What is calculus? Calculus came from Latin, which literally means pebble or small stone used in reckoning. Calculus is all about continuous change and its mathematical way of studying it. It is in the same way the study of shape is geometry and the study of generalizations of arithmetic operations is algebra. Calculus composes of two major branches, and those are differential calculus and integral calculus. Differential calculus is a subfield of calculus concerned with the study of the rates at which quantities change. It is one of the two traditional divisions of calculus, the other being integral calculus. It deals with the concepts of derivative and differential and the manner of using them in the study of functions.
The development of differential calculus is closely connected with that of integral calculus. Indissoluble is also their content. Together they form the base of mathematical analysis, which is extremely important in the natural sciences and in technology. On the other hand, Integral calculus is a another subfield of calculus in which the notion of an integral, its properties and methods of calculation are studied. an integral assigns numbers to functions in a way that can describe displacement, area, volume, and other concepts that arise by combining infinitesimal data. Integration is one of the two main operations of calculus, with its inverse, differentiation, being the other. Integral calculus is intimately related to differential calculus, and together with it constitutes the foundation of mathematical analysis. These two branches are related to each other by the fundamental theorem of calculus. The use of the fundamental notions of convergence of infinite sequences and infinite series to a well-defined limit are present in both branches.Calculus is a part of modern mathematics education. A course in calculus is a gateway to other, more advanced courses in mathematics devoted to the study of functions and limits, broadly called mathematical analysis. Calculus has historically been called the calculus of infinitesimals , or infinitesimal calculus .
The term calculus (plural calculi) is also used for naming specific methods of calculation or notation as well as some theories, such as propositional calculus, Ricci calculus, calculus of variations, lambda calculus, and process calculus.Who invented calculus? Generally, modern calculus is considered to have been developed in the 17th century by Isaac Newton and Gottfried Wilhelm Leibniz. Calculus, known in its early history as infinitesimal calculus, is a mathematical discipline focused on limits, functions, derivatives, integrals, and infinite series. Isaac Newton and Gottfried Leibniz independently discovered calculus in the mid-17th century. However, each inventor claimed the other stole his work in a bitter dispute that continued until the end of their lives.It has been long disputed who should take credit for inventing calculus first, but both independently made discoveries that led to what we know now as calculus.
Newton discovered the inverse relationship between the derivative (slope of a curve) and the integral (the area beneath it), which deemed him as the creator of calculus. Thereafter, calculus was actively used to solve the major scientific dilemmas of the time.For Newton, the applications for calculus were geometrical and related to the physical world – such as describing the orbit of the planets around the sun. For Leibniz, calculus was more about analysis of change in graphs. Leibniz’s work was just as important as Newton’s, and many of his notations are used today, such as the notations for taking the derivative and the integral. They both were instrumental in its creation, they thought of the fundamental concepts in very different ways. While Newton considered variables changing with time, Leibniz thought of the variables x and y as ranging over sequences of infinitely close values. He introduced dx and dy as differences between successive values of these sequences. Leibniz knew that dy/dx gives the tangent but he did not use it as a defining property. On the other hand, Newton used quantities x’ and y’, which were finite velocities, to compute the tangent. Of course neither Leibniz nor Newton thought in terms of functions, but both always thought in terms of graphs. For Newton the calculus was geometrical while Leibniz took it towards analysis.It is interesting to note that Leibniz was very conscious of the importance of good notation and put a lot of thought into the symbols he used. Newton, on the other hand, wrote more for himself than anyone else.
Consequently, he tended to use whatever notation he thought of on that day. This turned out to be important in later developments. Leibniz’s notation was better suited to generalizing calculus to multiple variables and in addition it highlighted the operator aspect of the derivative and integral. As a result, much of the notation that is used in Calculus today is due to Leibniz.With calculus, we can apply the concept of calculus in our everyday lives. For example when going to school, as I go to school by commuting in a jeepney. Along the way, we can see road signs, the best exanple is a speed limit sign. For example, there is a speed limit and it’s eighty kilometers per hour. The vehicles on the road cannot go further 80 km, that is there limit. They can go 79.99999 km per hour, but not 80 km per hour. Another example, I am in a diet. I restricted myself from eating no more than a cup of rice per meal. My limit is only 1 cup, let’s say 1 cup of rice is 150 grams. I can eat 149.99999 grams, but not the limit, which is 150 grams. Lastly, our teacher gave us an assignment and it’s an essay. He/she says the limit is 500 words. So, I can right 499 words, but not 500.Calculus is used in important things, this includes include physics, engineering, economics, statistics, and medicine. It is used to create mathematical models in order to arrive into an optimal solution. Without it, the world will not be the same the way it is today.