Friday, December 1, 2017

Some considerations in the study of Calculus

Calculus has been invented a few hundred years ago by Sir Isaac Newton and Leibniz Gottfried to study the motion of planets and moons. After the work of these pioneers, several mathematicians have widened the field of Calculus by developing concepts and methods. The applications of Calculus have been extended to the study of phenomena in the physical, biological and social sciences.

Calculus is based on a few simple ideas and these have allowed the development of applications in different fields. The study of Calculus is based on a multi-representational approach to the concepts, methods, and applications represented numerically. analytically and graphically. The interesting element in the study of Calculus is that its core ideas are closed related. For example, the study of limits, derivatives, and integrals form a whole.

Calculus is the study of change and this is best modeled by the study of the behavior of functions. Functions have been studied in Pre-calculus, Different combinations of functions such as addition, multiplication, division and composition have been studied. Other properties of functions have been explored. The study of Calculus is more concerned about the behavior of functions closed to certain points. For example, the study of the different values of a function as the dependent variable comes closer and closer to a certain value leads to the notion of limits. The study of the slope of a tangent line to the graph of a function leads to the notion of derivative. The study of the area between curves leads to the study of integrals.

The study of limits helps in the understanding of the derivatives and integrals. The limit of the slope of a secant line to a curve allows to find the slope of a tangent line to this curve. The slope of the tangent line is the derivative of the function. The limit of the sum of the rectangles of the area between two curves leads to a better approximation of the area between these curves. This leads to the notion of integrals.

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