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If ? > 0, the curve is a hyperbola, ? = 0 the curve is an parabola, and ? < 0 the equation is a ellipse. The analogy of the classification of PDEs is obvious. There is no other significance to the terminology and thus the terms hyperbolic, parabolic, and elliptic are simply three convenient names to classify PDEs.

Definitions. A partial differential equation is an equation containing an unknown function of two or more variables and its partial derivatives with respect to these variables.

Most chemical reactions can be classified into one or more of five basic types: acid?base reactions, exchange reactions, condensation reactions (and the reverse, cleavage reactions), and oxidation?reduction reactions. The general forms of these five kinds of reactions are summarized in Table 7.10.

Classifying Chemical Reactions Synthesis reactions. Two or more reactants combine to make 1 new product. ... Decomposition reactions. A single reactant breaks down to form 2 or more products. ... Single-replacement reactions. A single element replaces a similar element of an adjacent reactant compound. ... Double-replacement reactions.

I Physical state of reactants and products. ii Conditions such as temperature pressure heat etc. iii Catalyst involved. iv Change in the state.

Ordinary differential equations or (ODE) are equations where the derivatives are taken with respect to only one variable. That is, there is only one independent variable. Partial differential equations or (PDE) are equations that depend on partial derivatives of several variables.

The pde is hyperbolic (or parabolic or elliptic) on a region D if the pde is hyperbolic (or parabolic or elliptic) at each point of D. A second order linear pde can be reduced to so-called canonical form by an appropriate change of variables ? = ?(x, y), ? = ?(x, y). = ?x?y ? ?x?y.