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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 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.
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.
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: [...]
| Erscheinungsjahr: | 2009 |
|---|---|
| Fachbereich: | Analysis |
| Genre: | Mathematik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Buch |
| 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. |
| Hersteller: |
Springer New York
Springer US, New York, N.Y. 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 |
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.
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: [...]
| Erscheinungsjahr: | 2009 |
|---|---|
| Fachbereich: | Analysis |
| Genre: | Mathematik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Buch |
| 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. |
| Hersteller: |
Springer New York
Springer US, New York, N.Y. 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 |
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