Analysis in Rn Space
Authors
Description
This book deals with Differential and Integral Calculus for functions of several variables, and can be used as a follow-up to Real Analysis Vol.1, by the same author. It contains a succinct and rigorous presentation of the most important facts relating to differentiability in n-dimensional space.
Its origin is the mimeographed notes of a course taught at the Seventh Brazilian Mathematics Colloquium, followed by a more polished version published by the Editora da Universidade de Brasília, which had been out of print for many years.
In the current edition, several inaccuracies have been corrected, but the text remains basically the same.
Target audience
Higher education
Name: Analysis in Rn Space
Author(s): e Elon Lages Lima
Pages: 120
Publication: IMPA, 2025
ISBN: 978-85-244-0581-5
Edition: 3
1 Differentiable applications
1 Definition of a differentiable application
2 Generalization
3 Exercises
2 Examples
3 Differentiability classes
1 Derivatives of order 2
2 Derivatives of higher order
3 Examples
4 Observation on sectionally differentiable paths
5 Exercises
4 The chain rule
5 The inequality of the average value
6 Integrals
1 Path integration
2 Relations between derivatives and integrals
3 Repeated integrals
4 Multiple integrals
5 Exercises
7 Partial derivatives
8 Schwarz’s Theorem
9 Taylor’s formula
1 Taylor’s theorems
2 Maxima and minima
3 Exercises
10 Implicit functions
1 The Inverse Function Theorem
2 The local form of submersions
3 The local form of immersions
4 The rank theorem
5 Exercises
11 Change of variables in multiple integrals
A Normed vector spaces
Bibliography