Calculus on $$\mathbb {R}^{n}$$ R n

Manjusha Majumdar () and Arindam Bhattacharyya
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Manjusha Majumdar: University of Calcutta, Department of Pure Mathematics
Arindam Bhattacharyya: Jadavpur University, Department of Mathematics

Chapter Chapter 1 in An Introduction to Smooth Manifolds, 2023, pp 1-34 from Springer

Abstract: Abstract Let $$\mathbb {R}$$ R denote the set of real numbers. For an integer $$n>0$$ n > 0 , let $$\mathbb {R}^{n}$$ R n denote the set of all ordered n-tuples $$(x^{1},x^{2},\ldots ,x^{n})$$ ( x 1 , x 2 , … , x n ) of real numbers. Individual n-tuple will be denoted at times by a single letter, e.g. $$x = (x^{1},x^{2},\ldots ,x^{n}),\;y = (y^{1},y^{2},\ldots ,y^{n})$$ x = ( x 1 , x 2 , … , x n ) , y = ( y 1 , y 2 , … , y n ) and so on.

Date: 2023
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DOI: 10.1007/978-981-99-0565-2_1

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