# An Introduction to Multivariable Analysis from Vector to Manifold

• Piotr Mikusiński
• Michael D. Taylor
Textbook

1. Front Matter
Pages i-x
2. Piotr Mikusiński, Michael D. Taylor
Pages 1-41
3. Piotr Mikusiński, Michael D. Taylor
Pages 43-73
4. Piotr Mikusiński, Michael D. Taylor
Pages 75-112
5. Piotr Mikusiński, Michael D. Taylor
Pages 113-151
6. Piotr Mikusiński, Michael D. Taylor
Pages 153-188
7. Piotr Mikusiński, Michael D. Taylor
Pages 189-217
8. Piotr Mikusiński, Michael D. Taylor
Pages 219-290
9. Back Matter
Pages 291-295

### Introduction

Multivariable analysis is an important subject for mathematicians, both pure and applied. Apart from mathematicians, we expect that physicists, mechanical engi­ neers, electrical engineers, systems engineers, mathematical biologists, mathemati­ cal economists, and statisticians engaged in multivariate analysis will find this book extremely useful. The material presented in this work is fundamental for studies in differential geometry and for analysis in N dimensions and on manifolds. It is also of interest to anyone working in the areas of general relativity, dynamical systems, fluid mechanics, electromagnetic phenomena, plasma dynamics, control theory, and optimization, to name only several. An earlier work entitled An Introduction to Analysis: from Number to Integral by Jan and Piotr Mikusinski was devoted to analyzing functions of a single variable. As indicated by the title, this present book concentrates on multivariable analysis and is completely self-contained. Our motivation and approach to this useful subject are discussed below. A careful study of analysis is difficult enough for the average student; that of multi variable analysis is an even greater challenge. Somehow the intuitions that served so well in dimension I grow weak, even useless, as one moves into the alien territory of dimension N. Worse yet, the very useful machinery of differential forms on manifolds presents particular difficulties; as one reviewer noted, it seems as though the more precisely one presents this machinery, the harder it is to understand.

### Keywords

Mathematica applied mathematics calculus differential geometry ksa measure theory multivariable analysis theoretical physics

#### Authors and affiliations

• Piotr Mikusiński
• 1
• Michael D. Taylor
• 1
1. 1.Department of MathematicsUniversity of Central FloridaOrlandoUSA

### Bibliographic information

• DOI https://doi.org/10.1007/978-1-4612-0073-4
• Copyright Information Birkhäuser Boston 2002
• Publisher Name Birkhäuser, Boston, MA
• eBook Packages
• Print ISBN 978-1-4612-6600-6
• Online ISBN 978-1-4612-0073-4
• Buy this book on publisher's site