Differentiation in $$\mathbb {R}^{n}$$ R n

Celso Melchiades Doria ()
Additional contact information
Celso Melchiades Doria: Universidade Federal de Santa Catarina, Department of Mathematics, CFM

Chapter Chapter 1 in Differentiability in Banach Spaces, Differential Forms and Applications, 2021, pp 1-76 from Springer

Abstract: Abstract The analysis of the behavior of a function is efficiently carried out when we study the way in which the function varies. In this chapter, techniques used in studying functions of one real variable $$ f:I\rightarrow \mathbb {R}$$ f : I → R , defined in an open interval $$I\subset \mathbb {R}$$ I ⊂ R , are extended for functions of several real variables $$f:U\rightarrow \mathbb {R}^{m}$$ f : U → R m defined over an open subset $$U\subset \mathbb {R}^{n}$$ U ⊂ R n . Several real variables is understood to mean a finite number of variables $$(x_{1},\ldots ,x_{n})\in \mathbb {R}^{n}$$ ( x 1 , … , x n ) ∈ R n . The simple topological nature of $$\mathbb {R}^{n}$$ R n allows the theory to be more easily understood as all the concepts and techniques. The same concepts and techniques will be studied in the chapters ahead within the framework of Banach spaces.

Date: 2021
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-77834-7_1

Ordering information: This item can be ordered from
http://www.springer.com/9783030778347

DOI: 10.1007/978-3-030-77834-7_1

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().