Calculus is a part of mathematics that studies the continuous change mathematically, the way geometry is the study of shapes, and algebra for studying the generalizations of arithmetic operations. Within its study, there are two branches, differential and integral.
Differential deals with the instantaneous rate of change a slope of the curve. Whereas, Integral deals with the accumulation of quantities and the areas between curves. If you notice carefully, you will find that these two branches of this are related to one another. You can see this relation in the fundamental theorem, that links the concepts of differentiation and integration. The two branches use the fundamental notion of convergence of infinite series as well as infinite sequences into a well-defined limit. While in today’s time, calculus is widespread, and people use it in various fields such as science, engineering, and economics. In mathematics alone, it is denoting the course of elementary mathematical analysis, focused mainly on functions and limits.
You can see that the earlier calculus idea was taken from China, Greece, India, Japan, Persia, and Iraq. However, Europe saw the use of calculus in the 17th century due to the works of Sir Isaac Newton and Gottfried Wilhelm Leibniz, to introduce the basic principles of mathematics. One can observe the development of this subject upon earlier concepts of instantaneous motions and area underneath curves. Differentiation was applied to compute velocity, acceleration, the slope of the curve and optimization. Integration was applied to compute, areas, the center of mass, volume, arc length, work, and pressure.
For centuries mathematicians have struggled with paradoxes that involve division by zero or sum of infinitely many numbers, these questions that arise in the study of motion and area. It provides tools, especially the limit and infinite series that help to resolve many of the existing paradoxes.
It has evolved through the ages, from ancient to modern and has many formulas that fulfill its purposes of answering the many unsolved questions of the ages.
Why is Calculus Important?
For this, we need to give a close look at the beginning of the Industrial Revolution. The time when it was starting to become famous and widespread. With Newton’s De Quadrature Curvarum published in 1676 and Methodus Fluxionum, the first steam engine was in 1698 and later Watt’s improved the steam engine in 1736. All because of Newtons work, and a better understanding of physics that could not have been established if not for the study of calculus.
With a better understanding of physics, today we can engineer the finest of technologies to a better life. It is the foundation of any approach of optimization, of equilibrium states and all dynamical states helping evolve engineering, be it civil, mechanical, electrical, electronic, nautical, or even aeronautical. It is also important for Quantum theory without which we would not have lasers or computers.
Calculus has been an important part of our lives since the 17th century, without which we would not have been this technically advanced. It has a huge application base. Its restriction is not only to mathematics but can be in exploration physics, chemistry, biology, engineering, and many more. With the help of it, the higher maths, we can analyze and measure life mathematically. For example, a person can use it to determine the amount of material used to build in an architectural structure. It can also be in-use in electrical engineering to determine the length of the cable and its exact power requirement.
A person can use this to determine the exact growth rate of bacteria in the field of medical science. This determination of growth rate helps us discover and cure diseases. If you’re a business person then it can help you survey data and evaluate the results. This survey and evaluation helps you to come to an exact development plan for growth and success. Surprisingly credit card companies can apply this to set minimum payment due on card statements. They can do this at the exact time by considering the varying variables. Varying variables such as fluctuating interest rates or available balance in the account.
Most professions deal with this to answer major questions and solve the issues at hand. While all may not directly deal it, it is still an important branch of mathematics. The branch that allows the growth of technology and the development of society with its understanding of physics and its aspects. It is the best way to understand optimization and apply it in real life to solve the daily problem we deal in our lives. Without it, there is no optimization which minimizes out chances of evolving at a fast and steady pace.
By studying calculus, we can introduce the basic concepts of maths, which are in-use to study almost every and any type of changing phenomena within the controlled setting. Also, by studying it, we develop an invaluable sense of science and practical engineering problem-solving skills.