Calculus is a discipline in mathematics that describes changes. Over the century, mathematicians have pored over examples from the real world and derived tools and theorems to help us solve and understand the volatility in application. Algebra alone is insufficient to represent problems in a mathematical and is often inadequate to represent the change processes in real world applications. This calls for calculus, the branch in mathematics many high school students are familiar with, albeit baffling many students in their exposure.
It is widely applied onto many areas of studies that are dynamical, that is to say, calculus is practically everywhere. Some examples are economics, science, and engineering.
Calculus is divided into two major branches, namely differential calculus and integral calculus. Differential calculus concerns itself with the process changes, quantifying the changes and applying an end result of the change in a system with an expression of the system. Integral calculus, on the other hand, concerns itself with the process, quantifying the process and deriving the very process from a given change. Simply put, differential calculus is the reverse process of integral calculus and vice versa.
The fundamental concept of calculus is the observance of change in a function, an expression. The very first development of calculus is by manipulating very small quantities. They are then put together for an aggregate effect. Limits, the very spirit of calculus, captures the small-scaled behavior of functions. It is done by assigning a variable to the change in a function, then expressing the function in such variable. It is then used to measure the change by inputting values that zoom up the function, enabling an observable value.
The most important concept of differential calculus is differentiation. An expression differentiated will result in another expression that expresses the change in its predecessor. That is called the derivative of a function. If the function is linear, the derivation is said to be the ratio of the rise versus the run. An approximation of a curved function is derived by the fraction of the change in the y-axis and the change in the x-axis. Differential calculus enables a person to compute the maximum and the minimum of a function, and to understand the slope, or gradient, of a function. These applications are used mostly widely in optimisation in processes and setting margins for standards.
Integral calculus is further divided into 2 areas, namely indefinite and definite integral. Indefinite integral expressions input with a change to derive the original function. Definite integral expressions input with a function and a region bound by numbers to give another number. This can be graphically understood as the number lines on the x-axis, the x-axis itself and the function curve. That will mean the area under the curve, and is called the Riemann sum. With the function revolving, we can get the volume of a solid that revolves around the x-axis. Many examples can be found in engineering, such as finding the volume of a bottle with the revolution of a function, or simply integrating a time function from the velocity profile to find the distance travelled.
In a nutshell, calculus is embedded into our very lives and we can definitely find calculus in our everyday lives.
Reference
Weinsstein, Eric W, 2009, Calculus [Online]. Available from: http://mathworld.wolfram.com/Calculus.html [Accessed on 6th September 2009]
Keisler, H. J. (2000). “Elementary Calculus: An Approach Using Infinitesimals” [Online] Available from: http://www.math.wisc.edu/~keisler/keislercalc1.pdf [Accessed on 6th September 2009]
