Abstract
Undergraduate calculus progresses from differentiation and integration of functions on the real line to functions in the plane and in 3-space. Then one encounters vectorvalued functions and learns about integrals on curves and surfaces. Real analysis extends differential and integral calculus from \( \mathbb{R}^3 to \mathbb{R}^n\). This book is about the extension of calculus from curves and surfaces to higher dimensions.
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© 2011 Springer Science+Business Media, LLC
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Tu, L.W. (2011). A Brief Introduction. In: An Introduction to Manifolds. Universitext. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-7400-6_1
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DOI: https://doi.org/10.1007/978-1-4419-7400-6_1
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Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-7399-3
Online ISBN: 978-1-4419-7400-6
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