Calculus

Isaac Newton was one of the key players in the development of calculus. His main motivation was to use it in finding mathematical laws relating to forces and motion, especially relating to the celestial bodies (planets, the moon, etc). ¹² The physics he developed distinguished between the changing states of the world and the unchanging laws that govern them 13 , and the laws he developed described how the two relate to eachother. Today calculus is used in countless areas -anywhere that finding the rate of change of something given it's value as a function (derivative) or finding the total amount of something given it's rate of change at any instant (integrals).

Examples:

• The time derivative (time rate of change) of velocity is acceleration.
• The time derivative (time rate of change) of the position is velocity.
• The derivative of a function modeling a population size tells you how fast the population is changing at any point.
• The time integral of acceleration is velocity.
• The time integral of the velocity is position.
• The integral of the flow rate of water, e.g., through a pipe, as a function of time is the total amount of water that passes through the pipe.
• The integral of a birth rate function tells you how many individuals are born in a certain time period.