Introduction to Functions of Several Real Variables

Giorgio Giorgi, Bienvenido Jiménez and Vicente Novo
Additional contact information
Giorgio Giorgi: University of Pavia
Bienvenido Jiménez: National University of Distance Education
Vicente Novo: National University of Distance Education

Chapter Chapter 2 in Lectures on Mathematics for Economic and Financial Analysis, 2025, pp 113-158 from Springer

Abstract: Abstract This chapter is concerned with a number of topics in multivariable calculus. The basic notions of limits and continuity for a function of several variables are recalled. Then, the notions of partial derivatives, differentiability and differentiability of composite functions are recalled. Section 2.4 introduces the classical notion of directional derivative, which is important for further developments in the so-called “nonsmooth analysis”. Section 2.5 is concerned with the notion of homogeneous functions, particularly important in production theory, such as the economic properties of the so-called “Cobb-Douglas function”. Section 2.6 is concerned with implicit functions, important not only in constrained optimization problems with equality constraints, but also in several economic questions, such as, for instance, the “comparative statics problems” considered by P. A. Samuelson. The final Sect. 2.7 is concerned with the classical Taylor’s formula for functions of several variables and with the mean value theorem.

Date: 2025
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:978-3-031-83339-7_2

Ordering information: This item can be ordered from
http://www.springer.com/9783031833397

DOI: 10.1007/978-3-031-83339-7_2

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 ().