PREFACE 
VII 
etion was 
> Calculus 
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s or mul- 
lamental 
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ormulas. 
Lagrange’s Multipliers appear in maxima and minima of functions 
of several variables. Fourier’s series and the allied developments 
into series of Bessel’s functions and zonal harmonics are treated from 
the point of view of making the integral of the square of the error 
a minimum. 
In the foregoing I have been describing those aims of the book 
which are not common in the text-books of the present day. To at 
tain these ends, a purely mathematical treatment, availing itself of 
that which is best in the mathematics of today, but at the same time 
adapted to the powers (and the weaknesses) of the Junior or Senior 
in our colleges and schools of technology, must go before ; and, indeed, 
not only the early parts of the various chapters, but by far the 
greater part of the space throughout the whole book is devoted to 
matters of an elementary nature. The book begins with the most 
rudimentary properties of polynomials and fractions, in preparation 
for integration, and the last chapter might well have been entitled : 
“The Story of V— 1.” It may seem exorbitant to spend ten pages 
on the study of integrals involving Va + bx + ex' 2 and yet, a thorough 
going understanding of all that is here involved covers substantially 
the whole field of systematic integration. But why should a physi 
cist worry about the sign of a factor removed from under a radical 
sign ? Merely becaiise an error here gives him a wrong result in a 
problem on attractions. 
The book is so written as to afford the greatest latitude in the 
order in which the various topics may be taken up. Thus the student 
may begin with the chapter on Partial Differentiation, or Double 
Integrals, or Differential Equations. Even within a chapter there is 
often a choice ; cf. for example the foot-notes on p.p. 44 and 106. Per 
sonally, I should not wish to begin the course with Chapter I. For, al 
though the subject is largely formal, testing the student’s training in 
high school algebra and teaching him how to evaluate somewhat intri 
cate integrals, the treatment should also serve to give him insight 
into the methods of algebra, and it should encourage him to become 
acquainted, for example, with the early chapters of Bocher’s 
Algebra. 
It is assumed that B. 0. Peirce’s A Short Table of Integrals, Ginn 
& Co., Boston, is in the hands of the student. The references to 
Analytic Geometry are to Osgood and Graustein’s Plane and Solid 
Analytic Geometry, Macmillan, 1921.