Bleecker, David
Overview
Works:  15 works in 106 publications in 3 languages and 1,556 library holdings 

Roles:  Author, Translator, htt 
Classifications:  QA329, 515.72 
Publication Timeline
.
Most widely held works by
David Bleecker
Topology and analysis : the AtiyahSinger index formula and gaugetheoretic physics by
Bernhelm Booss(
Book
)
21 editions published between 1985 and 1989 in English and German and held by 501 WorldCat member libraries worldwide
The Motivation. With intensified use of mathematical ideas, the methods and techniques of the various sciences and those for the solution of practical problems demand of the mathematician not only greater readiƯ ness for extramathematical applications but also more comprehensive orientations within mathematics. In applications, it is frequently less important to draw the most farreaching conclusions from a single matheƯ matical idea than to cover a subject or problem area tentatively by a proper "variety" of mathematical theories. To do this the mathematician must be familiar with the shared as weIl as specific features of differƯ ent mathematical approaches, and must have experience with their interƯ connections. The AtiyahSinger Index Formula, "one of the deepest and hardest results in mathematics", "probably has wider ramifications in topology and analysis than any other single result" (F. Hirzebruch) and offers perhaps a particularly fitting example for such an introduction to "Mathematics": In spi te of i ts difficulty and immensely rich interrelaƯ tions, the realm of the Index Formula can be delimited, and thus its ideas and methods can be made accessible to students in their middle * semesters. In fact, the AtiyahSinger Index Formula has become progressively "easier" and "more transparent" over the years. The discovery of deeper and more comprehensive applications (see Chapter 111. 4) brought with it, not only a vigorous exploration of its methods particularly in the manyƯ facetted and always new presentations of the material by M.F
21 editions published between 1985 and 1989 in English and German and held by 501 WorldCat member libraries worldwide
The Motivation. With intensified use of mathematical ideas, the methods and techniques of the various sciences and those for the solution of practical problems demand of the mathematician not only greater readiƯ ness for extramathematical applications but also more comprehensive orientations within mathematics. In applications, it is frequently less important to draw the most farreaching conclusions from a single matheƯ matical idea than to cover a subject or problem area tentatively by a proper "variety" of mathematical theories. To do this the mathematician must be familiar with the shared as weIl as specific features of differƯ ent mathematical approaches, and must have experience with their interƯ connections. The AtiyahSinger Index Formula, "one of the deepest and hardest results in mathematics", "probably has wider ramifications in topology and analysis than any other single result" (F. Hirzebruch) and offers perhaps a particularly fitting example for such an introduction to "Mathematics": In spi te of i ts difficulty and immensely rich interrelaƯ tions, the realm of the Index Formula can be delimited, and thus its ideas and methods can be made accessible to students in their middle * semesters. In fact, the AtiyahSinger Index Formula has become progressively "easier" and "more transparent" over the years. The discovery of deeper and more comprehensive applications (see Chapter 111. 4) brought with it, not only a vigorous exploration of its methods particularly in the manyƯ facetted and always new presentations of the material by M.F
Gauge theory and variational principles by
David Bleecker(
Book
)
12 editions published in 1981 in English and held by 450 WorldCat member libraries worldwide
12 editions published in 1981 in English and held by 450 WorldCat member libraries worldwide
Basic partial differential equations by
David Bleecker(
Book
)
34 editions published between 1992 and 2018 in English and Undetermined and held by 410 WorldCat member libraries worldwide
"Methods of solution for partial differential equations (PDEs) used in mathematics, science, and engineering are clarified in this selfcontained source. The reader will learn how to use PDEs to predict system behaviour from an initial state of the system and from external influences, and enhance the success of endeavours involving reasonably smooth, predictable changes of measurable quantities. This text enables the reader to not only find solutions of many PDEs, but also to interpret and use these solutions. It offers 6000 exercises ranging from routine to challenging. The palatable, motivated proofs enhance understanding and retention of the material. Topics not usually found in books at this level include but examined in this text:the application of linear and nonlinear firstorder PDEs to the evolution of population densities and to traffic shocksconvergence of numerical solutions of PDEs and implementation on a computerconvergence of Laplace series on spheresquantum mechanics of the hydrogen atomsolving PDEs on manifoldsThe text requires some knowledge of calculus but none on differential equations or linear algebra."Provided by publisher
34 editions published between 1992 and 2018 in English and Undetermined and held by 410 WorldCat member libraries worldwide
"Methods of solution for partial differential equations (PDEs) used in mathematics, science, and engineering are clarified in this selfcontained source. The reader will learn how to use PDEs to predict system behaviour from an initial state of the system and from external influences, and enhance the success of endeavours involving reasonably smooth, predictable changes of measurable quantities. This text enables the reader to not only find solutions of many PDEs, but also to interpret and use these solutions. It offers 6000 exercises ranging from routine to challenging. The palatable, motivated proofs enhance understanding and retention of the material. Topics not usually found in books at this level include but examined in this text:the application of linear and nonlinear firstorder PDEs to the evolution of population densities and to traffic shocksconvergence of numerical solutions of PDEs and implementation on a computerconvergence of Laplace series on spheresquantum mechanics of the hydrogen atomsolving PDEs on manifoldsThe text requires some knowledge of calculus but none on differential equations or linear algebra."Provided by publisher
Index theory with applications to mathematics and physics by
David Bleecker(
Book
)
11 editions published in 2013 in English and held by 87 WorldCat member libraries worldwide
Index Theory with Applications to Mathematics and Physics describes, explains, and explores the Index Theorem of Atiyah and Singer, one of the truly great accomplishments of twentiethcentury mathematics whose influence continues to grow, fifty years after its discovery. The Index Theorem has given birth to many mathematical research areas and exposed profound connections between analysis, geometry, topology, algebra, and mathematical physics. Hardly any topic of modern mathematics stands independent of its influence. In this ambitious new work, authors David Bleecker and Bernhelm BoossBavnbek give two proofs of the AtiyahSinger Index Theorem in impressive detail: one based on Ktheory and the other on the heat kernel approach. As a preparation for this, the authors explain all the background information on such diverse topics as Fredholm operators, pseudodifferential operators, analysis on manifolds, principal bundles and curvature, and Ktheorycarefully and with concern for the reader. Many applications of the theorem are given, as well as an account of some of the most important recent developments in the subject, with emphasis on gauge theoretic physical models and lowdimensional topology. The 18 chapters and two appendices of the book introduce different topics and aspects, often beginning from scratch without presuming full knowledge of all the preceding chapters. Learning paths, through a restricted selection of topics and sections, are suggested and facilitated. The chapters are written for students of mathematics and physics: some for the upperundergraduate level, some for the graduate level, and some as an inspiration and support for researchers. Index Theory with Applications to Mathematics and Physics is a textbook, a reference book, a survey, and much more. Written in a lively fashion, it contains a wealth of basic examples and exercises. The authors have included many discussion sections that are both entertaining and informative, which illuminate the thinking behind the more general theory. A detailed bibliography and index facilitate the orientation
11 editions published in 2013 in English and held by 87 WorldCat member libraries worldwide
Index Theory with Applications to Mathematics and Physics describes, explains, and explores the Index Theorem of Atiyah and Singer, one of the truly great accomplishments of twentiethcentury mathematics whose influence continues to grow, fifty years after its discovery. The Index Theorem has given birth to many mathematical research areas and exposed profound connections between analysis, geometry, topology, algebra, and mathematical physics. Hardly any topic of modern mathematics stands independent of its influence. In this ambitious new work, authors David Bleecker and Bernhelm BoossBavnbek give two proofs of the AtiyahSinger Index Theorem in impressive detail: one based on Ktheory and the other on the heat kernel approach. As a preparation for this, the authors explain all the background information on such diverse topics as Fredholm operators, pseudodifferential operators, analysis on manifolds, principal bundles and curvature, and Ktheorycarefully and with concern for the reader. Many applications of the theorem are given, as well as an account of some of the most important recent developments in the subject, with emphasis on gauge theoretic physical models and lowdimensional topology. The 18 chapters and two appendices of the book introduce different topics and aspects, often beginning from scratch without presuming full knowledge of all the preceding chapters. Learning paths, through a restricted selection of topics and sections, are suggested and facilitated. The chapters are written for students of mathematics and physics: some for the upperundergraduate level, some for the graduate level, and some as an inspiration and support for researchers. Index Theory with Applications to Mathematics and Physics is a textbook, a reference book, a survey, and much more. Written in a lively fashion, it contains a wealth of basic examples and exercises. The authors have included many discussion sections that are both entertaining and informative, which illuminate the thinking behind the more general theory. A detailed bibliography and index facilitate the orientation
Gauge theory and variational principles by
David Bleecker(
Book
)
14 editions published between 1981 and 2013 in English and held by 79 WorldCat member libraries worldwide
This text provides a framework for describing and organizing the basic forces of nature and the interactions of subatomic particles. A detailed and selfcontained mathematical account of gauge theory, it is geared toward beginning graduate students and advanced undergraduates in mathematics and physics. This wellorganized treatment supplements its rigor with intuitive ideas. Starting with an examination of principal fiber bundles and connections, the text explores curvature; particle fields, Lagrangians, and gauge invariance; Lagrange's equation for particle fields; and the inhomogeneous field
14 editions published between 1981 and 2013 in English and held by 79 WorldCat member libraries worldwide
This text provides a framework for describing and organizing the basic forces of nature and the interactions of subatomic particles. A detailed and selfcontained mathematical account of gauge theory, it is geared toward beginning graduate students and advanced undergraduates in mathematics and physics. This wellorganized treatment supplements its rigor with intuitive ideas. Starting with an examination of principal fiber bundles and connections, the text explores curvature; particle fields, Lagrangians, and gauge invariance; Lagrange's equation for particle fields; and the inhomogeneous field
Solution manual to accompany Basic partial differential equations by
David Bleecker(
Book
)
3 editions published in 1993 in English and held by 11 WorldCat member libraries worldwide
3 editions published in 1993 in English and held by 11 WorldCat member libraries worldwide
Topology and Analysis : The AtiyahSinger Index Formula and GaugeTheoretic Physics by
Bernhelm Booss(
)
in English and held by 5 WorldCat member libraries worldwide
in English and held by 5 WorldCat member libraries worldwide
Essential partial differential equations : for undergraduate students of mathematics, science and engineering by
David Bleecker(
Book
)
2 editions published in 1991 in English and held by 3 WorldCat member libraries worldwide
2 editions published in 1991 in English and held by 3 WorldCat member libraries worldwide
Gauge theory and variational principles by
David Bleecker(
Book
)
1 edition published in 1981 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 1981 in English and held by 2 WorldCat member libraries worldwide
Adviesen van de burgers J. Pontoi en D. Bleecker, over de wisselbank by
Julius Pontoi(
Book
)
2 editions published in 1796 in Undetermined and held by 2 WorldCat member libraries worldwide
2 editions published in 1796 in Undetermined and held by 2 WorldCat member libraries worldwide
Gauge Theory and Variational Principles(
Book
)
1 edition published in 1981 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 1981 in English and held by 2 WorldCat member libraries worldwide
Basic partial differential equations. Bleecker by
David Bleecker(
Book
)
1 edition published in 1992 in English and held by 1 WorldCat member library worldwide
1 edition published in 1992 in English and held by 1 WorldCat member library worldwide
Ji chu pian wei fen fang cheng by
David Bleecker(
Book
)
1 edition published in 2006 in Chinese and held by 1 WorldCat member library worldwide
Ben shu bao kuo ying yong pian wei fen fang cheng de ji ben nei rong:te zheng xian fa, Fen li bian liang fa, Fourier ji shu, SturmLiouville li lun, Duhamel yuan li, Bao jiao ying she fang fa deng
1 edition published in 2006 in Chinese and held by 1 WorldCat member library worldwide
Ben shu bao kuo ying yong pian wei fen fang cheng de ji ben nei rong:te zheng xian fa, Fen li bian liang fa, Fourier ji shu, SturmLiouville li lun, Duhamel yuan li, Bao jiao ying she fang fa deng
The Dirac operator and the scalar curvature of continuously deformed algebraic varieties by
Christian Bär(
Book
)
1 edition published in 1999 in English and held by 1 WorldCat member library worldwide
1 edition published in 1999 in English and held by 1 WorldCat member library worldwide
Topology and analysis : the atiyahsinger index formula and gaugetheoretic xFCb. Booss ; D.D. Bleecker by
Bernhelm Booss(
)
1 edition published in 1985 in English and held by 1 WorldCat member library worldwide
1 edition published in 1985 in English and held by 1 WorldCat member library worldwide
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Related Identities
 Booss, Bernhelm 1941 Author
 Csordas, George
 Mader, Adolf Translator
 Pontoi, J. Author
 Bär, Christian fl. 1982 Author
 李俊杰
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Alternative Names
Bleecker, D. 1948
Bleecker, D. D.
Bleecker, D. D. (David D.)
Bleecker, David
Bleecker, David D.
Bleecker, David D. 1948
David Bleecker American mathematician
David Bleecker Amerikaans wiskundige
David Bleecker matemàtic estatunidenc
David Bleecker matemático estadounidense
David Bleecker matematikan amerikan
David Bleecker USamerikanischer Mathematiker
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