DIFFERENTIATION AND ITS APPLICATION
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In Isaac Newton's day, one of the biggest problems was poor navigation at sea. Before calculus was developed, the stars were vital for navigation.
Shipwrecks occurred because the ship was not where the captain thought it should be. There was not a good enough understanding of how the Earth, stars and planets moved with respect to each other.Calculus (differentiation and integration) was developed to improve this understanding.
We use the derivative to determine the maximum and minimum values of particular functions (e.g. cost, strength, amount of material used in a building, profit, loss, etc.).
- Derivatives are met in many engineering and science problems, especially when modeling the behavior of moving objects.
- It is used ECONOMIC a lot, calculus is also a base of economics. In economics, calculus is used to compute marginal cost and marginal revenue, enabling economists to predict maximum profit in a specific setting.
- The Petronas Towers in Kuala Lumpur experience high forces due to winds.Integration was used to design the building for strength.
There are tons of applications, what differentiation and integration do is compute rates of change and areas/volumes under a curve respectively. This is found everywhere in the natural sciences and engineering. Many of these problems nowadays can be solved by discrete approximations using computers, but the algorithms are still built using the theory of differentiation and integration.
I guess I'll go over some common problems and how differentiation and integration help.
Differentiation and integration can be used to build (and solve) differential equations. The two sort of big divisions in differential equations are ordinary and partial differential equations.
Ordinary differential equations are typically studied in the form of dynamical systems, applications include population dynamics, modelling of epidemics, neural networks, robotics, and cognitive science (links for this)