Analysis by Its History (Undergraduate Texts in Mathematics)

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9780387770314: Analysis by Its History (Undergraduate Texts in Mathematics)

This book presents first-year calculus roughly in the order in which it was first discovered. The first two chapters show how the ancient calculations of practical problems led to infinite series, differential and integral calculus and to differential equations. The establishment of mathematical rigour for these subjects in the 19th century for one and several variables is treated in chapters III and IV. Many quotations are included to give the flavor of the history. The text is complemented by a large number of examples, calculations and mathematical pictures and will provide stimulating and enjoyable reading for students, teachers, as well as researchers.

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This book presents first-year calculus roughly in the order in which it first was discovered. The first two chapters show how the ancient calculations of practical problems led to infinite series, differential and integral calculus and to differential equations. The establishment of mathematical rigour for these subjects in the 19th century for one and several variables is treated in chapters III and IV. The text is complemented by a large number of examples, calculations and mathematical pictures and will provide stimulating and enjoyable reading for students, teachers, as well as researchers.

 

From the reviews:

The aim of this interesting new contribution to the series Readings in Mathematics is an attempt to restore the historical order in the presentation of basic mathematical analysis...such a historical approach can provide a very fruitful and interesting approach to mathematical analysis.

- Jean Mawhin, Zentralblatt

The authors include a large number of once-traditional subjects which have now vanished from the analysis curriculum, at least in the standard American courses. Thus we find continued fractions, elliptic integrals, the Euler-MacLaurin summation formula, etc., most of which are found only in more compendious works. Many of the exercises are inspired by original papers, with the bibliographic references sometimes given. The work is very well illustrated. The book is definitely an analysis text, rather than a history, but a great deal of reliable historical material is included. For those seeking an alternative to the traditional approach, it seems to me to be of great interest.

- Thomas Archibald, Mathematical Reviews

The authors...have assembled an impressive array of annotated results, quotations, tables, charts, figures and drawings, many copied from original documents....they write with great enthusiasm and with evident affection for both analysis and history.

- John Troutman, American Mathematical Monthly

Review:

"...well done, attractively designed...And above all, it proposes an interesting approach to teaching analysis." Internationale Mathematische Nachrichten

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1.

Gerhard Wanner, Ernst Hairer
Editorial: Springer-Verlag New York Inc., United States (2008)
ISBN 10: 0387770313 ISBN 13: 9780387770314
Nuevos Paperback Cantidad: 1
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The Book Depository
(London, Reino Unido)
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Descripción Springer-Verlag New York Inc., United States, 2008. Paperback. Estado de conservación: New. 1st ed. 1996. 2nd printing 2008. Language: English . Brand New Book. This book presents first-year calculus roughly in the order in which it was first discovered. The first two chapters show how the ancient calculations of practical problems led to infinite series, differential and integral calculus and to differential equations. The establishment of mathematical rigour for these subjects in the 19th century for one and several variables is treated in chapters III and IV. Many quotations are included to give the flavor of the history. The text is complemented by a large number of examples, calculations and mathematical pictures and will provide stimulating and enjoyable reading for students, teachers, as well as researchers. Nº de ref. de la librería LIB9780387770314

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Gerhard Wanner, Ernst Hairer
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ISBN 10: 0387770313 ISBN 13: 9780387770314
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Descripción Springer-Verlag New York Inc., United States, 2008. Paperback. Estado de conservación: New. 1st ed. 1996. 2nd printing 2008. 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 book presents first-year calculus roughly in the order in which it was first discovered. The first two chapters show how the ancient calculations of practical problems led to infinite series, differential and integral calculus and to differential equations. The establishment of mathematical rigour for these subjects in the 19th century for one and several variables is treated in chapters III and IV. Many quotations are included to give the flavor of the history. The text is complemented by a large number of examples, calculations and mathematical pictures and will provide stimulating and enjoyable reading for students, teachers, as well as researchers. Nº de ref. de la librería LIE9780387770314

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Descripción Springer 2008-06, 2008. Estado de conservación: New. This item is printed on demand. Brand new book, sourced directly from publisher. Dispatch time is 24-48 hours from our warehouse. Book will be sent in robust, secure packaging to ensure it reaches you securely. Nº de ref. de la librería NU-LSI-07008098

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Descripción Springer New York 2008-06-02, New York, 2008. paperback. Estado de conservación: New. Nº de ref. de la librería 9780387770314

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Gerhard Wanner, Ernst Hairer
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ISBN 10: 0387770313 ISBN 13: 9780387770314
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Descripción Springer-Verlag New York Inc., United States, 2008. Paperback. Estado de conservación: New. 1st ed. 1996. 2nd printing 2008. Language: English . Brand New Book. This book presents first-year calculus roughly in the order in which it was first discovered. The first two chapters show how the ancient calculations of practical problems led to infinite series, differential and integral calculus and to differential equations. The establishment of mathematical rigour for these subjects in the 19th century for one and several variables is treated in chapters III and IV. Many quotations are included to give the flavor of the history. The text is complemented by a large number of examples, calculations and mathematical pictures and will provide stimulating and enjoyable reading for students, teachers, as well as researchers. Nº de ref. de la librería LIB9780387770314

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Ernst Hairer; Gerhard Wanner
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Descripción Springer, 2008. Estado de conservación: New. Nº de ref. de la librería L9780387770314

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Descripción Springer-Verlag New York Inc., 2008. PAP. Estado de conservación: New. New Book. Shipped from US within 10 to 14 business days. THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000. Nº de ref. de la librería IQ-9780387770314

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Descripción Springer, 2016. Paperback. Estado de conservación: New. PRINT ON DEMAND Book; New; Publication Year 2016; Not Signed; Fast Shipping from the UK. No. book. Nº de ref. de la librería ria9780387770314_lsuk

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Gerhard Wanner
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Descripción Springer-Verlag New York Inc., 2008. PAP. Estado de conservación: New. New Book. Delivered from our UK warehouse in 3 to 5 business days. THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000. Nº de ref. de la librería LQ-9780387770314

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ERNST HAIRER
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Descripción Springer, 2008. Paperback. Estado de conservación: NEW. 9780387770314 This listing is a new book, a title currently in-print which we order directly and immediately from the publisher. Nº de ref. de la librería HTANDREE0274499

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