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A Course in Multivariable Calculus and Analysis
Buch von Balmohan V. Limaye (u. a.)
Sprache: Englisch

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Beschreibung
This self-contained textbook gives a thorough exposition of multivariable calculus. It can be viewed as a sequel to the one-variable calculus text, A Course in Calculus and Real Analysis, published in the same series. The emphasis is on correlating general concepts and results of multivariable calculus with their counterparts in one-variable calculus. For example, when the general definition of the volume of a solid is given using triple integrals, the authors explain why the shell and washer methods of one-variable calculus for computing the volume of a solid of revolution must give the same answer. Further, the book includes genuine analogues of basic results in one-variable calculus, such as the mean value theorem and the fundamental theorem of calculus.

This book is distinguished from others on the subject: it examines topics not typically covered, such as monotonicity, bimonotonicity, and convexity, together with their relation to partial differentiation, cubature rules for approximate evaluation of double integrals, and conditional as well as unconditional convergence of double series and improper double integrals. Moreover, the emphasis is on a geometric approach to such basic notions as local extremum and saddle point.

Each chapter contains detailed proofs of relevant results, along with numerous examples and a wide collection of exercises of varying degrees of difficulty, making the book useful to undergraduate and graduate students alike. There is also an informative section of "Notes and Comments¿¿ indicating some novel features of the treatment of topics in that chapter as well as references to relevant literature. The only prerequisite for this text is a course in one-variable calculus.
This self-contained textbook gives a thorough exposition of multivariable calculus. It can be viewed as a sequel to the one-variable calculus text, A Course in Calculus and Real Analysis, published in the same series. The emphasis is on correlating general concepts and results of multivariable calculus with their counterparts in one-variable calculus. For example, when the general definition of the volume of a solid is given using triple integrals, the authors explain why the shell and washer methods of one-variable calculus for computing the volume of a solid of revolution must give the same answer. Further, the book includes genuine analogues of basic results in one-variable calculus, such as the mean value theorem and the fundamental theorem of calculus.

This book is distinguished from others on the subject: it examines topics not typically covered, such as monotonicity, bimonotonicity, and convexity, together with their relation to partial differentiation, cubature rules for approximate evaluation of double integrals, and conditional as well as unconditional convergence of double series and improper double integrals. Moreover, the emphasis is on a geometric approach to such basic notions as local extremum and saddle point.

Each chapter contains detailed proofs of relevant results, along with numerous examples and a wide collection of exercises of varying degrees of difficulty, making the book useful to undergraduate and graduate students alike. There is also an informative section of "Notes and Comments¿¿ indicating some novel features of the treatment of topics in that chapter as well as references to relevant literature. The only prerequisite for this text is a course in one-variable calculus.
Über den Autor

Sudhir R. Ghorpade is Institute Chair Professor in the Department of Mathematics at the Indian Institute of Technology (IIT) Bombay. He has received several awards, including the All India Council for Technical Education (AICTE) Career Award for Young Teachers and the Prof. S.C. Bhattacharya Award for Excellence in Pure Sciences. His research interests lie in algebraic geometry, combinatorics, coding theory, and commutative algebra.

Balmohan V. Limaye is Professor Emeritus in the Department of Mathematics at the Indian Institute of Technology (IIT) Bombay. He is the author of several research monographs and textbooks, including Linear Functional Analysis for Scientists and Engineers (Springer, 2016). He worked at IIT Bombay for more than 40 years and has twice received the Award for Excellence in Teaching from IIT Bombay. His research interests include Banach algebras, approximation theory, numerical functional analysis, and linear algebra.

The authors' companion volume A Course in Calculus and Real Analysis, 2e (2018) is also in the UTM series.

Zusammenfassung

Neatly ties up multivariable calculus with its relics in one variable calculus

Caters to theoretical as well as practical aspects of multivariable calculus

Contains extensive material on topics not typically covered in multivariable calculus textbooks, such as: monotonicity and bimonotonicity of functions of two variables and their relationship with partial differentiation; higher order directional derivatives and their use in Taylor's Theorem

Includes supplementary material: [...]

Inhaltsverzeichnis
Vectors and Functions.- Sequences, Continuity, and Limits.- Partial and Total Differentiation.- Applications of Partial Differentiation.- Multiple Integration.- Applications and Approximations of Multiple Integrals.- Double Series and Improper Double Integrals.
Details
Erscheinungsjahr: 2009
Fachbereich: Analysis
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Seiten: 488
Reihe: Undergraduate Texts in Mathematics
Inhalt: xii
477 S.
279 s/w Illustr.
74 farbige Illustr.
477 p. 353 illus.
74 illus. in color.
ISBN-13: 9781441916204
ISBN-10: 1441916202
Sprache: Englisch
Herstellernummer: 12542772
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Limaye, Balmohan V.
Ghorpade, Sudhir R.
Auflage: 2010
Hersteller: Springer US
Springer New York
Undergraduate Texts in Mathematics
Maße: 241 x 160 x 35 mm
Von/Mit: Balmohan V. Limaye (u. a.)
Erscheinungsdatum: 10.12.2009
Gewicht: 0,982 kg
preigu-id: 101475479
Über den Autor

Sudhir R. Ghorpade is Institute Chair Professor in the Department of Mathematics at the Indian Institute of Technology (IIT) Bombay. He has received several awards, including the All India Council for Technical Education (AICTE) Career Award for Young Teachers and the Prof. S.C. Bhattacharya Award for Excellence in Pure Sciences. His research interests lie in algebraic geometry, combinatorics, coding theory, and commutative algebra.

Balmohan V. Limaye is Professor Emeritus in the Department of Mathematics at the Indian Institute of Technology (IIT) Bombay. He is the author of several research monographs and textbooks, including Linear Functional Analysis for Scientists and Engineers (Springer, 2016). He worked at IIT Bombay for more than 40 years and has twice received the Award for Excellence in Teaching from IIT Bombay. His research interests include Banach algebras, approximation theory, numerical functional analysis, and linear algebra.

The authors' companion volume A Course in Calculus and Real Analysis, 2e (2018) is also in the UTM series.

Zusammenfassung

Neatly ties up multivariable calculus with its relics in one variable calculus

Caters to theoretical as well as practical aspects of multivariable calculus

Contains extensive material on topics not typically covered in multivariable calculus textbooks, such as: monotonicity and bimonotonicity of functions of two variables and their relationship with partial differentiation; higher order directional derivatives and their use in Taylor's Theorem

Includes supplementary material: [...]

Inhaltsverzeichnis
Vectors and Functions.- Sequences, Continuity, and Limits.- Partial and Total Differentiation.- Applications of Partial Differentiation.- Multiple Integration.- Applications and Approximations of Multiple Integrals.- Double Series and Improper Double Integrals.
Details
Erscheinungsjahr: 2009
Fachbereich: Analysis
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Seiten: 488
Reihe: Undergraduate Texts in Mathematics
Inhalt: xii
477 S.
279 s/w Illustr.
74 farbige Illustr.
477 p. 353 illus.
74 illus. in color.
ISBN-13: 9781441916204
ISBN-10: 1441916202
Sprache: Englisch
Herstellernummer: 12542772
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Limaye, Balmohan V.
Ghorpade, Sudhir R.
Auflage: 2010
Hersteller: Springer US
Springer New York
Undergraduate Texts in Mathematics
Maße: 241 x 160 x 35 mm
Von/Mit: Balmohan V. Limaye (u. a.)
Erscheinungsdatum: 10.12.2009
Gewicht: 0,982 kg
preigu-id: 101475479
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