Difference between revisions of "Differential equation"
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* Functions usually represent [[Physical quantity|physical quantities]] | * Functions usually represent [[Physical quantity|physical quantities]] | ||
| − | * [[ | + | * [[Derivatives]] represent their [[Rate of change|rates of change]] |
* The equation defines a [[Relationship (mathematics)|relationship]] between the two | * The equation defines a [[Relationship (mathematics)|relationship]] between the two | ||
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Such relations are common; differential equations play a prominent role in many disciplines, including: | Such relations are common; differential equations play a prominent role in many disciplines, including: | ||
| − | * Engineering | + | * [[Engineering]] |
| − | * Physics | + | * [[Physics]] |
* Economics | * Economics | ||
* Biology | * Biology | ||
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== See also == | == See also == | ||
| + | * [[Complex differential equation]] | ||
| + | * [[Control theory]] | ||
* [[Derivative]] | * [[Derivative]] | ||
| + | * [[Engineering]] | ||
| + | * [[Equations of motion]] | ||
| + | * [[Exact differential equation]] | ||
| + | * [[Finite difference method]] | ||
* [[Function (mathematics)]] | * [[Function (mathematics)]] | ||
| + | * [[Initial condition]] | ||
| + | * [[Integral equation]] | ||
* [[Mathematical model]] | * [[Mathematical model]] | ||
* [[Mathematics]] | * [[Mathematics]] | ||
* [[Numerical analysis]] | * [[Numerical analysis]] | ||
| + | * [[Picard–Lindelöf theorem]] on existence and uniqueness of solutions | ||
| + | Recurrence relation, also known as 'Difference Equation'* [[Physics]] | ||
* [[Strange attractor]] | * [[Strange attractor]] | ||
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* [https://en.wikipedia.org/wiki/Differential_equation Differential equation] @ Wikipedia | * [https://en.wikipedia.org/wiki/Differential_equation Differential equation] @ Wikipedia | ||
| + | |||
| + | [[Category:Functions]] | ||
| + | [[Category:Mathematics]] | ||
Latest revision as of 19:52, 24 August 2016
A differential equation is a mathematical equation that relates some function with its derivatives.
Contents
Applications
In applications:
- Functions usually represent physical quantities
- Derivatives represent their rates of change
- The equation defines a relationship between the two
Disciplines
Such relations are common; differential equations play a prominent role in many disciplines, including:
- Engineering
- Physics
- Economics
- Biology
Pure mathematics
In pure mathematics, differential equations are studied from several different perspectives, mostly concerned with their solutions -- the set of functions that satisfy the equation.
Only the simplest differential equations are solvable by explicit formulas; however, some properties of solutions of a given differential equation may be determined without finding their exact form.
Approximation using computers
If a self-contained formula for the solution is not available, the solution may be numerically approximated using computers.
The theory of dynamical systems puts emphasis on qualitative analysis of systems described by differential equations
Numerical analysis can yield solutions with a given degree of accuracy.
See also
- Complex differential equation
- Control theory
- Derivative
- Engineering
- Equations of motion
- Exact differential equation
- Finite difference method
- Function (mathematics)
- Initial condition
- Integral equation
- Mathematical model
- Mathematics
- Numerical analysis
- Picard–Lindelöf theorem on existence and uniqueness of solutions
Recurrence relation, also known as 'Difference Equation'* Physics
External links
- Differential equation @ Wikipedia
