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This textbook is a self-contained introduction to partial differential equations. It is designed for undergraduate and first year graduate students who are mathematics, physics, engineering or, in general, science majors. The goal is to give an introduction to the basic equations of mathematical physics and the properties of their solutions, based on classical calculus and ordinary differential equations. Advanced concepts such as weak solutions and discontinuous solutions of nonlinear conservation laws are also considered. The material is illustrated with model examples. Mathematics software products such as Mathematica and Maple in ScientificWorkPlace are used in both graphical and computational aspects.