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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From the Back Cover:

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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Hairer, Ernst
Editore: Springer 2008-06 (2008)
ISBN 10: 0387770313 ISBN 13: 9780387770314
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Descrizione libro Springer 2008-06, 2008. Condizione libro: 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. Codice libro della libreria NU-LSI-07008098

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Gerhard Wanner, Ernst Hairer
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Descrizione libro Springer-Verlag New York Inc., United States, 2008. Paperback. Condizione libro: New. 1st ed. 1996. 2nd printing 2008. Language: English . Brand New Book ***** Print on Demand *****. 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. Codice libro della libreria AAV9780387770314

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Ernst Hairer, Gerhard Wanner
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Descrizione libro Springer-Verlag New York Inc., United States, 2008. Paperback. Condizione libro: New. 1st ed. 1996. 2nd printing 2008. Language: English . Brand New Book ***** Print on Demand *****.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. Codice libro della libreria AAV9780387770314

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Gerhard Wanner, Ernst Hairer
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Descrizione libro Springer-Verlag New York Inc., United States, 2008. Paperback. Condizione libro: 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. Codice libro della libreria LIE9780387770314

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Descrizione libro Springer. Condizione libro: Brand New. Ships from USA. FREE domestic shipping. Codice libro della libreria 0387770313

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Descrizione libro Springer-Verlag New York Inc., 2008. 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-9780387770314

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Descrizione libro Springer, 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 ria9780387770314_lsuk

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Descrizione libro Springer-Verlag New York Inc., 2008. 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-9780387770314

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Descrizione libro Springer, 2008. Paperback. Condizione libro: NEW. 9780387770314 This listing is a new book, a title currently in-print which we order directly and immediately from the publisher. Codice libro della libreria HTANDREE0274499

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Descrizione libro Springer, 2008. Paperback. Condizione libro: New. This item is printed on demand. Codice libro della libreria DADAX0387770313

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