Editing Mathematical model (section)

==Significance in the natural sciences==

Mathematical models are of great importance in the natural sciences, particularly in [[physics]]. Physical [[theory|theories]] are almost invariably expressed using mathematical models. Throughout history, more and more accurate mathematical models have been developed. [[Newton's laws of motion|Newton's laws]] accurately describe many everyday phenomena, but at certain limits [[theory of relativity]] and [[quantum mechanics]] must be used.

It is common to use idealized models in physics to simplify things. Massless ropes, point particles, [[ideal gases]] and the [[particle in a box]] are among the many simplified models used in physics. The laws of physics are represented with simple equations such as Newton's laws, [[Maxwell's equations]] and the [[Schrödinger equation]]. These laws are a basis for making mathematical models of real situations. Many real situations are very complex and thus modeled approximately on a computer, a model that is computationally feasible to compute is made from the basic laws or from approximate models made from the basic laws. For example, molecules can be modeled by [[molecular orbital]] models that are approximate solutions to the Schrödinger equation. In [[engineering]], physics models are often made by mathematical methods such as [[finite element analysis]].

Different mathematical models use different geometries that are not necessarily accurate descriptions of the geometry of the universe. [[Euclidean geometry]] is much used in classical physics, while [[special relativity]] and [[general relativity]] are examples of theories that use [[geometry|geometries]] which are not Euclidean.