### Quick description

Applied mathematics is about creating and studying models of the world. The tools used to do this frequently involve differential equations (especially for the physical sciences), although there are many useful discrete models (especially in economics and social behavior).

Modeling is basic to this activity. This requires a combination of mathematical expertise and knowledge of the area being modeled. Part of this subject is outside of the domain of the Tricki, but a number of useful tips about how to create models will be given.

Mathematical aspects that contribute to modeling efforts can include existence of solutions, uniqueness of solutions, continuous (or otherwise) dependence of solutions on the data of the problem, approximation of one model by others (for example, using perturbation analysis). Numerical methods are often crucial in using mathematical models because the information that we desire from the model (e.g., predictions) are not usually directly calculable from the model itself.

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