Slate Slate Slate is a fine-grained, foliated, homogeneous metamorphic rock derived from an original shale-type sedimentary rock composed of clay or volcanic ash through low-grade regional metamorphism. It is the finest grained foliated metamorphic rock. Foliation may not correspond to the original sedimentary layering, but instead is in planes perpendicular to the direction of metamorphic compression. The foliation in slate is called "slaty cleavage". It is caused by strong compression causing fine grained clay flakes to regrow in planes perpendicular to the compression. When expertly "cut" by striking parallel to the foliation, with a specialized tool in the quarry, many slates
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