A **differential equation** is a mathematical equation that relates some function with its derivatives. In applications, the functions usually represent physical quantities, the derivatives represent their rates of change, and the equation defines a relationship between the two. Because such relations are extremely common, differential equations play a prominent role in many disciplines including engineering, physics, economics, and biology. From Wikipedia contributors. "Differential equation." *Wikipedia, The Free Encyclopedia*. Web. 17 Feb. 2015.

**Applied mathematics** is a branch of mathematics that deals with mathematical methods that find use in science, engineering, business, computer science, and industry. Thus, "applied mathematics" is a mathematical science with specialized knowledge. The term "applied mathematics" also describes the professional specialty in which mathematicians work on practical problems by formulating and studying mathematical models. From Wikipedia contributors. "Applied mathematics." *Wikipedia, The Free Encyclopedia*. Wed. 19 Feb. 2015.

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