Functions Of Several Real Variables

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9789814299275: Functions Of Several Real Variables
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THIS BOOK BEGINS WITH THE BASICS OF THE GEOMETRY AND TOPOLOGY OF EUCLIDEAN SPACE AND CONTINUES WITH THE MAIN TOPICS IN THE THEORY OF FUNCTIONS OF SEVERAL REAL VARIABLES INCLUDING LIMITS, CONTINUITY, DIFFERENTIATION AND INTEGRATION. ALL TOPICS AND IN PARTICULAR, DIFFERENTIATION AND INTEGRATION, ARE TREATED IN DEPTH AND WITH MATHEMATICAL RIGOR. THE CLASSICAL THEOREMS OF DIFFERENTIATION AND INTEGRATION SUCH AS THE INVERSE AND IMPLICIT FUNCTION THEOREMS, LAGRANGES MULTIPLIER RULE, FUBINIS THEOREM, THE CHANGE OF VARIABLES FORMULA, GREENS, STOKES AND GAUSS THEOREMS ARE PROVED IN DETAIL AND MANY OF THEM WITH NOVEL PROOFS. THE AUTHORS DEVELOP THE THEORY IN A LOGICAL SEQUENCE BUILDING ONE RESULT UPON THE OTHER, ENRICHING THE DEVELOPMENT WITH NUMEROUS EXPLANATORY REMARKS AND HISTORICAL FOOTNOTES. A NUMBER OF WELL CHOSEN ILLUSTRATIVE EXAMPLES AND COUNTER-EXAMPLES CLARIFY MATTERS AND TEACH THE READER HOW TO APPLY THESE RESULTS AND SOLVE PROBLEMS IN MATHEMATICS, THE OTHER SCIENCES AND ECONOMICS.EACH OF THE CHAPTERS CONCLUDES WITH GROUPS OF EXERCISES AND PROBLEMS, MANY OF THEM WITH DETAILED SOLUTIONS WHILE OTHERS WITH HINTS OR FINAL ANSWERS. MORE ADVANCED TOPICS, SUCH AS MORSES LEMMA, SARDS THEOREM , THE WEIERSTRASS APPROXIMATION THEOREM, THE FOURIER TRANSFORM, VECTOR FIELDS ON SPHERES, BROUWERS FIXED POINT THEOREM, WHITNEYS EMBEDDING THEOREM, PICARDS THEOREM, AND HERMITE POLYNOMIALS ARE DISCUSSED IN STARED SECTIONS.

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"This is a nice and almost exhaustive introduction to the theory of functions of several real variables. The volume is a comprehensive introduction to this important field and it is intended for advanced undergraduates or beginning graduate students in mathematics, physics or engineering ... The book is well conceived and well written. It is also richer than many of the current crop of real analysis texts. Teachers wanting a solid and interesting treatment that goes right to the point and does not bore good students with verbose explanations will find this book much to their liking."-- MAA Reviews

"This book is useful for undergraduate students studying calculus. It contains formulations and proofs of the results, and some information, not included usually in the calculus texts. There are many exercises for the students, and for some of the exercises solutions are given." --Zentralblatt MATH

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This book begins with the basics of the geometry and topology of Euclidean space and continues with the main topics in the theory of functions of several real variables including limits, continuity, differentiation and integration. All topics and in particular, differentiation and integration, are treated in depth and with mathematical rigor. The classical theorems of differentiation and integration such as the Inverse and Implicit Function theorems, Lagrange's multiplier rule, Fubini's theorem, the change of variables formula, Green's, Stokes' and Gauss' theorems are proved in detail and many of them with novel proofs. The authors develop the theory in a logical sequence building one result upon the other, enriching the development with numerous explanatory remarks and historical footnotes. A number of well chosen illustrative examples and counter-examples clarify matters and teach the reader how to apply these results and solve problems in mathematics, the other sciences and economics.Each of the chapters concludes with groups of exercises and problems, many of them with detailed solutions while others with hints or final answers. More advanced topics, such as Morse's lemma, Sard's theorem , the Weierstrass approximation theorem, the Fourier transform, Vector fields on spheres, Brouwer's fixed point theorem, Whitney's embedding theorem, Picard's theorem, and Hermite polynomials are discussed in stared sections.

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9789814299268: Functions of Several Real Variables

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ISBN 10:  981429926X ISBN 13:  9789814299268
Editorial: World Scientific Publishing Company, 2011
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Fotios C. Paliogiannis, Martin A. Moskowitz
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Descripción World Scientific Publishing Co Pte Ltd, Singapore, 2011. Paperback. Condición: New. Language: English . Brand New Book. This book begins with the basics of the geometry and topology of Euclidean space and continues with the main topics in the theory of functions of several real variables including limits, continuity, differentiation and integration. All topics and in particular, differentiation and integration, are treated in depth and with mathematical rigor. The classical theorems of differentiation and integration such as the Inverse and Implicit Function theorems, Lagrange s multiplier rule, Fubini s theorem, the change of variables formula, Green s, Stokes and Gauss theorems are proved in detail and many of them with novel proofs. The authors develop the theory in a logical sequence building one result upon the other, enriching the development with numerous explanatory remarks and historical footnotes. A number of well chosen illustrative examples and counter-examples clarify matters and teach the reader how to apply these results and solve problems in mathematics, the other sciences and economics.Each of the chapters concludes with groups of exercises and problems, many of them with detailed solutions while others with hints or final answers. More advanced topics, such as Morse s lemma, Sard s theorem , the Weierstrass approximation theorem, the Fourier transform, Vector fields on spheres, Brouwer s fixed point theorem, Whitney s embedding theorem, Picard s theorem, and Hermite polynomials are discussed in stared sections. Nº de ref. del artículo: AAZ9789814299275

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Descripción World Scientific Publishing Co Pte Ltd, 2011. PAP. Condición: New. New Book. Shipped from US within 10 to 14 business days. Established seller since 2000. Nº de ref. del artículo: IB-9789814299275

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Fotios C. Paliogiannis, Martin A. Moskowitz
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Descripción World Scientific Publishing Co Pte Ltd, Singapore, 2011. Paperback. Condición: New. Language: English . Brand New Book. This book begins with the basics of the geometry and topology of Euclidean space and continues with the main topics in the theory of functions of several real variables including limits, continuity, differentiation and integration. All topics and in particular, differentiation and integration, are treated in depth and with mathematical rigor. The classical theorems of differentiation and integration such as the Inverse and Implicit Function theorems, Lagrange s multiplier rule, Fubini s theorem, the change of variables formula, Green s, Stokes and Gauss theorems are proved in detail and many of them with novel proofs. The authors develop the theory in a logical sequence building one result upon the other, enriching the development with numerous explanatory remarks and historical footnotes. A number of well chosen illustrative examples and counter-examples clarify matters and teach the reader how to apply these results and solve problems in mathematics, the other sciences and economics.Each of the chapters concludes with groups of exercises and problems, many of them with detailed solutions while others with hints or final answers. More advanced topics, such as Morse s lemma, Sard s theorem , the Weierstrass approximation theorem, the Fourier transform, Vector fields on spheres, Brouwer s fixed point theorem, Whitney s embedding theorem, Picard s theorem, and Hermite polynomials are discussed in stared sections. Nº de ref. del artículo: AAZ9789814299275

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MARTIN MOSKOWITZ (author)
Publicado por World Scientific 2011-05-06, Singapore |London (2011)
ISBN 10: 9814299278 ISBN 13: 9789814299275
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Descripción World Scientific 2011-05-06, Singapore |London, 2011. paperback. Condición: New. Nº de ref. del artículo: 9789814299275

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Martin A. Moskowitz, Fotios Paliogiannis
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Descripción World Scientific Publishing Co Pte Ltd. Paperback. Condición: new. BRAND NEW, Functions of Several Real Variables, Martin A. Moskowitz, Fotios Paliogiannis, This book begins with the basics of the geometry and topology of Euclidean space and continues with the main topics in the theory of functions of several real variables including limits, continuity, differentiation and integration. All topics and in particular, differentiation and integration, are treated in depth and with mathematical rigor. The classical theorems of differentiation and integration are proved in detail and many of them with novel proofs. The authors develop the theory in a logical sequence building one theorem upon the other, enriching the development with numerous explanatory remarks and historical footnotes. In this title, a number of well chosen illustrative examples and counter-examples clarify the theory and teach the reader how to apply it to solve problems in mathematics and other sciences and economics. Each of the chapters concludes with groups of exercises and problems, many of them with detailed solutions while others with hints or final answers. More advanced topics, such as Morse's lemma, Brouwer's fixed point theorem, Picard's theorem and the Weierstrass approximation theorem are discussed in stared sections. Nº de ref. del artículo: B9789814299275

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Martin Moskowitz
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ISBN 10: 9814299278 ISBN 13: 9789814299275
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Descripción World Scientific Publishing Co, 2011. Paperback. Condición: New. Never used!. Nº de ref. del artículo: 9814299278

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Moskowitz, Martin A.; Paliogiannis, Fotios
Publicado por World Scientific Publishing Co Pte Ltd (2011)
ISBN 10: 9814299278 ISBN 13: 9789814299275
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Descripción World Scientific Publishing Co Pte Ltd, 2011. Condición: New. 2011. 1st Edition. Paperback. Describes the basics of the geometry and topology of Euclidean space and the main topics in the theory of functions of several real variables including limits, differentiation and integration. This title discusses advanced topics, such as Morse's lemma, Brouwer's fixed point theorem, Picard's theorem and the Weierstrass approximation theorem. Num Pages: 732 pages, black & white illustrations, figures. BIC Classification: PBK. Category: (UP) Postgraduate, Research & Scholarly. Dimension: 227 x 153 x 40. Weight in Grams: 1066. . . . . . . Nº de ref. del artículo: V9789814299275

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Martin Moskowitz; Fotios Paliogiannis
Publicado por World Scientific Publishing Company (2011)
ISBN 10: 9814299278 ISBN 13: 9789814299275
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Descripción World Scientific Publishing Company, 2011. Paperback. Condición: New. Nº de ref. del artículo: INGM9789814299275

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