How Isaac Newton Changed the World with the Invention of Calculus
Isaac Newton changed the world when he invented Calculus in 1665. We take this for granted today, but what Newton accomplished at the age of 24 is simply astonishing.
Calculus has uses in physics, chemistry, biology, economics, pure mathematics, all branches of engineering, and more. Its not an overstatement to say Newton's insight in the development of calculus has truly revolutionized our ability to pursue new branches of science and engineering. It is used in problems when a quantity changes as a function of time, which is how most problems behave in reality.
When he invented calculus and outlined its uses, Isaac Newton made one of the most important breakthroughs in mathematics history, and it's still vital to this day.
What Is Calculus?
At its most basic, calculus is all about studying the rate of change of a quantity over time. In particular, it can be narrowed down to the study of the rate of change and summation of quantities. The two categories of calculus are called differential calculus and integral calculus. Differential calculus deals with the rate of change of a quantity such as how the position of an object changes compared to time. Integral calculus is all about accumulation, or summing up infinitely small quantities. The fundamental theorem of calculus is what connects these two categories. This theorem guarantees the existence of antiderivatives for continuous functions. You can learn more about the differential and integral calculus by reading the information below. We'll then look into how this affects curves.
When looking into differential calculus and trying to understand it, it's important to compare it to algebra. Algebra is all about working out the slope of a straight line between two points. But with calculus, it's all about the slope of a curve, which means the slope at one point will be different than the slope at another point further along the same curved function. By looking closely at the slope of the line between the two points on the curve, the rate at which the slope changes can be calculated. This is called finding the derivative of a function at a point.
Integral calculus is often used when the area of a region under a graph needs to be calculated. If a simple square or rectangular area needs to be calculated, this can be done easily using algebra. But when the area has one sloping line, that's not possible, and integral calculus has to be used instead. Integral calculus helps us break up a smooth line into lots of very small straight rectangles. We can then work out the area under the original function because the line is no longer curved once you zoom in further and further and break down the line into many rectangles. When each rectangle is infinitesimally small, an accurate area beneath the curved line can be found.
In other words, calculus is used when algebra can't be used. It's based on the idea that sloped lines can be handled mathematically by approximating them as very small line segments, then allowing these segments to become infinitely small. This is used in many ways in the real world, so it's not all about abstract ideas that are only taught in lecture rooms. Later on, we'll look at some of the industries that rely on calculus and the precise ways in which it can be used. You might be surprised by how varied and common its usage is.
How & Why Isaac Newton Invented Calculus
First of all, you'll need to know who Isaac Newton was and why he was and remains so important. He was a physicist, mathematician and cosmologist who was prominent in the 17th century. He's probably best-known for formulating the laws of motion and universal gravitation. His influence can't be overstated. One of his many achievements was the invention of calculus. His own work in physics undoubtedly brought him to this issue, and he felt a need to solve it with a new mathematical framework that simply hadn't existed up to that point in time. His focus on gravity and laws of motion are linked to his breakthrough in calculus.
Newton started by trying to describe the speed of a falling object. When he did this, he found that the speed of a falling object increases every second, but that there was no existing mathematical explanation for this. The issue of movement and the rate of change had not yet been explored to any significant degree in the field of mathematics, so Newton saw a void that needed to be filled. He began work on this right way, incorporating planetary ellipses into his theory too to try to explain the orbit of the planets. He found that by using calculus, he could explain how planets moved and why the orbits of planets are in an ellipse. This is one of Newton's break throughs: that the gravitational force that holds us to the ground is the same force that causes the planets to orbit the Sun and the Moon to orbit Earth.
All this shows that when Newton came to develop the idea of calculus and its focus on the rate of change, it fed into his previous work. He was aided by his already strong conceptual understanding of physics and movement. It wasn't a complete departure from his other work. And this perhaps demonstrates best of all the direct link between the field of mathematics and the field of physics. For Newton at least, the two went hand in hand. Newton used rates of changes to form the foundation of Calculus, and his revised theory was published in 1676.
Gottfried Wilhelm Leibniz is another mathematician who did a lot of work on using numbers to help describe nature and motion. There was a dispute between the two men over who actually came up with calculus first and who the true inventor was. Although Leibniz did come up with vital symbols that help with the understanding of mathematical concepts, Newton's work was carried out about eight years before Leibniz's. Both men contributed a great deal to mathematics in general and calculus in particular. And since then, the concept has been developed even further.
What Is Calculus Used For?
Calculus is used in all branches of math, science, engineering, biology, and more. There is a lot that goes into the use of calculus, and there are entire industries that rely on it very heavily. For example, any sector that plots graphs and analyzes them for trends and changes will probably use calculus in one way or another. There are certain formulae in particular that demand the use of calculus when plotting graphs. And if a graph's dimensions have to be accurately estimated, calculus will be used. It's sometimes necessary to predict how a graph's line might look in the future using various calculations, and this demands the use of calculus too.
Engineering is one sector that uses calculus extensively. Mathematical models often have to be created to help with various forms of engineering planning. And the same applies to the medical industry. Anything that deals with motion, such as vehicle development, acoustics, light and electricity will also use calculus a great deal because it is incredibly useful when analyzing any quantity that changes over time. So, it's quite clear that there are many industries and activities that need calculus to function in the right way. It might be close to 350 years since the idea was invented and developed, but its importance and vitality has not diminished since it was invented.
There are also other advanced physics concepts that have relied on the use of calculus to make further breakthroughs. In many cases, one theory and discovery can act as the starting point for others that come after it. For example, Albert Einstein wouldn't have been able to derive his famous and groundbreaking theory of relativity if it wasn't for calculus. Relativity is all about how space and time change with respect to one another, and as a result calculus is central to the theory.
In addition, calculus is often used when data is being collected and analyzed. The social sciences, therefore, must rely on calculus very heavily. For example, calculating things like trends in rates of birth and rates of death wouldn't be possible without the use of calculus. And economic forecasts and predictions certainly use calculus a great deal. The economy would function in a very different way if we didn't have calculus and other important mathematical concepts and inventions to use to explain and predict physical observations.
There is no end to the influence that Isaac Newton and his invention of calculus have had on the world.