In mathematics, a differential equation is an equation in which the derivative or differential of one variable or quantity, say y, with respect to a second variable, say x, appears as well as the variables themselves, x and y. [1]
Quotes
The following are notable quotes:
“First causes are not known to us, but they are subjected to simple and constant laws that can be studied by observation and whose study is the goal of natural philosophy … Heat penetrates, as does gravity, all the substances of the universe; its rays occupy all regions of space. The aim of our work is to expose the mathematical laws that this element follows … The differential equations for the propagation of heat express the most general conditions and reduce physical questions to problems in pure analysis that is properly the object of the theory.”
— James Maxwell (date), Publication [2]
“Differential equations form the basis for the scientific view of the world.”
— Vladimir Arnold (date), Publication [2]
“The solution to this paradox is that an organism inherits rules that spell out the progression. The rules are, or are like, time-based differential equations which have the ability to encode complex sequences with high efficiency. Thus on hast to regard development as an integration through space and time, the genome providing the equivalent of the differential equations.”
— Paul Green (c.1990) (Ѻ) [3]
See also
● Complete differential
● Exact differential
● History of differential equations
● Partial differential equation
● Total differential
References
1. Daintith, John. (2005). Oxford Dictionary of Science. Oxford University Press.
2. Myint-U, TYn, and Debnath, Lokkenath. (2007). Linear Partial Differential Equations for Scientists and Engineers (pdf) (pg. vii). Springer, 2011.
3. Harrison, Lionel G. (2011). The Shaping of Life: the Generation of Biological Pattern (pg. 11). Cambridge University Press.
External links
● Differential equation – Wikipedia.
