Differential equation

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In mathematics, a differential equation is an equation in which the derivatives of a function appear as variables. Differential equations have many applications in physics and chemistry, and are widespread in mathematical models explaining biological, social, and economic phenomena.

Differential equations are divided into two types:

The order of a differential equation is that of the highest derivative that it contains. For instance, a first-order differential equation contains only first derivatives.

A stochastic differential equation (SDE) is a differential equation in which one or more of the terms is a stochastic process, thus resulting in a solution which is itself a stochastic process.

The study of differential equations is a wide field in both pure and applied mathematics. Pure mathematicians study the types and properties of differential equations, such as whether or not solutions exist, and should they exist, whether they are unique. Applied mathematicians, physicists and engineers are usually more interested in how to compute solutions to differential equations. These solutions are then used to simulate celestial motions, design bridges, automobiles, aircraft, sewers, etc. Often, these equations do not have closed form solutions and are solved using numerical methods.

Famous differential equations include:

References

Major fields of mathematics Edit
Logic | Set theory | Combinatorics | Probability | Mathematical statistics | Number theory | Optimization | Linear algebra | Abstract algebra | Category theory | Algebraic geometry | Geometry | Topology | Algebraic topology | Analysis | Differential equations | Functional analysis | Numerical analysis

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