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  1. Partial Differential Equations - Dave Rusin; The Mathematical Atlas
    A short article designed to provide an introduction to partial differential equations. Like ordinary differential equations, partial differential equations are equations to be solved in which the unknown element is a function, but in PDEs the function is one of several variables, and so of course the known information relates the function and its partial derivatives with respect to the several variables. Again, one generally looks for qualitative statements about the solution. For example, in many cases, solutions exist only if some of the parameters lie in a specific set (say, the set of integers). Various broad families of PDE's admit general statements about the behavior of their solutions. This area has a long-standing close relationship with the physical sciences, especially physics, thermodynamics, and quantum mechanics: for many of the topics in the field, the origins of the problem and the qualitative nature of the solutions are best understood by describing the corresponding result in physics. History; applications and related fields and subfields; textbooks, reference works, and tutorials; software and tables; other web sites with this focus.