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Differential Calculus

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Part of the Graduate Texts in Mathematics book series (GTM,volume 160)

Abstract

We shall recall briefly the notion of derivative and some of its useful properties. As mentioned in the foreword, Chapter VIII of Dieudonné’s book or my book on real analysis [La 93] give a self-contained and complete treatment for Banach spaces. We summarize certain facts concerning their properties as topological vector spaces, and then we summarize differential calculus. The reader can actually skip this chapter and start immediately with Chapter II if the reader is accustomed to thinking about the derivative of a map as a linear transformation. (In the finite dimensional case, when bases have been selected, the entries in the matrix of this transformation are the partial derivatives of the map.) We have repeated the proofs for the more important theorems, for the ease of the reader.

Keywords

  • Banach Space
  • Open Subset
  • Open Neighborhood
  • Topological Vector Space
  • Differential Calculus

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© 1995 Springer-Verlag New York, Inc.

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Lang, S. (1995). Differential Calculus. In: Lang, S. (eds) Differential and Riemannian Manifolds. Graduate Texts in Mathematics, vol 160. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-4182-9_1

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  • DOI: https://doi.org/10.1007/978-1-4612-4182-9_1

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-8688-2

  • Online ISBN: 978-1-4612-4182-9

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