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Partial differential equations (PDEs) describe the relationships among the derivatives of an unknown function with respect to different independent variables, such as time and position. For example, the heat equation can be used to describe the change in heat distribution along a metal rod over time. PDEs arise as part of the mathematical modeling of problems connected to different branches of science, such as physics, biology, and chemistry. In these fields, experiment and observation provide information about the connections between rates of change of an important quantity, such as heat, with respect to different variables. These connections must be exploited to find an explicit way of calculating the unknown quantity, given the values of the independent variables that is, to derive certain laws of nature. While we do not know why partial differential equations provide what has been termed the “unreasonable effectiveness of mathematics in the natural sciences” (the title of a 1960 paper by physicist… Details:
http://www.saylor.org/courses/ma222/
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