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PrudensOptimus
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What is the true use of Differential Equations?
Originally posted by PrudensOptimus
What is the true use of Differential Equations?
Originally posted by StarThrower
This question is very vague. The origin of differential equations, was to explain the motion of bodies. If you know the initial conditions, then you also know the future. This was the central idea behind the pioneering work. But to say that predicting the future is the true use of differential equations, is misleading. The true use of differential equations, is this:
Universities can sell knowledge to people, and so make a whole lot of money. That is the true 'use' of differential equations. :)
The main purpose of using differential equations in scientific research is to model and describe how a system changes over time. This allows scientists to make predictions and understand the behavior of complex systems in various fields such as physics, engineering, biology, and economics.
Yes, differential equations can be used to solve a wide range of real-world problems, such as predicting the spread of diseases, understanding population dynamics, and designing efficient electrical circuits. They are also used in many engineering applications, such as designing aircrafts and buildings.
In order for a differential equation to have a unique solution, the initial conditions must be specified. These conditions provide information about the system at a particular point in time, and with this information, the solution can be determined using mathematical methods.
Ordinary differential equations (ODEs) involve a single independent variable, while partial differential equations (PDEs) involve multiple independent variables. ODEs describe the behavior of a system over time, while PDEs describe the behavior of a system in space and time.
Differential equations are used extensively in physics to model and describe the behavior of physical systems. They are used to describe the motion of objects, the flow of fluids, and the behavior of electric and magnetic fields. They are also used in quantum mechanics to study the behavior of subatomic particles.