LEADER 03878nam 22006375 450 001 9910299973903321 005 20200630063332.0 010 $a81-322-2104-4 024 7 $a10.1007/978-81-322-2104-3 035 $a(CKB)3710000000306337 035 $a(SSID)ssj0001386770 035 $a(PQKBManifestationID)11824978 035 $a(PQKBTitleCode)TC0001386770 035 $a(PQKBWorkID)11374488 035 $a(PQKB)10567240 035 $a(DE-He213)978-81-322-2104-3 035 $a(MiAaPQ)EBC5589181 035 $a(PPN)18308912X 035 $a(EXLCZ)993710000000306337 100 $a20141115d2014 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aSmooth Manifolds$b[electronic resource] /$fby Rajnikant Sinha 205 $a1st ed. 2014. 210 1$aNew Delhi :$cSpringer India :$cImprint: Springer,$d2014. 215 $a1 online resource (IX, 485 p. 10 illus.) 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a81-322-2103-6 327 $aChapter 1. Differentiable Manifolds -- Chapter 2. Tangent Spaces -- Chapter 3. Multivariable Differential Calculus -- Chapter 4. Topological Properties of Smooth Manifolds -- Chapter 5. Immersions, Submersions, and Embeddings -- Chapter 6. Sard?s Theorem -- Chapter 7. Whitney Embedding Theorem -- Bibliography. 330 $aThis book offers an introduction to the theory of smooth manifolds, helping students to familiarize themselves with the tools they will need for mathematical research on smooth manifolds and differential geometry. The book primarily focuses on topics concerning differential manifolds, tangent spaces, multivariable differential calculus, topological properties of smooth manifolds, embedded submanifolds, Sard?s theorem and Whitney embedding theorem. It is clearly structured, amply illustrated and includes solved examples for all concepts discussed. Several difficult theorems have been broken into many lemmas and notes (equivalent to sub-lemmas) to enhance the readability of the book. Further, once a concept has been introduced, it reoccurs throughout the book to ensure comprehension. Rank theorem, a vital aspect of smooth manifolds theory, occurs in many manifestations, including rank theorem for Euclidean space and global rank theorem. Though primarily intended for graduate students of mathematics, the book will also prove useful for researchers. The prerequisites for this text have intentionally been kept to a minimum so that undergraduate students can also benefit from it. It is a cherished conviction that ?mathematical proofs are the core of all mathematical joy,? a standpoint this book vividly reflects. 606 $aGeometry, Differential 606 $aGravitation 606 $aGlobal analysis (Mathematics) 606 $aManifolds (Mathematics) 606 $aDifferential Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M21022 606 $aClassical and Quantum Gravitation, Relativity Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/P19070 606 $aGlobal Analysis and Analysis on Manifolds$3https://scigraph.springernature.com/ontologies/product-market-codes/M12082 615 0$aGeometry, Differential. 615 0$aGravitation. 615 0$aGlobal analysis (Mathematics) 615 0$aManifolds (Mathematics) 615 14$aDifferential Geometry. 615 24$aClassical and Quantum Gravitation, Relativity Theory. 615 24$aGlobal Analysis and Analysis on Manifolds. 676 $a516.07 700 $aSinha$b Rajnikant$4aut$4http://id.loc.gov/vocabulary/relators/aut$0721177 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910299973903321 996 $aSmooth manifolds$91410001 997 $aUNINA