Mathematical Analysis: Functions of One Variable - Softcover

Giaquinta, Mariano; Modica, Giuseppe

Softcover

ISBN 10: 1461265703 ISBN 13: 9781461265702

Publisher: Birkhäuser, 2012

Synopsis

This self-contained work introduces the main ideas and fundamental methods of analysis at the advanced undergraduate/graduate level. It provides the historical context out of which these concepts emerged, and aims to develop connections between analysis and other mathematical disciplines (e.g., topology and geometry) as well as physics and engineering. A rigorous exposition, numerous examples, beautiful illustrations, good problems, comprehensive bibliography, and index are some of the key features of the book. Excellent for self -study or the classroom.

About this title

From the Back Cover

This self-contained work on linear and metric structures focuses on studying continuity and its applications to finite- and infinite-dimensional spaces.

The book is divided into three parts. The first part introduces the basic ideas of linear and metric spaces, including the Jordan canonical form of matrices and the spectral theorem for self-adjoint and normal operators. The second part examines the role of general topology in the context of metric spaces and includes the notions of homotopy and degree. The third and final part is a discussion on Banach spaces of continuous functions, Hilbert spaces and the spectral theory of compact operators.

Mathematical Analysis: Linear and Metric Structures and Continuity motivates the study of linear and metric structures with examples, observations, exercises, and illustrations. It may be used in the classroom setting or for self-study by advanced undergraduate and graduate students and as a valuable reference for researchers in mathematics, physics, and engineering.

Other books recently published by the authors include: Mathematical Analysis: Functions of One Variable, and Mathematical Analysis: Approximation and Discrete Processes. This book builds upon the discussion in these books to provide the reader with a strong foundation in modern-day analysis.

Review

From the reviews:

"Many teachers and students could benefit from thinking about its unique perspectives."

---SIAM Review

"Giaquinta . . . and Modica . . . present the differential and integral calculus for real functions of a single real variable from a sophisticated point of view. Their book is far better suited as a source of unique perspectives on the logical development of calculus ideas and their physical applications . . . [so that] it will better serve the experienced calculus instructor seeking new approaches to familiar material, or the student who has already mastered the basic ideas and techniques of calculus but wishes to see it all again, 'done right,' . . . Highly recommended."

---CHOICE

"This self-contained book introduces the main ideas and fundamental methods of mathematical analysis without loosing sight of the context in which it was developed and the role played in science, particularly in physics.... Each chapter has a short summary where the most important facts discussed are collected. There is also a large number of exercises inserted at various points into the text.... The book is meant principally for students in mathematics, physics, engineering, and computer science, but it can be used at technological and scientific faculties by anyone who wants to approach these topics."

---ZENTRALBLATT MATH

"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 exericeses with different requirements. The aim of the authors was very successful[ly] realized, and 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

"This is the first of several volumes on analysis by these authors. ... It is essentially a calculus book at the advanced undergraduate level, or an analysis textbook for someone who has never seen calculus before. ... I like this book ... ." (Warren Johnson, The Mathematical Association of America, October, 2009)

Edition details

• Publisher: Birkhäuser
• Publication date: 2012
• Language: English
• ISBN 10: 1461265703
• ISBN 13: 9781461265702
• Binding: Paperback
• Number of pages: 366