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2015 | OriginalPaper | Buchkapitel

1. Differential Calculus

verfasst von : Jacques Lafontaine

Erschienen in: An Introduction to Differential Manifolds

Verlag: Springer International Publishing

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Abstract

In this chapter, we review and reinforce the basics of differential calculus in preparation for our subsequent study of manifolds.

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Fußnoten
1
This elegant argument was communicated to me by Max Karoubi on the terrace of a Parisian caf.
 
2
“Formally” because the operator is not defined on the whole space.
 
3
We can invoke Banach’s theorem that ensures that the inverse of a bijective continuous linear map from one Banach space to another is continuous. In fact, in all of the examples we are confronted with this continuity is very easily verified.
 
Literatur
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Metadaten
Titel
Differential Calculus
verfasst von
Jacques Lafontaine
Copyright-Jahr
2015
DOI
https://doi.org/10.1007/978-3-319-20735-3_1