Titlebook: Smooth Manifolds; Rajnikant Sinha Textbook 2014 Springer India 2014 Differential manifolds.Multivariable differential calculus.Sard’s theo

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folds.Proves Sard’s theorem, for the first time, in case n =.This 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 focuse

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Foolproof

Multivariable Differential Calculus,om their early courses, but the exact form of theorems we need here are generally missing from their collection of theorems. So this is somewhat long chapter on multivariable differential calculus that is pertinent here for a good understanding of smooth manifolds.

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沙草纸

Whitney Embedding Theorem,eloped at that time. Fortunately, in this chapter, we have all the prerequisite for its proof in the special case of compact smooth manifolds. For the general case, which is more difficult, one can find its proof somewhere else.

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Textbook 2014ematical 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 theore

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Tangent Spaces, generalize the concept of tangent line in the case of curves in two-dimensional Euclidean space, and tangent plane in the case of surfaces in three-dimensional Euclidean space, using abstract tools of algebra, and analysis.