Application of Calculus to the major/future career - Essay Example

Altogether, these calculus fundamentals which necessarily include applications of algebra, trigonometry, and analytic geometry are tools of advantage for students like me in the field of science and medical studies. With the right foundation of calculus with analytical geometry during the undergraduate stage, I would be confident to pursue higher levels of math required for my majors in biology and chemistry especially those involving multiple systems that deal with determination of various unknowns.

During elementary level of math education, one merely learns that divisibility by zero is not in any way valid or possible and becomes content at treating such case as closed without entertaining its logic any further. In Calculus, however, though the concept widely recognizes that functions do have domains and ranges within which they remain defined, the subject goes beyond such point as extending concern to limits of a function. By using the principle behind the asymptotes for instance whenever a function is rational, logarithmic, or exponential, Calculus enables a student to strive to grasp and appreciate the idea regarding how a function may come really close or approach a value at least even if it is never meant to cross its exact location.

I suppose that scientists would not have discovered azeotropes and their essence in distillation without acquiring knowledge on asymptotes firsthand since azeotropic setups indicate the feasibility or the extent to which separation of components may proceed. As a concrete instance, in ethanol-water mixture, it is found that the pinch of azeotrope is at approximately 87% of ethanol which means that this is the percent purity of ethanol which may be yielded at due to close boiling points of the two substances so even if infinite steps are taken, the highest achievable or the limit in this binary case is still that percentage, unless a third component is incorporated to break the asymptotic or limiting azeotrope.

A function, according to Calculus, is said to be continuous in an interval [a, b] if it is continuous and defined at any point within this same interval. If this initial condition is not satisfied, then the non-continuity implies that the function is also non-differentiable within [a, b]. Equivalently, the two-sided limits are stated in theorems that guide the study of whether a function’s limit does exist or not as x approaches a certain value and this requires tests to be conducted prior to conclusion.

These accounts are essential in discerning the significance of derivative which by pertains to an instantaneous rate of change or the slope of a tangent line to a curve at a point. While the concept of finding derivative is useful in applications that relate displacement, velocity, and acceleration, the reverse process of getting the antiderivative proves to be of crucial advantage in determining an area under the curve or a volume of a solid generated by revolving a strip of an element in a bounded region about a specific axis or line of revolution.

Since functions come in different types and complexities, Calculus thereby promotes a variety of ways or techniques by which integration may be carried out yet where no method seems adequate in evaluating a definite integral, numerical means of approximations are employed as a more flexible alternative. Partial derivatives and integration are of