Ebook: A Course of Mathematical Analysis, Volume II, Part II

AUTHOR'S PREFACE SECOND FRENCH EDITION



The first part of this volume has undergone only slight changes,
while the rather important modifications that have been made
appear only in the last chapters.

In the first edition I was able to devote but a few pages to par-
tial differential equations of the second order and to the calculus
of variations. In order to present in a less summary manner such
broad subjects, I have concluded to defer them to a third volume,
which will contain also a sketch of the recent theory of integral
equations. The suppression of the last chapter has enabled me to
make some additions, of which the most important relate to linear
differential equations and to partial differential equations of the

firSt Order " E. GOUESAT



iii



TRANSLATORS' PREFACE

As the title indicates, the present volume is a translation of the
first half of the second volume of Goursat's "Cours d' Analyse." The
decision to publish the translation in two parts is due to the evi-
dent adaptation of these two portions to the introductory courses in
American colleges and universities in the theory of functions and
in differential equations, respectively.

After the cordial reception given to the translation of Goursat's
first volume, the continuation was assured. That it has been
delayed so long was due, in the first instance, to our desire to await
the appearance of the second edition of the second volume in
French. The advantage in doing so will be obvious to those who
have observed the radical changes made in the second (French)
edition of the second volume. Volume I was not altered so radi-
cally, so that the present English translation of that volume may be
used conveniently as a companion to this ; but references are given
here to both editions pf the first volume, to avoid any possible
difficulty in this connection.

Our thanks are due to Professor Goursat, who has kindly given
us his permission to make this translation, and has approved of the
plan of publication in two parts. He has also seen all proofs in
English and has approved a few minor alterations made in transla-
tion as well as the translators' notes. The responsibility for the

latter rests, however, with the translators.

E. R. HEDRICK

OTTO DUNKEL