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This first volume in the series "Algorithms and Computation in Mathematics" is destined to become the standard reference work in the field. Manuel Bronstein is a leading expert on this topic and his book is the first to treat the subject both comprehensively and in sufficient detail - incorporating new results along the way. The book addresses mathematicians and computer scientists interested in symbolic computation, developers and programmers of computer algebra systems as well as users of symbolic integration methods. Many algorithms are given in pseudocode ready for immediate implementation, making the book equally suitable as a textbook for lecture courses on symbolic integration.
This second edition offers a new chapter on parallel integration, as well as a few comments on obtaining continuous antiderivatives and additional exercises.
From the Reviews
"The goal of this well-written book is to present the state of the art in the domain of "integration in finite terms". ... Both aspects of the work, mathematics and implementation, are present in the book. Moreover, Bronstein has chosen a good level of detail, and in such a way that he only deals with the case of transcendental functions. ..." J.M.Ollagnier, Mathematical Reviews 2002
"... It makes an excellent textbook for courses in computer algebra. It contains many exercises and the algorithms are presented in pseudocode, which is easy to implement in any computer algebra system. For those interested in symbolic integration it will become the standard reference." N.A.van Arkel, Medelingen van het wiskundig genootschap 1998
"... The writing is excellent, and the author provides a clear and coherent treatment of the problem of symbolic integration of transcendental functions. Each chapter includes several worked examples and a list of additional exercises. Every researcher and teacher in symbolic computation should have access to this book." F.Winkler, Computing Reviews1997
"My first thought on seeing this book was "I wish I had written it" - it resembles my lecture notes on the subject, but is better and more complete. ... In sum, the book does what it sets out to do, does it well, and should be on the bookshelf of every implementer or teacher." J.Davenport, The SAC Newsletter 2, 1997
This second edition offers a new chapter on parallel integration, as well as a few comments on obtaining continuous antiderivatives and additional exercises.
From the Reviews
"The goal of this well-written book is to present the state of the art in the domain of "integration in finite terms". ... Both aspects of the work, mathematics and implementation, are present in the book. Moreover, Bronstein has chosen a good level of detail, and in such a way that he only deals with the case of transcendental functions. ..." J.M.Ollagnier, Mathematical Reviews 2002
"... It makes an excellent textbook for courses in computer algebra. It contains many exercises and the algorithms are presented in pseudocode, which is easy to implement in any computer algebra system. For those interested in symbolic integration it will become the standard reference." N.A.van Arkel, Medelingen van het wiskundig genootschap 1998
"... The writing is excellent, and the author provides a clear and coherent treatment of the problem of symbolic integration of transcendental functions. Each chapter includes several worked examples and a list of additional exercises. Every researcher and teacher in symbolic computation should have access to this book." F.Winkler, Computing Reviews1997
"My first thought on seeing this book was "I wish I had written it" - it resembles my lecture notes on the subject, but is better and more complete. ... In sum, the book does what it sets out to do, does it well, and should be on the bookshelf of every implementer or teacher." J.Davenport, The SAC Newsletter 2, 1997
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From the reviews of the second edition:
"It discusses ... the integration of transcendental functions ... . Indeed, one of the most remarkable characteristics of this book is that it requires from its readers very little beyond a basic knowledge of calculus and algebra. ... This is an extremely well-written book on a beautiful topic that deserves to be better known to practising mathematicians and teachers of mathematics alike."
S. C. Coutinho, The Mathematical Gazette, Vol. 90 (5l9), 2006
"[...] The book contains many examples and exercises for the reader to get a feeling not only of the theoretical but also the practical aspects of the algorithms. It is designed as a textbook and well suited for courses about these constructive aspects of calculus. A "must have" for the bookshelf of every library."
H.-G.Gräbe, Zeitschrift für Angewandte Analysis und Ihre Anwendungen, Vol. 24, Issue 4, 2005
"The second edition of Bronstein's excellent book [...] contains a new chapter on parallel integration (also called the new Risch algorithm or the Risch-Norman
algorithm) [...] The first nine chapters of the book contain some improvements and a couple of additional exercises. Bronstein's book still presents the state of the art in the domain of integration of transcendental functions. Its unique blend of detailed mathematics and clear description of algorithms make it both a standard reference and a handbook for researchers and designers of computer algebra systems and a useful, easy to read textbook for teachers and students."
Friedrich Schwarz (Paderborn), Zentralblatt MATH 1059
From the reviews of the first edition:
"The goal of this well-written book is to present the state of the art in the domain of "integration in finite terms". ... Both aspects of the work, mathematics and implementation, are present in the book. Moreover, Bronstein has chosen a goodlevel of detail, and in such a way that he only deals with the case of transcendental functions. ..."
J.M.Ollagnier, Mathematical Reviews 2002
"... It makes an excellent textbook for courses in computer algebra. It contains many exercises and the algorithms are presented in pseudocode, which is easy to implement in any computer algebra system. For those interested in symbolic integration it will become the standard reference."
N.A.van Arkel, Medelingen van het wiskundig genootschap 1998
"... The writing is excellent, and the author provides a clear and coherent treatment of the problem of symbolic integration of transcendental functions. Each chapter includes several worked examples and a list of additional exercises. Every researcher and teacher in symbolic computation should have access to this book."
F.Winkler, Computing Reviews 1997
"... In fact, this book is an excellent blend of mathematics and algorithms. ... This well-written book serves as a good foundation to the topic of symbolic integration. ... Highly recommendable."
P.Kravanja, Journal of Computational and Applied Mathematics / Newsletter on Computational and Applied Mathematics 1997
"My first thought on seeing this book was "I wish I had written it" - it resembles my lecture notes on the subject, but is better and more complete. ... In sum, the book does what it sets out to do, does it well, and should be on the bookshelf of every implementer or teacher. For the latter, the author indicates various ways through the material, depending on the aims and background of the course being taught."
J.Davenport, The SAC Newsletter 2, 1997
"Symbolic Integration I is the second edition of an extremely thorough account of the problem of integration in finite terms for transcendental functions. ... This book was written by the world's leading expert in the area. ... it does what it setsout to do and does it extremely well." (Sam Blake, SIAM Review, Vol. 50 (1), 2008)
"It discusses ... the integration of transcendental functions ... . Indeed, one of the most remarkable characteristics of this book is that it requires from its readers very little beyond a basic knowledge of calculus and algebra. ... This is an extremely well-written book on a beautiful topic that deserves to be better known to practising mathematicians and teachers of mathematics alike."
S. C. Coutinho, The Mathematical Gazette, Vol. 90 (5l9), 2006
"[...] The book contains many examples and exercises for the reader to get a feeling not only of the theoretical but also the practical aspects of the algorithms. It is designed as a textbook and well suited for courses about these constructive aspects of calculus. A "must have" for the bookshelf of every library."
H.-G.Gräbe, Zeitschrift für Angewandte Analysis und Ihre Anwendungen, Vol. 24, Issue 4, 2005
"The second edition of Bronstein's excellent book [...] contains a new chapter on parallel integration (also called the new Risch algorithm or the Risch-Norman
algorithm) [...] The first nine chapters of the book contain some improvements and a couple of additional exercises. Bronstein's book still presents the state of the art in the domain of integration of transcendental functions. Its unique blend of detailed mathematics and clear description of algorithms make it both a standard reference and a handbook for researchers and designers of computer algebra systems and a useful, easy to read textbook for teachers and students."
Friedrich Schwarz (Paderborn), Zentralblatt MATH 1059
From the reviews of the first edition:
"The goal of this well-written book is to present the state of the art in the domain of "integration in finite terms". ... Both aspects of the work, mathematics and implementation, are present in the book. Moreover, Bronstein has chosen a goodlevel of detail, and in such a way that he only deals with the case of transcendental functions. ..."
J.M.Ollagnier, Mathematical Reviews 2002
"... It makes an excellent textbook for courses in computer algebra. It contains many exercises and the algorithms are presented in pseudocode, which is easy to implement in any computer algebra system. For those interested in symbolic integration it will become the standard reference."
N.A.van Arkel, Medelingen van het wiskundig genootschap 1998
"... The writing is excellent, and the author provides a clear and coherent treatment of the problem of symbolic integration of transcendental functions. Each chapter includes several worked examples and a list of additional exercises. Every researcher and teacher in symbolic computation should have access to this book."
F.Winkler, Computing Reviews 1997
"... In fact, this book is an excellent blend of mathematics and algorithms. ... This well-written book serves as a good foundation to the topic of symbolic integration. ... Highly recommendable."
P.Kravanja, Journal of Computational and Applied Mathematics / Newsletter on Computational and Applied Mathematics 1997
"My first thought on seeing this book was "I wish I had written it" - it resembles my lecture notes on the subject, but is better and more complete. ... In sum, the book does what it sets out to do, does it well, and should be on the bookshelf of every implementer or teacher. For the latter, the author indicates various ways through the material, depending on the aims and background of the course being taught."
J.Davenport, The SAC Newsletter 2, 1997
"Symbolic Integration I is the second edition of an extremely thorough account of the problem of integration in finite terms for transcendental functions. ... This book was written by the world's leading expert in the area. ... it does what it setsout to do and does it extremely well." (Sam Blake, SIAM Review, Vol. 50 (1), 2008)
"Laut Springer-Verlag soll dieses Werk die Standardreferenz auf diesem Gebiet sein bzw. werden: Umfassend und auch detailliert wäre die Darstellung; viele Algorithmen wären in einem Pseudocode vorhanden, auch hätte der Autor, ein hochrangiger Experte, einiges Neue eingearbeitet. Man kann dem nur zustimmen: Die vorliegende 2. Auflage hat ein neues Kapitel über parallele Integration, neue Übungsaufgaben und sonstige Verbesserungen. ... Das Buch wendet sich - in erfolgreicher Weise - an Mathematiker und Informatiker, die an symbolic computation interessiert sind. .." H.Prodinger, Internationale Mathematische Nachrichten 201, p. 33-34, 2006 "Kurz vor seinem Tod (...) ist die zweite Auflage dieser Monographie über symbolische Integration erschienen. Die erste Auflage erschien 1997 und wurde damals vom Unterzeichner im Computeralgebra-Rundbrief mit der Nummer 20 vom Frühjahr 1997 ausführlich besprochen (http://www.fachgruppe-computeralgebra.de/CAR/CAR20/node14.html). Das Buch ist das Standardwerk zur Frage, wie algorithmisch entschieden werden kann, ob die Stammfunktion einer elementaren Funktion wieder elementar ist oder nicht. Im ersten Fall wird diese dann auch berechnet. Die römische Eins bezieht sich auf die in diesem Buch ausschließlich behandelte Klasse der transzendenten Funktionen. ... Komplett neu hingegen ist ein Kapitel 10 zur "Parallel Integration". Hier hat der Autor Ideen von Risch, Norman, Davenport, Trager und anderen, die teilweise bis ins Jahr 1976 zurückgehen, im Stil des Buches aufgearbeitet und ergänzt. ... Meine Besprechung der ersten Auflage 1997 endete mit dem folgenden Wunsch: "Dem rundum gelungenen Buch ist eine weite Verbreitung zu wünschen, dem Autor die Zeit um bald einen zweiten Teil zur Theorie der symbolischen Integration algebraischer Funktionen folgen zu lassen!" Der erste Teil des Wunsches ist mit diesr Neuauflage in Erfüllung gegangen und gilt weiter, der zweite Teil kann nich mehr in Erfüllung gehen." Johannes Grabmeier, Computeralgebra Rundbrief Oktober 2005, Ausgabe 37