Courant & Hilbert - Methods of Mathematical Physics Vol. 1
Springer, Berlin, in 1924. A second edition, revised and improved
with the help of I(. O. Friedrichs, R. Luneburg, F. Rellich, and other
unselfish friends, followed in 1930. The second volume appeared in
1938. In the meantime I had been forced to leave Germany and was
fortunate and grateful to be given the opportunities open in the
United States. During the Second World War the German book be-
came unavailable and later was even suppressed by the National
Socialist rulers of Germany. Thus the survival of the book was
secured when the United States Government seized the copyright
and licensed a reprint issued by Interscience Publishers, New York.
Such a license also had to be obtained from the Alien Property Cus-
todian for the present English edition.
This edition follows the German original fairly closely but contains
a large nmvLber of additions and modifications. I have had to post-
pone a plan to completely rewrite and modernize the book in collabo-
ration xvith K. O. Friedrichs, because the pressure for publication of
an English "Courant-Hilbert" has become irresistible. Even so, it
is hoped that the work in its present form xvill be useful to mathe-
maticians and physicists alike, as the numerous demands from all
sides seem to indicate.
The objective of the book can still today be expressed almost as
in the preface to the first German edition. "Since the seventeenth
century, physical intuition has served as a vital source for mathe-
matical problems and methods. Recent trends and fashions have,
ho;vever, weakened the connection between mathematics and physics;
mathematicians, turning away from the roots of mathematics in
intuition, have concentrated on refinement and emphasized the postu-
lational side of mathematics, and at times have overlooked the unity
of their science vith physics and other fields. In many cases, physi-
cists have ceased to appreciate the attitudes of mathematicians.
This rift is unquestionably a serious threat to science as a whole; the
broad stream of scientific development may spht into smaller and
smaller rivulets and dry out. It seems therefore important to direct
our efforts toward reuniting divergent trends by clarifying the com-
mon features and interconnections of many distinct and diverse
scientific facts. Only thus can the student attain some mastery of
the material and the basis be prepared for further oganic develop-
ment of research.
"The present work is designed to serve this purpose for the field of
mathematical physics. Mathematical methods originating in prob-
lems of physics are developed and the attempt is made to shape re-
sults into unified mathematical theories. Completeness is not at-
tempted, but it is hoped that access to a rich and important field
will be facilitated by the book.
"The responsibility for the present book rests with me. Yet the
name of my teacher, colleague, and friend, D. Hilbert, on the title
page seems justified by the fact that much material from Hilbert's
papers and lectures has been used, as well as by the hope that the
book expresses some of Hilbert's spirit, which has had such a decisive
influence on mathematical research and education."
I am greatly indebted to many helpers in all phases of the task of
preparing this edition: to Peter Ceike, Ernest Courant, and Anneli
Lax, who provided most of the first draft of the translation'; to Hah'an
Rubin and Herbert Kranzer, who have given constructive criticism;
to Wilhelm Magnus, who is responsible for the appendix to Chapter
VII; and to Natascha Artin and Lucile Gardner, who carried the
burden of the editorial work. Most cordial thanks also are due to
Interscience Publishers for their patient and helpful attitude and to
my old friend and publisher, Dr. Ferdinand Springer in Heidelberg,
the great pioneer of modern scientific publishing, for his sympathetic
understanding of the situation, which has so greatly changed since the
old days of our close cooperation.
R. COURANT
- Paperback: 560 pages
- Publisher: Wiley-VCH; Volume 1 edition (January 4, 1989)
- Language: English
- ISBN-10: 0471504475
- ISBN-13: 978-0471504474
- Product Dimensions: 6.8 x 1.2 x 9.6 inches
Springer, Berlin, in 1924. A second edition, revised and improved
with the help of I(. O. Friedrichs, R. Luneburg, F. Rellich, and other
unselfish friends, followed in 1930. The second volume appeared in
1938. In the meantime I had been forced to leave Germany and was
fortunate and grateful to be given the opportunities open in the
United States. During the Second World War the German book be-
came unavailable and later was even suppressed by the National
Socialist rulers of Germany. Thus the survival of the book was
secured when the United States Government seized the copyright
and licensed a reprint issued by Interscience Publishers, New York.
Such a license also had to be obtained from the Alien Property Cus-
todian for the present English edition.
This edition follows the German original fairly closely but contains
a large nmvLber of additions and modifications. I have had to post-
pone a plan to completely rewrite and modernize the book in collabo-
ration xvith K. O. Friedrichs, because the pressure for publication of
an English "Courant-Hilbert" has become irresistible. Even so, it
is hoped that the work in its present form xvill be useful to mathe-
maticians and physicists alike, as the numerous demands from all
sides seem to indicate.
The objective of the book can still today be expressed almost as
in the preface to the first German edition. "Since the seventeenth
century, physical intuition has served as a vital source for mathe-
matical problems and methods. Recent trends and fashions have,
ho;vever, weakened the connection between mathematics and physics;
mathematicians, turning away from the roots of mathematics in
intuition, have concentrated on refinement and emphasized the postu-
lational side of mathematics, and at times have overlooked the unity
of their science vith physics and other fields. In many cases, physi-
cists have ceased to appreciate the attitudes of mathematicians.
This rift is unquestionably a serious threat to science as a whole; the
broad stream of scientific development may spht into smaller and
smaller rivulets and dry out. It seems therefore important to direct
our efforts toward reuniting divergent trends by clarifying the com-
mon features and interconnections of many distinct and diverse
scientific facts. Only thus can the student attain some mastery of
the material and the basis be prepared for further oganic develop-
ment of research.
"The present work is designed to serve this purpose for the field of
mathematical physics. Mathematical methods originating in prob-
lems of physics are developed and the attempt is made to shape re-
sults into unified mathematical theories. Completeness is not at-
tempted, but it is hoped that access to a rich and important field
will be facilitated by the book.
"The responsibility for the present book rests with me. Yet the
name of my teacher, colleague, and friend, D. Hilbert, on the title
page seems justified by the fact that much material from Hilbert's
papers and lectures has been used, as well as by the hope that the
book expresses some of Hilbert's spirit, which has had such a decisive
influence on mathematical research and education."
I am greatly indebted to many helpers in all phases of the task of
preparing this edition: to Peter Ceike, Ernest Courant, and Anneli
Lax, who provided most of the first draft of the translation'; to Hah'an
Rubin and Herbert Kranzer, who have given constructive criticism;
to Wilhelm Magnus, who is responsible for the appendix to Chapter
VII; and to Natascha Artin and Lucile Gardner, who carried the
burden of the editorial work. Most cordial thanks also are due to
Interscience Publishers for their patient and helpful attitude and to
my old friend and publisher, Dr. Ferdinand Springer in Heidelberg,
the great pioneer of modern scientific publishing, for his sympathetic
understanding of the situation, which has so greatly changed since the
old days of our close cooperation.
R. COURANT
