What is Calculus?
Calculus is a Latin word meaning, ’small stone’. In ancient times, stones were used by Romans for counting. Gradually mathematicians also started using the same term for counting small numbers. This is understandable as Calculus essentially involves understanding things by looking at small pieces. Calculus is classified into two forms, Differential calculus, and Integral calculus. In simple terms, Differential calculus involves cutting something to observe the changes that it undergoes. Integral calculus, on the other hand, joins small pieces to find out how much there is. The basic concepts of Calculus include derivatives of a function. Mathematically, the Derivative formula is used to find the slope of a curve and the slope of a line. The derivative formula is used to determine how the value of the dependent variable changes concerning the value of an independent variable.
Calculus was developed in the 17th century by an English scientist, Isaac Newton, and German scientist, Gottfried Wilhelm Leibniz. It is widely used to solve diverse practical problems such as predicting the rising pressure behind a dam due to the rising water level or tracking the position of a space shuttle etc. Although calculus is considered difficult computers have made it easier to understand.
Differentiation and Integration
The formula for the slope of a tangent to a curve at any point at it, when the formula for the curve is given was established by Isaac Newton and Leibniz. The Derivative is used to determine the instantaneous rate of change of a function. We can use differentiation to find the rate of change of velocity with respect to time.
Integration is the reverse of Differentiation and is of two types, Definite integration, and indefinite integration. While we use Differentiation to calculate the gradient of a curve, the area under or between the curve is determined with the help of Integration. Both differentiation and integration are parts of a coin called Calculus.
Both integration and differentiation require limits for their determination and satisfy the property of linearity. While the derivative of a function is always unique, this is not true for the integral of a function.
What are the applications of Calculus in everyday life?
- Differential calculus is used to determine the rate of growth of bacterial culture with changes in variables like food source and temperature etc.
- It is used to predict the position of planets in space and to calculate the trajectory of an object.
- Calculus is used by architects to build curved constructions such as a dome and to measure its weight. It is widely used in the construction of bridges too.
- Calculus is also used by electrical engineers to find the length of cable needed to connect two power substations located miles apart from each other.
- The orbiting velocity of earth and different planets is calculated with the help of Calculus.
- Calculus finds use in Graphics too. Artists use it to find out how 3D models will behave under changing conditions and use it to create a realistic effect in movies and video games.
- The rate of a chemical reaction is determined with the help of Differentiation.
- Scientists rely on Calculus to find out the rate of spread of infectious diseases and take necessary action to stop it.
- Calculus is used by Credit card companies to set the minimum payment due on the card, keeping in mind fluctuating interest rates and other factors.
- Research analysts use calculus to compare different variables and take steps to increase productivity and revenue.
Thus, it is evident how Calculus is associated with every sphere of our lives. Several online platforms are available nowadays that can help clarify your doubts and solve all your queries regarding Calculus. Cuemath is one such platform where experienced teachers simplify the concepts of Algebra, geometry, and Trigonometry so that you understand the concepts of Calculus thoroughly. Once you understand the basics, you will enjoy solving the problems associated with the concept.