Mathematical Analysis

Foundations and Advanced Techniques for Functions of Several Variables

Authors: Giaquinta, Mariano, Modica, Giuseppe

  • Provides theoretical foundation for analysis of functions of several variables
  • Motivates the topics with examples, observations, exercises, and illustrations
  • Includes appendix of mathematicians who made important contributions to analysis
  • Exciting historical background motivates the subject
see more benefits

Buy this book

eBook $59.99
price for USA (gross)
  • ISBN 978-0-8176-8310-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $79.99
price for USA
  • ISBN 978-0-8176-8309-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the eBook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
About this Textbook

Mathematical Analysis: Foundations and Advanced Techniques for Functions of Several Variables builds upon the basic ideas and techniques of differential and integral calculus for functions of several variables, as outlined in an earlier introductory volume. The presentation is largely focused on the foundations of measure and integration theory.

The book begins with a discussion of the geometry of Hilbert spaces, convex functions and domains, and differential forms, particularly k-forms. The exposition continues with an introduction to the calculus of variations with applications to geometric optics and mechanics. The authors conclude with the study of measure and integration theory – Borel, Radon, and Hausdorff measures and the derivation of measures. An appendix highlights important mathematicians and other scientists whose contributions have made a great impact on the development of theories in analysis.

This work may be used as a supplementary text in the classroom or for self-study by advanced undergraduate and graduate students and as a valuable reference for researchers in mathematics, physics, and engineering. One of the key strengths of this presentation, along with the other four books on analysis published by the authors, is the motivation for understanding the subject through examples, observations, exercises, and illustrations.

Table of contents (6 chapters)

  • Spaces of Summable Functions and Partial Differential Equations

    Giaquinta, Mariano (et al.)

    Pages 1-65

  • Convex Sets and Convex Functions

    Giaquinta, Mariano (et al.)

    Pages 67-148

  • The Formalism of the Calculus of Variations

    Giaquinta, Mariano (et al.)

    Pages 149-212

  • Differential Forms

    Giaquinta, Mariano (et al.)

    Pages 213-282

  • Measures and Integration

    Giaquinta, Mariano (et al.)

    Pages 283-338

Buy this book

eBook $59.99
price for USA (gross)
  • ISBN 978-0-8176-8310-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $79.99
price for USA
  • ISBN 978-0-8176-8309-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the eBook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
Loading...

Recommended for you

Loading...

Bibliographic Information

Bibliographic Information
Book Title
Mathematical Analysis
Book Subtitle
Foundations and Advanced Techniques for Functions of Several Variables
Authors
Copyright
2012
Publisher
Birkhäuser Basel
Copyright Holder
Springer Science+Business Media, LLC
eBook ISBN
978-0-8176-8310-8
DOI
10.1007/978-0-8176-8310-8
Hardcover ISBN
978-0-8176-8309-2
Edition Number
1
Number of Pages
XIII, 405
Number of Illustrations and Tables
66 b/w illustrations
Topics