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This book presents recent and very elementary developments§of a theory of multiplication of distributions in the field§of explicit and numerical solutions of systems of PDEs of§physics (nonlinear elasticity, elastoplasticity,§hydrodynamics, multifluid flows, acoustics). The§prerequisites are kept to introductory calculus level so§that the book remains accessible at the same time to pure§mathematicians (as a smoothand somewhat heuristic§introdcution to this theory) and to applied mathematicians,§numerical engineers and theoretical physicists (as a tool to§treat problems involving products of distributions).