Introductory Course on Differentiable Manifolds (eBook)

Siavash Shahshahani (Autor)

eBook Download: EPUB

2017 | 1., First Edition, First
368 Seiten
Dover Publications (Verlag)
978-0-486-82082-8 (ISBN)

Infos

Rigorous course for advanced undergraduates and graduate students requires a strong background in undergraduate mathematics. Complete, detailed treatment, enhanced with philosophical and historical asides and more than 200 exercises. 2016 edition.

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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.

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.

Produkt-Details

• Erscheint lt. Verlag: 23.3.2017
• Reihe/Serie: Aurora: Dover Modern Math Originals
• Sprache: englisch
• Maße: 150 x 150 mm
• Gewicht: 612 g
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
• Schlagworte: books on math • Complex • differentiable manifolds • Differential Calculus in a Normed Space. • differential mathematics • elementary abstract algebra • exterior derivative • Geometric Structures • homogeneous spaces • integrating vector fields • Integration and Cohomology • Lie bracket • Lie derivative • Lie groups • linear algebra • manifolds and vector bundles • Mappings • mathematical studies • Multivariable Calculus • Non-fiction • phenomenon, Aurora • point set topology • science and math • Smooth structures • tensor algebra of linear spaces • tensor fields • Tensors • Theoretical • The Tangent Bundle • Topological Manifolds, Smooth Manifolds • Vector Bundles and Fields • Vector fields
• ISBN-10: 0-486-82082-3 / 0486820823
• ISBN-13: 978-0-486-82082-8 / 9780486820828