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This superb and self-contained work is an introductory presentation of basic ideas, structures, and results of differential and integral calculus for functions of several variables. The wide range of topics covered include the differential calculus of several variables, including that of Banach spaces.
FORMATPaperback LANGUAGEEnglish CONDITIONBrand New Publisher Description
This self-contained work is an introductory presentation of basic ideas, structures, and results of differential and integral calculus for functions of several variables.The wide range of topics covered include: differential calculus of several variables, including differential calculus of Banach spaces, the relevant results of Lebesgue integration theory, differential forms on curves, a general introduction to holomorphic functions, including singularities and residues, surfaces and level sets, and systems and stability of ordinary differential equations. An appendix highlights important mathematicians and other scientists whose contributions have made a great impact on the development of theories in analysis.Mathematical Analysis: An Introduction to Functions of Several Variables motivates the study of the analysis of several variables 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, Mathematical Analysis: Approximation and Discrete Processes, and Mathematical Analysis: Linear and Metric Structures and Continuity, all of which provide the reader with a strong foundation in modern-day analysis.
Notes
This self-contained work is an introductory presentation of basic ideas, structures, and results of differential and integral calculus for functions of several variables. Mathematical Analysis: An Introduction to Functions of Several Variables motivates the study of the analysis of several variables 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.
Back Cover
This text introduces basic ideas, structures, and results of differential and integral calculus for functions of several variables. The presentation is engaging and motivates the reader with numerous examples, remarks, illustrations, and exercises. Mathematical Analysis: An Introduction to Functions of Several Variables may be used in the classroom setting for advanced undergraduate and graduate students or as a self-study. It is also a valuable reference for researchers in most mathematical disciplines. An appendix highlights mathematicians and scientists who have made important contributions in the development of theories in the subject. Other books recently published by the authors include: Mathematical Analysis: Functions of One Variable, Mathematical Analysis: Approximation and Discrete Processes, and Mathematical Analysis: Linear and Metric Structures and Continuity, all of which provide the reader with a strong foundation in modern-day analysis. Reviews of previous volumes in 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 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
Author Biography
Giaquinto is with the University of Pisa.
Table of Contents
Differential Calculus.- Integral Calculus.- Curves and Differential Forms.- Holomorphic Functions.- Surfaces and Level Sets.- Systems of Ordinary Differential Equations.
Review
From the reviews:"This is a comprehensive introduction to the study of functions of several variables that includes several areas not commonly included in comparable textbooks. … The Current book has a generally broader scope … . There is a huge amount of mathematics here, presented carefully and with style. … The treatment of holomorphic functions here is nicely done … . In the end, I find that this text would be an agreeable source for most of its individual topics … ." (William J. Satzer, The Mathematical Association of America, August, 2009)"This is a classical textbook on functions of several variables. On 348 pages it covers the content of a graduate course of mathematical analysis devoted to the higher dimensional spaces. … The textbook is suitable for students of mathematics, physics, engineering and technology, as well as for researchers." (Vladimír Janiš, Zentralblatt MATH, Vol. 1177, 2010)"This is a part of an ampler project of the authors … . The applications and the examples included in the book make it more attractive. There are also exercises at the end of each chapter. … will supply the reader with a fairly complete account of the fundamental results in mathematical analysis and applications, including Lebesgue integration in Rn and complex analysis of one variable. … can be used for courses in real or complex analysis and their applications." (Tiberiu Trif, Studia Universitatis Babes-Bolyai, Mathematica, Vol. LV (4), December, 2010)"This is a textbook on analysis of functions of several real variables and of functions of one complex variable. … The book is concise and nicely written and may well serve as source for (graduate) courses in the areas covered as well as a textbook for students and as a reference book for the working mathematician." (R. Steinbauer, Monatshefte für Mathematik, Vol. 165 (3-4), March, 2012)
Long Description
This self-contained work is an introductory presentation of basic ideas, structures, and results of differential and integral calculus for functions of several variables. The wide range of topics covered include: differential calculus of several variables, including differential calculus of Banach spaces, the relevant results of Lebesgue integration theory, differential forms on curves, a general introduction to holomorphic functions, including singularities and residues, surfaces and level sets, and systems and stability of ordinary differential equations. An appendix highlights important mathematicians and other scientists whose contributions have made a great impact on the development of theories in analysis. Mathematical Analysis: An Introduction to Functions of Several Variables motivates the study of the analysis of several variables 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, Mathematical Analysis: Approximation and Discrete Processes, and Mathematical Analysis: Linear and Metric Structures and Continuity , all of which provide the reader with a strong foundation in modern-day analysis.
Review Quote
From the reviews: "This is a comprehensive introduction to the study of functions of several variables that includes several areas not commonly included in comparable textbooks. ... The Current book has a generally broader scope ... . There is a huge amount of mathematics here, presented carefully and with style. ... The treatment of holomorphic functions here is nicely done ... . In the end, I find that this text would be an agreeable source for most of its individual topics ... ." (William J. Satzer, The Mathematical Association of America, August, 2009) "This is a classical textbook on functions of several variables. On 348 pages it covers the content of a graduate course of mathematical analysis devoted to the higher dimensional spaces. ... The textbook is suitable for students of mathematics, physics, engineering and technology, as well as for researchers." (Vladim
Feature
Introductory text for analysis of functions of several variables Covers wide range of topics and applications Motivates the topics with examples, observations, exercises, and illustrations Exciting historical background motivates the subject
Description for Sales People
This self-contained work is an introductory presentation of basic ideas, structures, and results of differential and integral calculus for functions of several variables. Mathematical Analysis: An Introduction to Functions of Several Variables motivates the study of the analysis of several variables 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.
Details ISBN0817645071 Author Giuseppe Modica Language English ISBN-10 0817645071 ISBN-13 9780817645076 Media Book Format Paperback Imprint Birkhauser Boston Inc Subtitle An Introduction to Functions of Several Variables Place of Publication Secaucus Country of Publication United States Birth 1947 Short Title MATHEMATICAL ANALYSIS 2009/E Pages 348 Edition 2009th DOI 10.1007/978-0-8176-4612-7 Year 2009 Publication Date 2009-12-01 UK Release Date 2009-12-01 AU Release Date 2009-12-01 NZ Release Date 2009-12-01 US Release Date 2009-12-01 Illustrations 105 Illustrations, black and white; XII, 348 p. 105 illus. Publisher Birkhauser Boston Inc Edition Description 2009 ed. Alternative 9780817645090 DEWEY 515.84 Audience Professional & Vocational We've got this
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