Slate industry in Spain Slate industry in Spain 90% of Europes's natural slate used for roofing originates from the slate industry in Spain, with the region of Galicia being the primary source of production. Slate is a fine-grained metamorphic rock that splits into thin, smooth-surfaced layers. Metamorphic rock is rock which was once igneous or sedimentary and has been subsequently subjected to heat and pressure in varying degrees thereby altering its composition, structure and appearance. It is used extensively in the building industry, particularly for roofing tiles. The production of slate is estimated at 4 million tons per year. Galicia is situated on the
Change of variables (PDE) can thus be visualized as rotation on torii. As a particular example, consider the simple harmonic oscillator, with formula_70 and formula_71, with Hamiltonian formula_72. This system can be rewritten as formula_73, formula_74, where formula_75 and formula_76 are the canonical polar coordinates: formula_77 and formula_78. See V. I. Arnold, `Mathematical Methods of Classical Mechanics', for more details. Change of variables (PDE) Often a partial differential equation can be reduced to a simpler form with a known solution by a suitable change of variables. The article discusses change of variable for PDEs below in two ways: For example, the following simplified form