Many fundamental laws of physics and chemistry can be formulated as differential equations.
In biology and economics, differential equations are used to model the behavior of
complex systems. The mathematical theory of differential equations first developed together
with the sciences where the equations had originated and where the results found
application. However, diverse problems, sometimes originating in quite distinct scientific
fields, may give rise to identical differential equations. Whenever this happens, mathematical
theory behind the equations can be viewed as a unifying principle behind diverse
phenomena. As an example, consider propagation of light and sound in the atmosphere,
and of waves on the surface of a pond. All of them may be described by the same secondorder
partial differential equation, the wave equation, which allows us to think of light
and sound as forms of waves, much like familiar waves in the water.
- معلم: fatima mostefai