Excursions in calculus: an interplay of the continuous and the discrete
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Washington, DC
Mathematical Assoc. of America
1992
|
| Schriftenreihe: | The Dolciani mathematical expositions
13 |
| Schlagwörter: | |
| Links: | 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 |
| Umfang: | XIV, 417 S. Ill., graph. Darst. |
| ISBN: | 0883853175 |
Internformat
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| 264 | 1 | |a Washington, DC |b Mathematical Assoc. of America |c 1992 | |
| 300 | |a XIV, 417 S. |b Ill., graph. Darst. | ||
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Datensatz im Suchindex
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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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| id | DE-604.BV008407781 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T09:21:12Z |
| institution | BVB |
| isbn | 0883853175 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-005537720 |
| oclc_num | 26867564 |
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| physical | XIV, 417 S. Ill., graph. Darst. |
| publishDate | 1992 |
| publishDateSearch | 1992 |
| publishDateSort | 1992 |
| publisher | Mathematical Assoc. of America |
| record_format | marc |
| series | The Dolciani mathematical expositions |
| series2 | The Dolciani mathematical expositions |
| 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 |
| url | 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 |
| volume_link | (DE-604)BV001900740 |
| work_keys_str_mv | AT youngrobertm excursionsincalculusaninterplayofthecontinuousandthediscrete |