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Calculus

Calculus is a branch of mathematics involving the measurement of change. It is used to look at trends and predict the future based on the trends. Calculus is not only relevant to mathematics, but it also has applications in other fields like physics, economics, chemistry, engineering, astronomy, medicine and sociology.

We use calculus almost every day in our lives. When we are looking at a trend line like the movement of the stock market, or the population growth curve, or the usage of water from a dam, we are using calculus to analyse the performance over time, or over a small interval of time to make a future prediction.

Since the trend line keeps changing over time, calculus is dynamic in nature.

There are two main branches of calculus:

  • Differentiation
  • Integration

 

Differentiation

This involves calculation of the rate at which two variables change in relation to each other. For example, speed is measured by a change in distance over a change in time period. 

In a linear function or co-ordinate geometry, we find the relationship between the change in 'y' direction with a change in 'x' direction variables. This ratio is defined as the slope or gradient of the function. Differential calculus involves finding the gradient of a curve or a function.

 

Integration or integral calculus

Integration is the opposite of differentiation – it gives us the area bounded by the curve between the region under consideration. In other words, we examine the original function by looking at the given rate of change, and the integration of a function is the summation of all the small changes in a region.

In addition, we will look at the volume of solids revolving about their x or y axis using the area bounded by their curves.