An Introductory Course on Differentiable Manifolds (Aurora: Dover Modern Math Originals) - Softcover

Shahshahani, Siavash

Softcover

ISBN 10: 0486807061 ISBN 13: 9780486807065

Verlag: Dover Publications Inc., 2016

Inhaltsangabe

Based on author Siavash Shahshahani's extensive teaching experience, this volume presents a thorough, rigorous course on the theory of differentiable manifolds. Geared toward advanced undergraduates and graduate students in mathematics, the treatment's prerequisites include a strong background in undergraduate mathematics, including multivariable calculus, linear algebra, elementary abstract algebra, and point set topology. More than 200 exercises offer students ample opportunity to gauge their skills and gain additional insights.
The four-part treatment begins with a single chapter devoted to the tensor algebra of linear spaces and their mappings. Part II brings in neighboring points to explore integrating vector fields, Lie bracket, exterior derivative, and Lie derivative. Part III, involving manifolds and vector bundles, develops the main body of the course. The final chapter provides a glimpse into geometric structures by introducing connections on the tangent bundle as a tool to implant the second derivative and the derivative of vector fields on the base manifold. Relevant historical and philosophical asides enhance the mathematical text, and helpful Appendixes offer supplementary material.

Über diesen Titel

Über die Autorin bzw. den Autor

Siavash Shahshahani studied at Berkeley with Steve Smale and received his PhD in 1969, after which he held positions at Northwestern and the University of Wisconsin, Madison. From 1974 until his 2012 retirement he was mainly at Sharif University of Technology in Tehran, Iran, where he helped develop a strong mathematics program.

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Based on author Siavash Shahshahani's extensive teaching experience, this volume presents a thorough, rigorous course on the theory of differentiable manifolds. Geared toward advanced undergraduates and graduate students in mathematics, the treatment's prerequisites include a strong background in undergraduate mathematics, including multivariable calculus, linear algebra, elementary abstract algebra, and point set topology. More than 200 exercises offer students ample opportunity to gauge their skills and gain additional insights.
The four-part treatment begins with a single chapter devoted to the tensor algebra of linear spaces and their mappings. Part II brings in neighboring points to explore integrating vector fields, Lie bracket, exterior derivative, and Lie derivative. Part III, involving manifolds and vector bundles, develops the main body of the course. The final chapter provides a glimpse into geometric structures by introducing connections on the tangent bundle as a tool to implant the second derivative and the derivative of vector fields on the base manifold. Relevant historical and philosophical asides enhance the mathematical text, and helpful Appendixes offer supplementary material.
Dover Aurora Modern Math Original.
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Details zur Ausgabe

• Verlag: Dover Publications Inc.
• Erscheinungsdatum: 2016
• Sprache: Englisch
• ISBN 10: 0486807061
• ISBN 13: 9780486807065
• Einband: Taschenbuch
• Auflage: 1
• Anzahl der Seiten: 360
• Kontakt zum Hersteller: Dover; info@galileo-mc.de; ; Dachauer Str. 5-7; F�rstenfeldbruck; 82256; Deutschland