What is the general definition of Calculus, and how do you explain it in general?

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durbanville | High School Teacher | (Level 2) Educator Emeritus

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Calculus is difficult to define as it is a broad branch of Maths with various purposes or uses. However, if your question is being asked so you can understand calculus a little better and then apply it yourself, the easiest way to explain it is as a rate of change.

Presumably you understand how graphs work - a straight line graph that has a gradient or slope changes according to the degree of the slope. It is precise and can be computed. 

A parabola  and other CURVES have an average gradient because finding the slope between two points cannot be exactly determined. Calculus is a method that can be used in order to calculate a more accurate answer based on the portion of the curve where the slope is required. This is differential calculus and is most widely taught in schools and colleges.

As calculus relates to a rate of change, it is not restricted to graphs themselves. Calculus is also used when finding or comparing surface area and volume and is widely used for questions involving speed and time changes.

Imagine a car travelling some distance which suddenly needs to stop. Calculus can be used in calculating the distance between the first application of the brake and the actual stopping of the car.   

Intergral calculus is used for higher learning in maths and is concerned with the area under the curve - again not easy to calculate precisely.