Why Should Calculus?

In simplest terms calculus is just an extension of algebra and geometry. It's not necessarily an entirely different subject, it just uses the tools of algebra to tackle new problems involving the rate of change for a curve whereas ordinary high school algebra and geometry do with straight lines and linear slopes. If you were to push a crate up an incline and that incline or straight you exert a constant force to move the crate up the slope since the slope is straight and unchanging. But if that's slope were curved, you have to exert different levels of force at different points along the slope. As you reach deeper points on the curve you have to exert extra force to deal with the extra steepness. Therefore the force which we are measuring is changing depending on where you are.

In this example, the amount of force on a Cartesian plane would represent y, and the distance covered would represent X. At any point, y would be dependent on X though X is constantly changing. They're two branches of calculus, one that measures the rate of change at any given specific point on the plan. And one that takes a specific point on the plane and works backwards to determine the rate of change. The first is known as the derivative second is known as the integral. They're really two sides the same coin. Calculus has many uses in science and engineering and also in business and economics. Very few things in the real world function with constant rates of change. The world is dynamic, chaotic and requires a former mathematics that can deal with its dynamic states. Therefore calculus is one of the most useful areas of knowledge that human beings have. Many people consider algebra and geometry simply to be preparation for calculus. Many students wonder what the applications are for much of what they learn in mathematics. It doesn't seem like the tools they learn in algebra and geometry have much use in the real world. But quite the opposite is true. For students who continue on the calculus, they begin to see how useful those skills are because they can be applied to many areas, and many disciplines ranging from mechanical engineering, to psychology, to medicine, to business.

Preparation for calculus should involve understanding how to work with polynomials, plane geometry and a good understanding of functions. Calculus basically studies functions on a Cartesian plane that are curved and changing. These functions are represented by nonlinear equations and polynomials and learning to manipulate nonlinear equations and polynomials is an important skill. These skills are developed during algebra and geometry and put into real application once calculus is reached to be able to study the real world the way it truly exists -in dynamic, kinetic and sometimes chaotic states rather than simple, clean linear ones.