The Basic Concepts of Calculus and Isaac Newton's Concept

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Sir Isaac Newton (1642-1727), a British scientist, invented the most important field of mathematics, Calculus. But there is a controversy about it. Some people believe that Gottfried Leibniz invented Calculus. However, Both Newton and Leibniz started to work on calculus around the same period.

A branch of mathematics that is used to determine the changes between values that are related by a particular function is known as calculus. The name ‘Calculus’ came from the Latin word ‘pebble’ which means ‘stone.’ Stone was used by Roman for counting. Mathematicians started to use the same term to count infinitely small numbers. The analysis of the relationship between mathematical quantities and physical is considered as an essential theme in calculus. We can describe this type of relationship in terms of formulas, numerical data, words, or graphs. Calculus will provide a way to analyze and view the physical world. It involves many equations and formulas.

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The process of finding the rate of change of a particular variable concerning another variable is known as differential calculus. We can apply it to determine the speed of a moving particle, the slope of a curve, the maximum and minimum point of the curve, etc. The process which is used to calculate the area underneath a graph of a particular function is known as Integration. For instance, if you see the speed of a walking person at different points concerning the time and if you draw the graph of the rate, then you will find the total distance of that person under the chart.

If a particular object is in motion (for instance, rocket), we can use the formulas of calculus to model it. Into space, the thrust of the rocket is mainly based on the calculus of motion. Scientist applies Newton’s second and third law to a rocket having variable mass. The mass of a rocket decreases over time when fuel burns off. The rocket experiences a very high rate of acceleration when the rocket fuel ignites. In the opposite direction, the backward acceleration will exert a push force. It will help the rocket to accelerate upward. The acting force on the rocket is called thrust.

From Newton’s third law, we know, ‘Every action has an equal and opposite reaction.’ So, if a particular material ejects backward (for instance, exhaust in a rocket launch), the rocket’s forward momentum should increase. The reason is an isolated system is not able to change its momentum. After launching, the rocket should be as small as possible. Otherwise, it will fail to achieve the desired final orbital velocity. So, calculus can be applied in the aerospace.

If you want to know the progression of the tumor of a patient, you can apply the concept of calculus here. You can model the growth of the patient’s tumor using calculus to analyze the progression of the disease. You need to create an exponential function to shape the progress of the growth of the tumor. Consider the service as V(t). By differentiating the function, we get the first derivative V'(t), which will show how much the tumor volume changes over time. This is known as the specific growth rate (SGR). So, the first derivative will provide you information about whether the patient’s tumor is shirking or growing. You can also get the rate at which it’s growing. If the SGR is high, we can say that the tumor is overgrowing.

Integration is commonly used by architecture engineers to determine the number of necessary materials. If you want to determine the exact length of power cable needs to join two different substations, Integration can also be used. When space flight engineers plans for long missions, they use the concept of calculus. Calculus is also essential for infrastructure, such as the bridge.

We can apply calculus in any scenario of change or motion. It can be aerospace, engineering, biology, economics, or medical science. The benefits of calculus cannot be described in words. If you find any kind of problem in any dynamic situation which involves motion or change, you can quickly solve all of your questions by using calculus.

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