David. Bleecker's Books

Gauge Theory and Variational Principles

By: David Bleecker

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Gauge Theory and Variational Principles

By: David Bleecker

This text provides a framework for describing and organizing the basic forces of nature and the interactions of subatomic particles. A detailed and self-contained mathematical account of gauge theory, it is geared toward beginning graduate students and advanced undergraduates in mathematics and physics. This well-organized 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 equation. Additional topics include free Dirac electron fields; interactions; calculus on frame bundle; and unification of gauge fields and gravitation. The text concludes with references, a selected bibliography, an index of notation, and a general index.

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Page Count

202

Publisher

Courier Corporation

Published Date

ISBN 10

0486445461

ISBN 13

9780486445465

Basic Partial Differential Equations

By: David. Bleecker

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Basic Partial Differential Equations

By: David. Bleecker

Methods of solution for partial differential equations (PDEs) used in mathematics, science, and engineering are clarified in this self-contained 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 first-order PDEs to the evolution of population densities and to traffic shocks convergence of numerical solutions of PDEs and implementation on a computer convergence of Laplace series on spheres quantum mechanics of the hydrogen atom solving PDEs on manifolds The text requires some knowledge of calculus but none on differential equations or linear algebra.

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Page Count

974

Publisher

CRC Press

Published Date

ISBN 10

1351086987

ISBN 13

9781351086981

Index Theory with Applications to Mathematics and Physics

By: David Bleecker,Bernhelm Booss

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Index Theory with Applications to Mathematics and Physics

By: David Bleecker,Bernhelm Booss

Describes, explains, and explores the Index Theorem of Atiyah and Singer, one of the truly great accomplishments of twentieth-century mathematics whose influence continues to grow, fifty years after its discovery. David Bleecker and Bernhelm Boo�-Bavnbek give two proofs of the Atiyah-Singer Index Theorem in impressive detail: one based on K-theory and the other on the heat kernel approach.

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Page Count

766

Publisher

Amer Mathematical Society

Published Date

ISBN 10

1571462643

ISBN 13

9781571462640

Book's by David. Bleecker

Gauge Theory and Variational Principles

Gauge Theory and Variational Principles

Basic Partial Differential Equations

Basic Partial Differential Equations

Index Theory with Applications to Mathematics and Physics

Index Theory with Applications to Mathematics and Physics

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