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OverviewBased 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. Full Product DetailsAuthor: Siavash ShahshahaniPublisher: Dover Publications Inc. Imprint: Dover Publications Inc. Edition: First Edition, First ed. Dimensions: Width: 15.10cm , Height: 2.20cm , Length: 22.80cm Weight: 0.593kg ISBN: 9780486807065ISBN 10: 0486807061 Pages: 352 Publication Date: 30 September 2016 Audience: College/higher education , Postgraduate, Research & Scholarly Format: Paperback Publisher's Status: Active Availability: In Print ![]() This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsReviewsAuthor InformationSiavash 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. Tab Content 6Author Website:Countries AvailableAll regions |