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The Resource Mathematical analysis : foundations and advanced techniques for functions of several variables, Mariano Giaquinta, Giuseppe Modica

Mathematical analysis : foundations and advanced techniques for functions of several variables, Mariano Giaquinta, Giuseppe Modica

Creator
Contributor
Summary
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 authorsconclude 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. Other books published by the authors - all of which provide the reader with a strong foundation in modern-day analysis - include: * Mathematical Analysis: Functions of One Variable * Mathematical Analysis: Approximation and Discrete Processes * Mathematical Analysis: Linear and Metric Structures and Continuity * Mathematical Analysis: An Introduction to Functions of Several Variables Reviews of previous volumes of Mathematical Analysis: The presentation of the theory is clearly arranged, all theorems have rigorous proofs, and every chapter closes with a summing up of the results and exercises with different requirements. ... This book is excellently suitable for students in mathematics, physics, engineering, computer science and all students of technological and scientific faculties.-Journal of Analysis and its Applications The exposition requires only a sound knowledge of calculus and the functions of one variable. A key feature of this lively yet rigorous and systematic treatment is the historical accounts of ideas and methods of the subject. Ideas in mathematics develop in cultural, historical and economical contexts, thus the authors made brief accounts of those aspects and used a large number of beautiful illustrations.-Zentralblatt MATH
Language
eng
Work
Publication
Extent
1 online resource (xiii, 405 pages)
Contents
  • Preface
  • Spaces of Summable Functions and Partial Differential Equations
  • Convex Sets and Convex Functions
  • The Formalism of the Calculus of Variations
  • Differential Forms
  • Measures and Integrations
  • Hausdorff and Radon Measures
  • Mathematicians and Other Scientists
  • Bibliographical Notes
  • Index
Isbn
9780817683108
Instance
Label
Mathematical analysis : foundations and advanced techniques for functions of several variables
Title
Mathematical analysis
Title remainder
foundations and advanced techniques for functions of several variables
Statement of responsibility
Mariano Giaquinta, Giuseppe Modica
Creator
Contributor
Subject
Language
eng
Summary
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 authorsconclude 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. Other books published by the authors - all of which provide the reader with a strong foundation in modern-day analysis - include: * Mathematical Analysis: Functions of One Variable * Mathematical Analysis: Approximation and Discrete Processes * Mathematical Analysis: Linear and Metric Structures and Continuity * Mathematical Analysis: An Introduction to Functions of Several Variables Reviews of previous volumes of Mathematical Analysis: The presentation of the theory is clearly arranged, all theorems have rigorous proofs, and every chapter closes with a summing up of the results and exercises with different requirements. ... This book is excellently suitable for students in mathematics, physics, engineering, computer science and all students of technological and scientific faculties.-Journal of Analysis and its Applications The exposition requires only a sound knowledge of calculus and the functions of one variable. A key feature of this lively yet rigorous and systematic treatment is the historical accounts of ideas and methods of the subject. Ideas in mathematics develop in cultural, historical and economical contexts, thus the authors made brief accounts of those aspects and used a large number of beautiful illustrations.-Zentralblatt MATH
Cataloging source
GW5XE
http://library.link/vocab/creatorDate
1947-
http://library.link/vocab/creatorName
Giaquinta, Mariano
Dewey number
515
Index
index present
Language note
English
LC call number
QA300
LC item number
.G53 2012
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
http://library.link/vocab/relatedWorkOrContributorName
Modica, Giuseppe
http://library.link/vocab/subjectName
  • Mathematical analysis
  • Mathematics
  • Mathematical analysis
Label
Mathematical analysis : foundations and advanced techniques for functions of several variables, Mariano Giaquinta, Giuseppe Modica
Instantiates
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
Preface -- Spaces of Summable Functions and Partial Differential Equations -- Convex Sets and Convex Functions -- The Formalism of the Calculus of Variations -- Differential Forms -- Measures and Integrations -- Hausdorff and Radon Measures -- Mathematicians and Other Scientists -- Bibliographical Notes -- Index
Control code
760288692
Dimensions
unknown
Extent
1 online resource (xiii, 405 pages)
File format
unknown
Form of item
online
Isbn
9780817683108
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-0-8176-8310-8
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
(OCoLC)760288692
Label
Mathematical analysis : foundations and advanced techniques for functions of several variables, Mariano Giaquinta, Giuseppe Modica
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
Preface -- Spaces of Summable Functions and Partial Differential Equations -- Convex Sets and Convex Functions -- The Formalism of the Calculus of Variations -- Differential Forms -- Measures and Integrations -- Hausdorff and Radon Measures -- Mathematicians and Other Scientists -- Bibliographical Notes -- Index
Control code
760288692
Dimensions
unknown
Extent
1 online resource (xiii, 405 pages)
File format
unknown
Form of item
online
Isbn
9780817683108
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-0-8176-8310-8
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
(OCoLC)760288692

Subject

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