Holdings: Excursions in calculus

Excursions in calculus: an interplay of the continuous and the discrete

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Bibliographic Details
Main Author:	Young, Robert M. (Author)
Format:	Book
Language:	English
Published:	Washington, DC Mathematical Assoc. of America 1992
Series:	The Dolciani mathematical expositions 13
Subjects:	Analyse (wiskunde) Calcul infinitésimal Calculus Mathematik Aufgabensammlung
Online Access:	Inhaltsverzeichnis
Physical Description:	XIV, 417 S. Ill., graph. Darst.
ISBN:	0883853175

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Record in the Search Index

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adam_text	CONTENTS Preface ix Chapter 1. Infinite Ascent, Infinite Descent: The Principle of Mathematical Induction 3 1. Patterns 4 Problems 9 2. Proof by Induction 15 Problems 18 3. Applications 22 Problems 34 4. Infinite Descent 38 Problems 53 Chapter 2. Patterns, Polynomials, and Primes: Three Applications of the Binomial Theorem 57 1. Disorder among the Primes 58 Problems 70 2. Summing the Powers of the Integers 74 Problems 94 3. Two Theorems of Fermat, the Little and the Great 100 Problems 114 Chapter 3. Fibonacci Numbers: Function and Form 123 1. Elementary Properties 125 Problems 134 xiii Xiv EXCURSIONS IN CALCULUS 2. The Golden Ratio 140 Problems 154 3. Generating Functions 159 Problems 164 4. Iterated Functions: From Order to Chaos 170 Problems 180 Chapter 4. On the Average 185 1. The Theorem of the Means 186 Problems 197 2. The Law of Errors 206 Problems 216 3. Variations on a Theme 219 Problems 239 Chapter 5. Approximation: From Pi to the Prime Number Theorem 247 1. Luck Runs in Circles 248 Problems 255 2. On the Probability Integral 267 Problems 272 3. Polynomial Approximation and the Dirac Delta Function 274 Problems 282 4. Euler s Proof of the Infinitude of the Primes 287 Problems 293 5. The Prime Number Theorem 296 Problems 306 Chapter 6. Infinite Sums: A Potpourri 309 1. Geometry and the Geometric Series 310 Problems 328 2. Summing the Reciprocals of the Squares 338 Problems 349 3. The Pentagonal Number Theorem 357 Appendix: The Congruence Notation 369 Problems 375 References 379 Sources for Solutions 397 Index 409
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indexdate	2024-07-09T17:19:13Z
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isbn	0883853175
language	English
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physical	XIV, 417 S. Ill., graph. Darst.
publishDate	1992
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series	The Dolciani mathematical expositions
series2	The Dolciani mathematical expositions
spelling	Young, Robert M. Verfasser aut Excursions in calculus an interplay of the continuous and the discrete Robert M. Young Washington, DC Mathematical Assoc. of America 1992 XIV, 417 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier The Dolciani mathematical expositions 13 Analyse (wiskunde) gtt Calcul infinitésimal Calculus Mathematik (DE-588)4037944-9 gnd rswk-swf (DE-588)4143389-0 Aufgabensammlung gnd-content Mathematik (DE-588)4037944-9 s DE-604 The Dolciani mathematical expositions 13 (DE-604)BV001900740 13 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005537720&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Young, Robert M. Excursions in calculus an interplay of the continuous and the discrete The Dolciani mathematical expositions Analyse (wiskunde) gtt Calcul infinitésimal Calculus Mathematik (DE-588)4037944-9 gnd
subject_GND	(DE-588)4037944-9 (DE-588)4143389-0
title	Excursions in calculus an interplay of the continuous and the discrete
title_auth	Excursions in calculus an interplay of the continuous and the discrete
title_exact_search	Excursions in calculus an interplay of the continuous and the discrete
title_full	Excursions in calculus an interplay of the continuous and the discrete Robert M. Young
title_fullStr	Excursions in calculus an interplay of the continuous and the discrete Robert M. Young
title_full_unstemmed	Excursions in calculus an interplay of the continuous and the discrete Robert M. Young
title_short	Excursions in calculus
title_sort	excursions in calculus an interplay of the continuous and the discrete
title_sub	an interplay of the continuous and the discrete
topic	Analyse (wiskunde) gtt Calcul infinitésimal Calculus Mathematik (DE-588)4037944-9 gnd
topic_facet	Analyse (wiskunde) Calcul infinitésimal Calculus Mathematik Aufgabensammlung
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