NOTATION. Letters near the beginning of the alphabet denote constants which may in general be positive or negative, whole or fractional, real quantities or numbers. Those near the end of the alphabet denote variables. The symbol stands for "denotes" or "is identical with." The symbols >,, <, stand for greater than, not greater than, less than, not less than, respectively. The symbols f(), F( ), ( ), 4( ), denote any function of the quantity placed inside the brackets, except when restricted by the context, X, E, X, x are briefer symbols for functions of x. Χ L, M, N, P, Q, R also sometimes denote functions of the variable. Y any function of the variable y which is independent of x. f(a) the same function of a that f(x) is of the variable x. д a=partial differentiation with respect to x. f(x,y)=the differential coefficient with respect to x of the function f(x,y) where x and y are independent variables. " " yx ƒ_(x,y)=f (x,y)=the second differential coefficient of f(x,y) with respect to x and y, where x and y are independent variables. NOTATION. Σ or ()=Sum of a series of terms of the same type as that following Σ or placed within the brackets. [ f(x)dx=f* f(x)dx =the_limiting_value towards which [ƒ(x)dx approaches as dz ap proaches the limiting value 0. n!=1×2×3----(n − 1) x n; (n being a positive integer). log10=log x in the Decimal or Common system of logarithms. log.x=log x in the Natural or Neperian e=2.7182818 1 1 1 =1+ + 21+31 = base of Neperian logarithms 2! 3! B1, B2----(Bernoulli's Numbers).* In trigonometric functions the angles are given in "circular measure," the unit being the radian which nearly. T'(x)= ["e ̄*2”-1da (the Gamma Function). See X. 1-6. |