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An Introduction to Multivariable Analysis from Vector to Manifold

  • Textbook
  • © 2002

Overview

Authors:
  1. Piotr Mikusiński

    1. Department of Mathematics, University of Central Florida, Orlando, USA

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    You can also search for this author in PubMed   Google Scholar

  2. Michael D. Taylor

    1. Department of Mathematics, University of Central Florida, Orlando, USA

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    You can also search for this author in PubMed   Google Scholar

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-x
    Download chapter PDF

  2. Vectors and Volumes

    • Piotr Mikusiński, Michael D. Taylor
    Pages 1-41

  3. Metric Spaces

    • Piotr Mikusiński, Michael D. Taylor
    Pages 43-73

  4. Differentiation

    • Piotr Mikusiński, Michael D. Taylor
    Pages 75-112

  5. The Lebesgue Integral

    • Piotr Mikusiński, Michael D. Taylor
    Pages 113-151

  6. Integrals On Manifolds

    • Piotr Mikusiński, Michael D. Taylor
    Pages 153-188

  7. K-Vectors and Wedge Products

    • Piotr Mikusiński, Michael D. Taylor
    Pages 189-217

  8. Vector Analysis on Manifolds

    • Piotr Mikusiński, Michael D. Taylor
    Pages 219-290

  9. Back Matter

    Pages 291-295
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Keywords

About this book

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.

Reviews

"This is a self-contained textbook devoted to multivariable analysis based on nonstandard geometrical methods. The book can be used either as a supplement to a course on single variable analysis or as a semester-long course introducing students to manifolds and differential forms."   —Mathematical Reviews

"The authors strongly motivate the abstract notions by a lot of intuitive examples and pictures. The exercises at the end of each section range from computational to theoretical. The book is highly recommended for undergraduate or graduate courses in multivariable analysis for students in mathematics, physics, engineering, and economics."   —Studia Universitatis Babes-Bolyai, Series Mathematica

"All this [the description on the book's back cover] is absolutely true, but omits any statement attesting to the high quality of the writing and the high level of mathematical scholarship. So, go and order a copy of this attractively produced, and nicely composed, scholarly tome. If you're not teaching this sort of mathematics, this book will inspire you to do so."   —MAA Reviews

Authors and Affiliations

  • Department of Mathematics, University of Central Florida, Orlando, USA

    Piotr Mikusiński, Michael D. Taylor

Bibliographic Information

  • Book Title: An Introduction to Multivariable Analysis from Vector to Manifold

  • Authors: Piotr Mikusiński, Michael D. Taylor

  • DOI: https://doi.org/10.1007/978-1-4612-0073-4

  • Publisher: Birkhäuser Boston, MA

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 2002

  • Hardcover ISBN: 978-0-8176-4234-1Published: 26 November 2001

  • Softcover ISBN: 978-1-4612-6600-6Published: 23 October 2012

  • eBook ISBN: 978-1-4612-0073-4Published: 06 December 2012

  • Edition Number: 1

  • Number of Pages: X, 295

  • Topics: Geometry, Analysis, Several Complex Variables and Analytic Spaces, Applications of Mathematics, Differential Geometry

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