# Download PDF by Gordon Lindsay; Christ for the Nations (Dallas, Tex.): Demon manifestations and delusions By Gordon Lindsay; Christ for the Nations (Dallas, Tex.)

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In Ames  we meet the equation Aa2Y/” = “ 2 ( Y / y F. RELATIONS BETWEEN + 1. 52) DEPENDENT VARIABLES Insight into the solution character of some partial differential equations may be obtained by assuming an unspecified relation between the dependent variables. The resulting simplification can be striking. 53) + Dy = 0. 54) v = F(u) for general F(u). 55) 16 1 The Origin of Nonlinear Equations that is, an ordinary differential equation in y , with parameter x. Selecting F = mu"'-', m > 1 we find that Eq.

With his methods ratios of the rate constants and not the constants themselves are computable. 28) where reactant A, has an effective constant concentration C because it is in excess, goes into solution as the reaction progresses and therefore C moles per unit volume are always present. 29f) where xi is the concentration of A, in moles per unit volume and k, are the rate constants in liters per gram mole second. 2 Homogeneous Equations 31 These redundancies are also obtainable from the equations.

Mech. , Univ. of Delaware, Newark, Delaware, October 1962. 53. , Proc. Nut. Acad. Sci. 43, 222 (1957). 54. Hottel, H. , and Sarofim, A. , “Radiative Transport,” McGraw-Hill, New York, 1965. 55. Crandall, S. , “Engineering Analysis,” McGraw-Hill, New York, 1956. 2 EXACT METHODS OF SOLUTION Introduction By exact methods we shall mean any procedure which enables the solution to be obtained by one or more quadratures of a function of one variable only. Thus we include any methods leading toy = J f ( x )dx or x = J g ( y )dy where x and y are independent and dependent variables, respectively.