Differential Equation
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A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and its derivatives of various orders. Differential equations play a prominent role in engineering, physics, economics, and other disciplines. Differential equations arise in many areas of science and technology, specifically whenever a deterministic relation involving some continuously varying quantities (modeled by functions) and their rates of change in space and/or time (expressed as derivatives) is known or postulated. This is illustrated in classical mechanics, where the motion of a body is described by its position and velocity as the time value varies. Newton's laws allow one (given the position, velocity, acceleration and various forces acting on the body) to express these variables dynamically as a differential equation for the unknown position of the body as a function of time. In some cases, this differential equation (called an equation of motion) may be solved explicitly. An example of modelling a real world problem using differential equations is the determination of the velocity of a ball falling through the air, considering only gravity and air resistance. The ball's acceleration towards the ground is the acceleration due to gravity minus the deceleration due to air resistance. Gravity is considered constant, and air resistance may be modeled as proportional to the ball's velocity. This means that the ball's acceleration, which is the derivative of its velocity, depends on the velocity. Finding the velocity as a function of time involves solving a differential equation. Differential equations are mathematically studied from several different perspectives, mostly concerned with their solutions —the set of functions that satisfy the equation. Only the simplest differential equations admit solutions given by explicit formulas; however, some properties of solutions of a given differential equation may be determined without finding their exact form. 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, while many numerical methods have been developed to determine solutions with a given degree of accuracy. From Wikipedia under the
GNU Free Documentation License Noundifferential equation (plural differential equations) Examples
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GNU Free Documentation License Matching Results for Differential Equation:Alan TuringMathematical reasoning may be regarded rather schematically as the exercise of a ... Science is a differential equation. Religion is a boundary condition. ... Edward Condon Edward Uhler Condon (March 2, 1902 – March 26, 1974) was a distinguished nuclear ... problem of a differential equation. So if you look for the differential equation which ... June 23 Science is a differential equation. Religion is a boundary condition. ... We thought: we're poor, we have nothing, but when we started losing one after ... From Wikiquote under the
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Science: Physics: This category includes sites about the basic laws of nature, such as the laws of motion, electromagnetism and atomic interactions. Webpages that focus more on mathematics ... Science: Math: Differential Equations See also: Science: Math: Calculus (90) Science: Physics: Mathematical Physics (214) This category in other languages: Russian (9) Spanish (2) Analytic Differential Equations ... Science: Math: Please submit sites that have substantial information about math in general that doesn''t fall into any of the math subcategories listed.
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