The first study of any portion of mathematics should not be done from a synopsis of compact results, such as this collection. The references, although they are far from complete, will be helpful, it is hoped, in showing where the derivation of the results is given or where further similar results may be found. A list of numbered references is given at the end of the book. These are referred to in the text as "Ref. 7, p. 32," etc., the page number being that of the publication to which reference is made. Letters are considered to represent real quantities unless otherwise stated. Where the square root of a quantity is indicated, the positive value is to be taken, unless otherwise indicated. Two vertical lines enclosing a quantity represent the absolute or numerical value of that quantity, that is, the modulus of the quantity. The absolute value is a positive quantity. Thus, log | - 3| = log 3. The constant of integration is to be understood after each integral. The integrals may usually be checked by differentiating. In algebraic expressions, the symbol log represents natural or Napierian logarithms, that is, logarithms to the base e. When any other base is intended, it will be indicated in the usual manner. When an integral contains the logarithm of a certain quantity, integration should not be carried from a negative to a positive value of that quantity. If the quantity is negative, the logarithm of the absolute value of the quantity may be used, since log (— 1) = (2k + 1)хг will be part of the constant of integration (see 409.03). Accordingly, in many cases, the logarithm of an absolute value is shown, in giving an integral, so as to indicate that it applies to real values, both positive and negative. Inverse trigonometric functions are to be understood as referring to the principal values. Suggestions and criticisms as to the material of this book and as to errors that may be in it, will be welcomed. v