It is probable that almost every teacher of advanced calculus feels the
need of a text suited to present conditions and adaptable to his use. To
write such a book is extremely difficult, for the attainments of students
who enter a second course in calculus are different, their needs are not
uniform, and the viewpoint of their teachers is no less varied. Yet in
view of the cost of time and money involved in producing an Advanced
Calculus, in proportion to the small number of students who will use it,
it seems that few teachers can afford the luxury of having their own
text; and that it consequently devolves upon an author to take as un-
unselfish and unprejudiced a view of the subject as possible, and, so far as
in him lies, to produce a book which shall have the maximum flexibility
and adaptability. It was the recognition of this duty that has kept the
present work in a perpetual state of growth and modification during
five or six years of composition. Every attempt has been made to write
in such a manner that the individual teacher may feel the minimum
embarrassment in picking and choosing what seems to him best to meet
the needs of any particular class.