An introduction to the study of the elements of the differential and integral calculus. From the German of the late Axel Harnack, With the permission of the author.

iv

Preface.

In the selection and ultimate limitation of the contents it was not
always easy to decide: there may be a diversity in judgments respecting
what belongs to the "Elements" of the Calculus. My purpose will be
fulfilled, if this Introduction be found useful as a preparation for the
study of differential equations, of algebraic curves and of algebraic
integrals. The theory of these integrals might have been joined on
immediately to the last chapter; but I had to omit it, since a short
sketch would have been of little use, and an investigation in detail
would have completely displaced the centre of gravity of my work.
I desire here also to express my thanks to my friend and
colleague Dr. Voss for all the benefit my work has derived from the
interest he has taken in it.
Dresden, February 1881.
Harnack.
NOTE BY THE TRANSLATOR.
An acquaintance of some years with Prof. Harnack's work: "die
Elemente der Differenzial- und Integralrechnung", Leipzig, B. G. Teubner,
1881, led me to desire that the subject should be made accessible to
English readers in the manner in which he has presented it. I
therefore wrote to the Author, on March 12, 1888, and asked his
sanction to publish a translation.
In his reply dated Dresden, March 15, 1888, Prof. Harnack gave
me his permission, and proceeded to say: -
I must add however, that my book, written rather rapidly and with
somewhat youthful lightness of heart eight years ago, seems to me now in
many places not sufficiently exact. * * Since its publication I have made a
considerable list of corrections, and noted many points on which attention
should be bestowed in any future Edition. These portions of the work I shall
therefore ask you to allow me to recast for your English Edition. I shall
make the alterations as concise as possible, so as to enable you to insert them
into your manuscript with no great labqur or loss of time. I hope to be able
to send you as a sample next week, the alterations I propose to make in the
first Book. Those in the second Book, I cannot send for about six weeks, as I
shall be in North Italy during the Easter Vacation. The rest will follow soon
after, so that the printing of your work need not be delayed.
Hoping that you will be able to accept my proposal, as it will conduce to
the improvement of the work,
I remain yours, etc.
Ax. Harnack.