What is the difference between mathematical models and math equations that describe physical phenomena ?

Question

Are mathematical models describing physical phenomena, the same thing as mathematical equations describing physical phenomena. Are the terms model and equation just different names for the same thing or do they describe different things.

Answer 1

More or less the same thing. A model is a series of equations that describes the behavior of a physical object in response to real world forces.

I believe that the term "model" is used because the equations used are assumed to be a simplification that only includes effects that are assumed to be significant.

Sometimes trivial forces are not so trivial after all, and a bridge collapses because the equation was not precise enough.

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A mathematical model is an abstract model that uses mathematical language to describe the behavior of a system. Mathematical models are used particularly in the natural sciences and engineering disciplines (such as physics, biology, and electrical engineering) but also in the social sciences (such as economics, sociology and political science); physicists, engineers, computer scientists, and economists use mathematical models most extensively.

Eykhoff (1974) defined a mathematical model as 'a representation of the essential aspects of an existing system (or a system to be constructed) which presents knowledge of that system in usable form'....

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Sorry, I didn't pay close attention to what you said. A "model" is usually more than one equation, because usually more than one physical phenomena is acting on the object (car, building, electrical circuit) that you are trying to analyze. So a "model" is usually more just an equation describing a single physical phenomena, I believe.

Answer 2

They're close to being the same thing. You could pretty much call any equation that describes a phenomenon a "model" and a scientist would understand you.

However, a single, simple math equation that describes phenomena, such as F = ma, is more commonly called a "law." In fact, when modeling a phenomenon with a single equation it's more common for a scientist to say "such-and-such obeys a power law" rather than "such-and-such is modelled by a power function."

Usually the word "model" is reserved for the process of deriving characteristics of a complex phenomenon with a set of equations. Moreover, while "laws" tend to be algebraic equations, models tend to be differential. For instance, when attepting to describe the interior of the Sun, astronomers write down the four equations of stellar structure: the equation of state, the equation of hydrostatic equilibrium, the equation of mass continuity, and the equation of radiation transfer. These are complex differential equations, that when solved, provide the density, pressure, chemistry, and temperature of the star as functions of radius. Definitely a model and not a law

Answer 3

Touch Me I'm Sick - Mudhoney Oh! The song "Big Little Baby" by The Reverend Horton Heat is about a gangly girl!

Answer 4

http://www.math.vt.edu/reDescriptions.php