What is Calculus?
It is difficult to put calculus into words. Calculus is a vast topic, and it forms the basis for much of modern mathematics. The two branches of calculus are differential calculus and integral calculus. Differential calculus is the study of rates of change of functions. This requires finding the tangent to a curve, which requires limits. You are normally introduced to differential calculus by learning how to find the derivative of a function in order to determine the slope of the graph of that function at any point. The differentiate command allows you to find the derivative of an expression with respect to any variable, although "x" and "y" are normally used.. You also have the option of specifying arbitrary functions within your expression and finding higher order derivatives. The differentiate command requires you to know all the rules of differential calculus including the chain rule, product rule and the quotient rule.
Integral calculus, also known as integration, is like doing a derivative in reverse. It is often introduced in school in terms of finding indefinite integrals and finding the area under a curve (definite integrals). The integrate command can be used to find either indefinite or definite integrals.
The applications of math, physics and other sciences normally oversimplifies the real world. For example, projectiles are often calculated using a constant speed, which ignores external forces such as wind, gravity and friction. Calculus goes beyond elementary math by using the limit process. The limit process allows us to analyze how small variations in one quantity affect another quantity. The limit process also allows us to find the sum of very small quantities.
Most high school students don’t see a lot of uses for calculus, except for being a math teacher. Unfortunately, high school students don’t realize that calculus is a requirement for most science and business degrees in university, and there is a reason for that. Many aspects of science, especially physics and engineering, require calculus calculations. Calculus is required for professions in astronomy, biology, chemistry, computer, earth sciences, engineering, physics, geology and business.