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.

Note by the Translator.

v

I replied, stating that I too was starting for Italy, and suggested
that we might possibly meet and confer upon the subject. But in
London, I received a post-card from Dr. Harnack, as follows: -
Dresden, 21 III 88.
I can propose no definite engagement to meet you in Italy, as I have been
ill for a week, and my journey has therefore become uncertain. Hence also I
have been able to work out very little as yet of the supplementary matter; but
I hope to be able to send you the notes to the first Book by April 16, and the
rest as you require it.
Soon after my return from Italy, I was shocked by receiving the
following letter -
Munich, 23 April, 1888.
You will have heard ere this of the unexpectedly sudden death of Prof.
A. Harnack, on April 3. A few days previously he had, as I learn, been in
correspondence with you about the publication of an English translation of his
work on the Differential and Integral Calculus, and had specially expressed his
wish to be allowed to nlake some needful improvements and alterations. In the
papers he has left, which I received yesterday from his Widow, there are
unfortunately only the beginnings of a revision, as far as page 40. * *
Dr. A. Voss.
Prof. d. Mathematik.
In answer to my reply to the above, Prof. Voss wrote as follows,
on May 6:I send you now the few sheets my dear friend put together shortly before
his death, (mostly in connexion with his edition of Serret's Cours de calcul
diff6rentiel). They show that he contemplated considerable changes 'in the
subsequent parts of his work, but nothing further has been found.
These notes by Prof. Harnack, as well as a few of his own
referring to the same part of the work, which Prof. Voss sent along
with them, I have adopted and incorporated in the translation.
He kindly offered also to take part in more extensive alterations, but
on full consideration I determined to adhere to the work in its original
form, and my decision was confirmed by the receipt of the following
letter from Prof. Voss: -
I have come to the opinion that the work should be kept exactly in its
present form, and in this my friends, Prof. Klein in Gottingen and Prof. N6ther
in Erlangen, also agree. Only I should regard it as due to the author, that it
should be stated in the preface to the English Edition, that Prof. Harnack
contemplated essential changes and improvements, which after his death could
not be made save at the risk of losing somewhat of the admitted freshness and
originality of the work. I believe that Prof. Harnack, in the further course of
his own revision, would have given up the idea of recasting it.