4-.] 6 



M the Moond eeeh U tn implicit function of the other, while in 

 the third * is an explicit function of y. 



The word . f<>r brevity, usually represented 



by a single 1 -has/, /', $, ^r,.; thus y = <( Z ) nieaos 



i dependent variable j% and is read 

 .ju.iU the 0-iun. ti'.n ..i jc" \ so also s ^(M, 

 mean- tli.it . i> >u of tlio independent variables u* r, 



r, and it is read, -2 equals the JP-f unction of *, r, an<i 

 A function is algebraic if it involves, so far as the inde- 

 pendent \. triable* are concerned, only a finite number of the 

 operations of addition, subtraction, multiplication, division, 

 raising to integer powers, and extracting roots. All other 

 s are transcendental. 



/ , , 2x* - tx - 17, ry + y - 7*. and 



; while 2*, <f 9 ainx, Uu ! x, and log I are tranaoendeuUl fuuo- 



6. Notation. In general, absolute constants are repre- 

 sented by the Arabir ils, while arbitrary constants and 

 variables are represented by letters. A few absolute con- 

 slant* are, however, by general consent, represented by let- 

 ters; examples of such constants are ir and e ( 

 Variables are usually represented by the last letters of the 

 alphabet, such as ti, t% tr, r, y, 2 ; while the first letters, 

 are reserved to represent constants. 



fixed values from among those that a variaMc 

 may assume are sometimes in quest io; the values, 



* = 2 and x = 1, for \vhi-h tin* function a 4 r 2 vanishes; 

 !- Mi.iv . onMMii.-ntly be denoted by affixing a sub- 

 script to tin- Irt tor rep resen ting the variable. Thusr p i^r r 

 will l>e used to denote particular values of the variable x. 



^ :ail.irlv, v.iriahlcs \Nhidi enter a pmlilem in analogous 



