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WHAT IS CALCULUS

Most individuals shy away when the term ' calculus ' is called into question. Nevertheless, it's not just for rocket scientists. Truth to be told is the subject matter is always enclosed by mathematics and whether you know it or not, you use calculus every day. Later on in this article, you will learn about what is meant by the term calculus and its applications. You can as well seek for calculus help today by getting in touch with us for prompt assistance.

Definition and History

Calculus is all about change. It is a branch of math that focuses on various variables and looks at how they change into infinitely small pieces. These small pieces are known as infinitesimals. The subject matter takes us back to the 17th century, where two European scientists trail blazed the study.

The British scientist, Sir Isaac Newton, and German scientist Gottfried Leibnitz independently developed and initiated the ideology of the principles of calculus. Amid the great controversy and antagonism in history between the two great minds of science, the laws focus on the study of sequence areas under curves and series.

It is also the first field in the calculation of velocity, which comprises of the speed and direction of movement. These ideologies touch on the diverse topics in mathematics such as symbolic math, geometry traditions to mention a few.

The term, 'calculus' has a simplistic origin from Latin, which means small pebble. In ancient times, people used to perform counting and calculation activities using the small stones and hence equated it to the terminology.

Calculus was adopted by illustrating the use of stone beads which were applied in keeping track of the grain reserves and livestock. Thus, the subject matter was a model of the system used by people in ancient time to do the arithmetic calculations. The principles by the founding fathers of calculus formulated a sense of understanding to the continuously changing of quantities.

Some of these alterations in the variables can be related to the articulation of gravity and the velocity concept. Hence to clearly understand these different variables, the principles of calculus are explained into two halves. They include differential calculus and integral calculus.

Principles of calculus

Differential Calculus

This is one side of the coin concerned with the function of a derivative. This subfield focuses on articulating the continuously changing variables and how it is applied in real-life situation.

The principle involves an explicit series of random numbers. These series of numbers is derived from the difference of numbers, which gives rise to the terminology, 'differential.' As stated earlier, differential calculus is the mathematical study of the properties, definitions, and applications of a function's derivative.

The process of finding the derivative function is known as differentiation. The derivative of a function, usually a linear operator, takes the function as its input and at the same time produces a second function which takes up as the output and the same time creates a second function.

The particular principle of calculus focuses on examining individual infinitely small pieces and what happens to them. A function's derivative is usually a slope of the tangent line on a graph of a function of a certain point.

Sir Isaac Newton's principle on differential calculus has played a unique role in explaining and illustrating specific contents in physics such as the derivative of the displacement of a movable body basing on the concept of velocity.

Integral Calculus

This is the second half of the principles. Based on Gottfried Leibnitz ideologies, integral calculus deals with the theories and applications of integral. The subfield of mathematics is majorly concerned with the total size and values of objects like the volume, length, area to mention a few.

Mathematically, an integral assigns values to functions based on the way they can describe or illustrate the displacement, volume, area, and other notions that emerge by combining the infinitely small pieces of data. Also denoted as anti-differentiation, it portrays basic concepts to find volume and area.

It is also fundamental in finding areas of various geometric shapes, definite integral which is utilized in calculating the area under a curve, the indefinite integral and diverse practical applications. The subfield is also imperative in articulating the most important theorem that is known as the fundamental theorems of calculus.

The fundamental theorem of calculus asserts that integration and differentiation are inverse operations. The theory generally relates the value of indefinite anti-derivatives to definite integrals.

Due to this, the fundamental theorem of calculus offers a practical way of computing the definite integrals. With this, it provides a method, algebraic of computing the diverse definite integrals by getting the formulas of differentiation.

Significance of the study

The subject matter takes up the central role by providing the foundation to other disciplines like engineering, physics, to mention a few. It makes use of substantial mathematical functions to describe and predict physical phenomena which are subject to continuous change.

Calculus is also a necessity in the study of the motion of particles and gases, the transfer of energy and interaction of forces. Chemistry, astronomy, economics, and statistics are also vital areas that rely on this field.

Medical and pharmacy schools use the subject's concepts as a screening tool to filter out the weaker functionaries on the assumption that people who are unwilling to handle the rigors of calculus and have little chance of surviving the hard work of studying medicine or pharmacology.

Business calculus is also used in the calculation of contents interest to mention a few. Physics makes particular use of calculus. Almost all concepts are attributed through calculus in classical mechanics and electromagnetism.

Using calculus can help find the mass of an object of known density, the moment of object inertia, as well as the total energy of an object within a conservative field. The subject matter has mostly influenced the development of new areas of mathematics like Non-Euclidean geometry, real and complex, to name a few with the existence of essential tools that aid in articulating the various functions.

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