# Derivatives and Integrals of Multivariable Functions

## Alberto Guzman

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This work provides a systematic examination of derivatives and integrals of multivariable functions. The approach taken here is similar to that of the author’s previous text, "Continuous Functions of Vector Variables": specifically, elementary results from single-variable calculus are extended to functions in several-variable Euclidean space. Topics encompass differentiability, partial derivatives, directional derivatives and the gradient; curves, surfaces, and vector fields; the inverse and implicit function theorems; integrability and properties of integrals; and the theorems of Fubini, Stokes, and Gauss. Prerequisites include background in linear algebra, one-variable calculus, and some acquaintance with continuous functions and the topology of the real line.

Written in a definition-theorem-proof format, the book is replete with historical comments, questions, and discussions about strategy, difficulties, and alternate paths.  "Derivatives and Integrals of Multivariable Functions" is a rigorous introduction to multivariable calculus that will help students build a foundation for further explorations in analysis and differential geometry.

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Review:

"Guzman . . . offers a well-crafted treatment of this standard material, intentionally more advanced than in the most widely used books. . . . With that emphasis on the theoretical aspects of the subject, the book will appeal . . . to students intending ultimately to pursue graduate work in mathematics . . . Recommended."

CHOICE

"The book under review presents a systematic introduction to the calculus of real functions of several variables.... The presentation of the material is very clear throughout. Proofs are carefully worked out, theorems are illustrated by examples, and exercises at the end of each section will help to master the calculus. The book is highly recommendable to students to build a foundation for further studies in analysis and differential geometry."

―ZENTRALBLATT MATH

"The book is evidently intended for undergraduate courses and opens the way for abstract generalization and exploring analysis, differential geometry and maybe also physics. The book is written very carefully and rigorously. The style is easily understandable with many comments supporting understanding. Problems with solutions at the end of the book are included.  This book together with the above mentioned volume of A. Guzman is a nice source for a one year course at the undergraduate level." ---Mathematica Bohemica

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## 1.Derivatives and Integrals of Multivariable Functions (Paperback)

Editore: Birkhauser Boston, Germany (2003)
ISBN 10: 0817642749 ISBN 13: 9780817642747
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Descrizione libro Birkhauser Boston, Germany, 2003. Paperback. Condizione libro: New. 2003 ed.. Language: English . Brand New Book ***** Print on Demand *****.This work provides a systematic examination of derivatives and integrals of multivariable functions. The approach taken here is similar to that of the author s previous text, Continuous Functions of Vector Variables : specifically, elementary results from single-variable calculus are extended to functions in several-variable Euclidean space. Topics encompass differentiability, partial derivatives, directional derivatives and the gradient; curves, surfaces, and vector fields; the inverse and implicit function theorems; integrability and properties of integrals; and the theorems of Fubini, Stokes, and Gauss. Prerequisites include background in linear algebra, one-variable calculus, and some acquaintance with continuous functions and the topology of the real line. Written in a definition-theorem-proof format, the book is replete with historical comments, questions, and discussions about strategy, difficulties, and alternate paths. Derivatives and Integrals of Multivariable Functions is a rigorous introduction to multivariable calculus that will help students build a foundation for further explorations in analysis and differential geometry. Codice libro della libreria AAV9780817642747

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## 2.Derivatives and Integrals of Multivariable Functions (Paperback)

Editore: Birkhauser Boston, Germany (2003)
ISBN 10: 0817642749 ISBN 13: 9780817642747
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Descrizione libro Birkhauser Boston, Germany, 2003. Paperback. Condizione libro: New. 2003 ed.. Language: English . This book usually ship within 10-15 business days and we will endeavor to dispatch orders quicker than this where possible. Brand New Book. This work provides a systematic examination of derivatives and integrals of multivariable functions. The approach taken here is similar to that of the author s previous text, Continuous Functions of Vector Variables : specifically, elementary results from single-variable calculus are extended to functions in several-variable Euclidean space. Topics encompass differentiability, partial derivatives, directional derivatives and the gradient; curves, surfaces, and vector fields; the inverse and implicit function theorems; integrability and properties of integrals; and the theorems of Fubini, Stokes, and Gauss. Prerequisites include background in linear algebra, one-variable calculus, and some acquaintance with continuous functions and the topology of the real line. Written in a definition-theorem-proof format, the book is replete with historical comments, questions, and discussions about strategy, difficulties, and alternate paths. Derivatives and Integrals of Multivariable Functions is a rigorous introduction to multivariable calculus that will help students build a foundation for further explorations in analysis and differential geometry. Codice libro della libreria LIE9780817642747

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## 3.Derivatives and Integrals of Multivariable Functions

Editore: BirkhÃ¤user (2016)
ISBN 10: 0817642749 ISBN 13: 9780817642747
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Descrizione libro BirkhÃ¤user, 2016. Paperback. Condizione libro: New. PRINT ON DEMAND Book; New; Publication Year 2016; Not Signed; Fast Shipping from the UK. No. book. Codice libro della libreria ria9780817642747_lsuk

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## 4.Derivatives and Integrals of Multivariable Functions

Editore: Birkhauser Boston (2003)
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Descrizione libro Birkhauser Boston, 2003. PAP. Condizione libro: New. New Book. Delivered from our UK warehouse in 3 to 5 business days. THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000. Codice libro della libreria LQ-9780817642747

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## 5.Derivatives and Integrals of Multivariable Functions

Editore: BirkhÃ¤user (2003)
ISBN 10: 0817642749 ISBN 13: 9780817642747
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Descrizione libro BirkhÃ¤user, 2003. Paperback. Condizione libro: NEW. 9780817642747 This listing is a new book, a title currently in-print which we order directly and immediately from the publisher. Codice libro della libreria HTANDREE0411755

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## 6.Derivatives and Integrals of Multivariable Functions (Paperback)

Editore: Birkhauser Boston, Germany (2003)
ISBN 10: 0817642749 ISBN 13: 9780817642747
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Descrizione libro Birkhauser Boston, Germany, 2003. Paperback. Condizione libro: New. 2003 ed.. Language: English . Brand New Book ***** Print on Demand *****. This work provides a systematic examination of derivatives and integrals of multivariable functions. The approach taken here is similar to that of the author s previous text, Continuous Functions of Vector Variables : specifically, elementary results from single-variable calculus are extended to functions in several-variable Euclidean space. Topics encompass differentiability, partial derivatives, directional derivatives and the gradient; curves, surfaces, and vector fields; the inverse and implicit function theorems; integrability and properties of integrals; and the theorems of Fubini, Stokes, and Gauss. Prerequisites include background in linear algebra, one-variable calculus, and some acquaintance with continuous functions and the topology of the real line. Written in a definition-theorem-proof format, the book is replete with historical comments, questions, and discussions about strategy, difficulties, and alternate paths. Derivatives and Integrals of Multivariable Functions is a rigorous introduction to multivariable calculus that will help students build a foundation for further explorations in analysis and differential geometry. Codice libro della libreria AAV9780817642747

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## 7.Derivatives and Integrals of Multivariable Functions

Editore: Birkhauser Boston (2003)
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Descrizione libro Birkhauser Boston, 2003. PAP. Condizione libro: New. New Book. Shipped from US within 10 to 14 business days. THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000. Codice libro della libreria IQ-9780817642747

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## 8.Derivatives and Integrals of Multivariable Functions

Editore: Birkhäuser (2013)
ISBN 10: 0817642749 ISBN 13: 9780817642747
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Descrizione libro Birkhäuser, 2013. Condizione libro: New. This item is printed on demand for shipment within 3 working days. Codice libro della libreria LP9780817642747

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## 9.Derivatives and Integrals of Multivariable Functions

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Descrizione libro Birkh?user. Condizione libro: Brand New. Ships from USA. FREE domestic shipping. Codice libro della libreria 0817642749

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## 10.Derivatives and Integrals of Multivariable Functions

Editore: Birkhäuser (2003)
ISBN 10: 0817642749 ISBN 13: 9780817642747
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Descrizione libro Birkhäuser, 2003. Paperback. Condizione libro: New. book. Codice libro della libreria 0817642749

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