the ever-changing supply-and-demand curve as "elastic," and the actions of the curve as "elasticity." To calculate an exact measure of elasticity at a particular point on a supply or demand curve, you need to think about infinitesimally small changes in price and, as a result, incorporate mathematical derivatives into your elasticity formulas. Calculus allows you to determine specific points on that ever-changing supply-and-demand curve.
Source
"Calculus Summary." Massachusetts Institute of Technology, January 10, 2000, Cambridge, MA."
So now you know a bit about Calculus and why it is important to know and why. Thou even myself I am a bit rusty from the last time I used this in College, but I know the basics and the above article shows we should understand the basics about the world around us. Do we need to calculate the change of a rolling rock down the hill? Most likely not unless it is heading towards you and your mind will do the calculation really fast while you get out of the way. :) I included a few Math funny images to make you smile as well.
Reference: https://www.thoughtco.com/definition-of-calculus-2311607
I have lost a lot of faith with the Medical Community and the Governments over the last several years, but there are a few good things that can raise above the corruption and the pushing of drugs a new approach to heal people. The following is from www.gaia.com and written by Hunter Parsons that does not involve any drug or pushing an ineffective so called vaccine that the drug company is not held accountable in any way but they use sound! The use of sound can regrow bone tissue! Here is the story:
"The future of regenerative medicine could be found within sound healing by regrowing bone cells with sound waves.
The use of sound as a healing modality has an ancient tradition all over the world. The ancient Greeks used sound to cure mental disorders; Australian Aborigines reportedly use the didgeridoo to heal; and Tibetan or Himalayan singing bowls were, and still are, used for spiritual healing ceremonies.
Recently, a study showed an hour-long sound bowl meditation reduced anger, fatigue, anxiety, and ...
Not a fan of a Defense Agency studying Anti-Gravity and other Exotic Tech, but if the commercial world and make this technology cheap that will change our world yet again. The following is about three minute read and from www.gaia.com. The below was written by Hunter Parsons:
"Wormholes, invisibility cloaks, and anti-gravity — it’s not science fiction, it’s just some of the exotic things the U.S. government has been researching.
A massive document dump by the Defense Intelligence Agency shows some of the wild research projects the United States government was, at least, funding through the Advanced Aerospace Threat Identification Program known as AATIP.
And another lesser-known entity called the Advanced Aerospace Weapons System Application Program or AAWSAP
The Defense Intelligence Agency has recently released a large number of documents to different news outlets and individuals who have filed Freedom of Information Act requests.
Of particular interest are some 1,600 pages released to Vice News, which ...
As our technology gets better we are discovering more about the history of mankind and pushing the timeline back further and further. The following article is from www.gaia.com and written by Michael Chary that discusses this new find that changes the historical timeline:
"Over the past decade, there have been a number of archeological revelations pushing back the timeline of human evolution and our ancient ancestors’ various diasporas. Initially, these discoveries elicit some resistance as archeologists bemoan the daunting prospect of rewriting the history books, though once enough evidence is presented to established institutions, a new chronology becomes accepted.
But this really only pertains to the era of human development that predates civilization — the epochs of our past in which we were merely hunter-gatherers and nomads roaming the savannahs. Try challenging the consensus timeline of human civilization and it’s likely you’ll be met with derision and rigidity.
Conversely, someone of an alternative...
Not sure if you have heard of a show on YouTube called "The Why Files". If not you should check it out it is interesting and has some humor with it on different subjects. Last weeks was on a different theory how the Universe works and how main stream Science is attempting to shut it down like is always seems to do if it goes aguest some special interest. Today it is akin to what happened to those who questioned the Earth was the Center of the Universe that main stream so called Science all believed during the Renaissance period, They called any theory that the Earth was not the Center of the Universe misinformation. Does this sound familiar today? People laughed and mocked people like Leonardo da Vinci, Nicolaus Copernicus, Georg Purbach as crack-pots, conspiracy theorists, nut-jobs and they were suppressed and even imprisoned for their radical thoughts and observations. Again it sounds like today in so many ways. In any event this is a good one to ponder and see even if a bad idea ...
Seemingly chaotic systems like the weather and the financial markets are governed by the laws of chaos theory.
We all have heard about chaos theory, but if you have not or have forgotten what chaos theory is well here you go from interestingengineering.com:
"Chaos theory deals with dynamic systems, which are highly sensitive to initial conditions, making it almost impossible to track the resulting unpredictable behavior. Chaos theory seeks to find patterns in systems that appear random, such as weather, fluid turbulence, and the stock market.
Since the smallest of changes can lead to vastly different outcomes, the long-term behavior of chaotic systems is difficult to predict despite their inherently deterministic nature.
As Edward Lorenz, who first proposed what became commonly known as the Butterfly Effect, eloquently said, "Chaos: When the present determines the future, but the approximate present does not approximately determine the future.""
You may have heard the term about chaos theory as a butterfly flaps its wings in Brazil,...
I for one have lost trust in Medical Doctors due to COVID and reflection that they seem to push pills for everything and untested so called vaccines that is using a unproven technology because the Government and the Medical Boards of the State told them to. There are a very few exceptions. Thus they do not address the key problem just prescribe more and more pills to keep you alive an sick longer for them and Big Phama to profit from you. Will AI do any better? Well that depends on what was used for the training of AI. If it also pushes pills and vaccines without question then you have the same problems noted above. However, if the AI Training includes all possible forms of treatment and they zero in on the right issues for the true problem then there is possibilities they would be way better than most of the current Medical Doctors today.
The following is from an article from interestingengineering.com and written by Paul Ratner:
"A new study looks at how accurately AI can diagnose patients. We interview the researcher, who weighs in on AI's role ...
