A radical approach to real analysis:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Washington, DC
Math. Assoc. of America
2007
|
| Edition: | 2. ed. |
| Series: | Classroom resource materials
|
| Subjects: | |
| Online Access: | Table of contents only Contributor biographical information Publisher description Inhaltsverzeichnis |
| Item Description: | Includes index |
| Physical Description: | XVI, 323 s. graph. Darst. 26 cm |
| ISBN: | 9780883857472 0883857472 |
Staff View
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| 245 | 1 | 0 | |a A radical approach to real analysis |c David M. Bressoud |
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Record in the Search Index
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| adam_text |
A RADICAL APPROACH TO REAL ANALYSIS SECOND EDITION DAVID M. BRESSOUD
MACALESTER COLLEGE PUBLISHED AND DISTRIBUTED BY THE MATHEMATICAL
ASSOCIATION OF AMERICA CONTENTS PREFACE IX 1 CRISIS IN MATHEMATICS:
FOURIER'S SERIES 1 1.1 BACKGROUND TO THE PROBLEM 1 1.2 DIFFICULTIES WITH
THE SOLUTION 4 2 INFINITE SUMMATIONS 9 2.1 THE ARCHIMEDEAN UNDERSTANDING
9 2.2 GEOMETRIC SERIES 17 2.3 CALCULATING N 22 2.4 LOGARITHMS AND THE
HARMONIC SERIES 28 2.5 TAYLOR SERIES 38 2.6 EMERGING DOUBTS ;E , 50 3
DIFFERENTIABILITY AND CONTINUITY 57 3.1 DIFFERENTIABILITY 58 3.2 CAUCHY
AND THE MEAN VALUE THEOREMS 71 3.3 CONTINUITY 78 3.4 CONSEQUENCE§-OF
CONTINUITY 95 3.5 CONSEQUENCES OF THE MEAN VALUE THEOREM 105 4 THE
CONVERGENCE OF INFINITE SERIES 117 4.1 THE BASIC TESTS OF CONVERGENCE
118 4.2 COMPARISON TESTS 129 XV XVI CONTENTS 4.3 THE CONVERGENCE OF
POWER SERIES 145 4.4 THE CONVERGENCE OF FOURIER SERIES 158 5
UNDERSTANDING INFINITE SERIES 171 5.1 GROUPINGS AND REARRANGEMENTS 172
5.2 CAUCHY AND CONTINUITY 181 5.3 DIFFERENTIATION AND INTEGRATION 191
5.4 VERIFYING UNIFORM CONVERGENCE 203 6 RETURN TO FOURIER SERIES 217 6.1
DIRICHLET'S THEOREM 218 6.2 THE CAUCHY INTEGRAL 236 6.3 THE RIEMANN
INTEGRAL 248 6.4 CONTINUITY WITHOUT DIFFERENTIABILITY 258 7 EPILOGUE 267
A EXPLORATIONS OF THE INFINITE 271 A.1 WALLIS ON N 271 A.2 BERNOULLI'S
NUMBERS 277 A.3 SUMS OF NEGATIVE POWERS 284 A.4 THE SIZE OF N! 293 B
BIBLIOGRAPHY 303 C HINTS TO SELECTED EXERCISES 305 INDEX 317 |
| adam_txt |
A RADICAL APPROACH TO REAL ANALYSIS SECOND EDITION DAVID M. BRESSOUD
MACALESTER COLLEGE PUBLISHED AND DISTRIBUTED BY THE MATHEMATICAL
ASSOCIATION OF AMERICA CONTENTS PREFACE IX 1 CRISIS IN MATHEMATICS:
FOURIER'S SERIES 1 1.1 BACKGROUND TO THE PROBLEM 1 1.2 DIFFICULTIES WITH
THE SOLUTION 4 2 INFINITE SUMMATIONS 9 2.1 THE ARCHIMEDEAN UNDERSTANDING
9 2.2 GEOMETRIC SERIES 17 2.3 CALCULATING N 22 2.4 LOGARITHMS AND THE
HARMONIC SERIES 28 2.5 TAYLOR SERIES 38 2.6 EMERGING DOUBTS ;E , 50 3
DIFFERENTIABILITY AND CONTINUITY 57 3.1 DIFFERENTIABILITY 58 3.2 CAUCHY
AND THE MEAN VALUE THEOREMS 71 3.3 CONTINUITY 78 3.4 CONSEQUENCE§-OF
CONTINUITY 95 3.5 CONSEQUENCES OF THE MEAN VALUE THEOREM 105 4 THE
CONVERGENCE OF INFINITE SERIES 117 4.1 THE BASIC TESTS OF CONVERGENCE
118 4.2 COMPARISON TESTS 129 XV XVI CONTENTS 4.3 THE CONVERGENCE OF
POWER SERIES 145 4.4 THE CONVERGENCE OF FOURIER SERIES 158 5
UNDERSTANDING INFINITE SERIES 171 5.1 GROUPINGS AND REARRANGEMENTS 172
5.2 CAUCHY AND CONTINUITY 181 5.3 DIFFERENTIATION AND INTEGRATION 191
5.4 VERIFYING UNIFORM CONVERGENCE 203 6 RETURN TO FOURIER SERIES 217 6.1
DIRICHLET'S THEOREM 218 6.2 THE CAUCHY INTEGRAL 236 6.3 THE RIEMANN
INTEGRAL 248 6.4 CONTINUITY WITHOUT DIFFERENTIABILITY 258 7 EPILOGUE 267
A EXPLORATIONS OF THE INFINITE 271 A.1 WALLIS ON N 271 A.2 BERNOULLI'S
NUMBERS 277 A.3 SUMS OF NEGATIVE POWERS 284 A.4 THE SIZE OF N! 293 B
BIBLIOGRAPHY 303 C HINTS TO SELECTED EXERCISES 305 INDEX 317 |
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| callnumber-first | Q - Science |
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| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV023256134 |
| illustrated | Illustrated |
| index_date | 2024-07-02T20:29:55Z |
| indexdate | 2024-07-20T04:10:08Z |
| institution | BVB |
| isbn | 9780883857472 0883857472 |
| language | English |
| lccn | 2006933946 |
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| physical | XVI, 323 s. graph. Darst. 26 cm |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | Math. Assoc. of America |
| record_format | marc |
| series2 | Classroom resource materials |
| spelling | Bressoud, David M. 1950- Verfasser (DE-588)136747221 aut A radical approach to real analysis David M. Bressoud 2. ed. Washington, DC Math. Assoc. of America 2007 XVI, 323 s. graph. Darst. 26 cm txt rdacontent n rdamedia nc rdacarrier Classroom resource materials Includes index Reelle Analysis swd Reelle Funktion swd Mathematical analysis Functions of real variables Reelle Funktion (DE-588)4048918-8 gnd rswk-swf Analysis (DE-588)4001865-9 gnd rswk-swf Reelle Funktion (DE-588)4048918-8 s DE-604 Analysis (DE-588)4001865-9 s http://www.loc.gov/catdir/toc/fy0709/2006933946.html Table of contents only http://www.loc.gov/catdir/enhancements/fy0713/2006933946-b.html Contributor biographical information http://www.loc.gov/catdir/enhancements/fy0713/2006933946-d.html Publisher description HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016441410&sequence=000009&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bressoud, David M. 1950- A radical approach to real analysis Reelle Analysis swd Reelle Funktion swd Mathematical analysis Functions of real variables Reelle Funktion (DE-588)4048918-8 gnd Analysis (DE-588)4001865-9 gnd |
| subject_GND | (DE-588)4048918-8 (DE-588)4001865-9 |
| title | A radical approach to real analysis |
| title_auth | A radical approach to real analysis |
| title_exact_search | A radical approach to real analysis |
| title_exact_search_txtP | A radical approach to real analysis |
| title_full | A radical approach to real analysis David M. Bressoud |
| title_fullStr | A radical approach to real analysis David M. Bressoud |
| title_full_unstemmed | A radical approach to real analysis David M. Bressoud |
| title_short | A radical approach to real analysis |
| title_sort | a radical approach to real analysis |
| topic | Reelle Analysis swd Reelle Funktion swd Mathematical analysis Functions of real variables Reelle Funktion (DE-588)4048918-8 gnd Analysis (DE-588)4001865-9 gnd |
| topic_facet | Reelle Analysis Reelle Funktion Mathematical analysis Functions of real variables Analysis |
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