An introduction to classical real analysis:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, Rhode Island
AMS Chelsea Publishing
[2015]
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| Ausgabe: | Reprinted with corrections |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Auf der letzten Seite: "This new printing contains a large number of corrections and a short author biography as well as a list of selected publications of the author" |
| Beschreibung: | xiv, 577 Seiten Illustration |
| ISBN: | 9781470425449 |
Internformat
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Datensatz im Suchindex
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| adam_text | CONTENTS ABOUT THE AUTHOR 0 xiii PRELIMINARIES 1 Sets and Subsets Operations on Sets Ordered Pairs and Relations Equivalence Relations Functions Products of Sets 1 Į 2 3 3 4ШШ 5 NUMBERS 7 Axioms for R The Supremum Principle The Natural Numbers Integers Decimal Representation of Natural Numbers Roots Rational and Irrational Numbers Complex Numbers Some Inequalities Extended Real Numbers Finite and Infinite Sets Newton’s Binomial Theorem Exercises v 8 Į2 13 16 17 20 21 22 24 27 28 33 35
ví 2 3 CONTENTS SEQUENCES AND SERIES 39 Sequences in C Sequences in R# Cauchy Sequences Subsequences Series of Complex Terms Series of Nonnegative Terms Decimal Expansions The Number e The Root and Ratio Tests Power Series Multiplication of Series Lebesgue Outer Measure Cantor Sets Exercises 39 43 51 52 53 59 65 67 69 71 72 76 80 84 LIMITS AND CONTINUITY 91 Metric Spaces Topological Spaces Compactness Connectedness Completeness Baire Category Exercises Limits of Functions at a Point Exercises Compactness, Connectedness, and Continuity Exercises Simple Discontinuities and Monotone Functions Exercises Exp and Log Powers Exercises Uniform Convergence Exercises Stone-Weierstrass Theorems Exercises Total Variation Absolute Continuity Exercises Equicontinuity Exercises 91 95 102 107 107 109 Ш 114 119 122 124 128 131 134 136 138 139 144 146 156 159 162 163 164 168
CONTENTS 4 5 6 vii DIFFERENTIATION ПО Dini Derivates **A Nowhere Differentiable, Everywhere Continuous, Function Some Elementary Formulas Local Extrema Mean Value Theorems L’Hospital’s Rule Exercises Higher Order Derivatives Taylor Polynomials Exercises ♦Convex Functions ♦Exercises Differentiability Almost Everywhere Exercises ♦Termwise Differentiation of Sequences ♦Exercises ♦Complex Derivatives ♦Exercises 170 174 175 177 178 179 182 188 192 · 197 199 203 206 2П 213 215 219 223 THE ELEMENTARY TRANSCENDENTAL FUNCTIONS 226 The Exponential Function The Trigonometric Functions The Argument Exercises ♦Complex Logarithms and Powers ♦Exercises ♦♦n is Irrational ♦♦Exercises ♦Log Series and the Inverse Tangent ♦♦Rational Approximation to π ♦Exercises ♦♦The Sine Product and Related Expansions ♦♦Stirling’s Formula ♦♦Exercises 226 227 231 232 236 240 240 242 242 245 246 247 253 255 INTEGRATION 257 Step Functions The First Extension Integrable Functions 257 263 264
viii CONTENTS Two Limit Theorems The Riemann Integral Exercises Measureable Functions Complex-Valued Functions Measurable Sets Structure of Measurable Functions Integration Over Measurable Sets Exercises The Fundamental Theorem of Calculus Integration by Parts Integration Substitution Two Mean Value Theorems ♦Arc Length Exercises Holder’s and Miiytcowski’s Inequalities The Lp Spaces Exercises Integration on R Iteration of Integrals Exercises Some Differential Calculus in Higher Dimensions Exercises Transformations of Integrals on R Exercises 7 INFINITE SERIES AND INFINITE PRODUCTS Series Having Monotone Terms Limit Comparison Tests “Two Log Tests ♦♦Other Ratio Tests ♦Exercises ♦♦Infinite Products ♦♦Exercises Some Theorems of Abel Exercises ♦♦Another Ratio Test and the Binomial Series ♦♦Exercises Rearrangements and Double Series Exercises * *The Gamma Function 266 269 274 285 289 293 300 305 306 318 323 323 327 329 331 339 341 343 345 349 356 364 376 385 393 398 398 401 404 406 409 4ĮJ. 418 420 426 434 440 443 454 460
CONTENTS 8 ІХ ••Exercises Divergent Series Exercises Tauberian Theorems Exercises 470 473 484 494 500 TRIGONOMETRIC SERIES 502 Trigonometric Series and Fourier Series Which Trigonometric Series are Fourier Series? Exercises •Divergent Fourier Series •Exercises Suihmability of Fourier Series Riemann Localization and Convergence Criteria Growth Rate of Partial Sums Exercises 503 510 518 526 530 534 541 551 554 BIBLIOGRAPHY 567 OTHER WORK BY THE AUTHOR 569 INDEX 571 •Sections marked with a single asterisk are not actually needed in conjunction with any of the unmarked sections. These sections may be safely omitted if time permits only a short course. ••Sections marked with a double asterisk are not actually needed in conjunction with any other section. They are included as interesting and useful applications of the theory.
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| discipline | Mathematik |
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| spelling | Stromberg, Karl R. 1931-1994 Verfasser (DE-588)105811041 aut An introduction to classical real analysis Karl R. Stromberg Reprinted with corrections Providence, Rhode Island AMS Chelsea Publishing [2015] 2015 xiv, 577 Seiten Illustration txt rdacontent n rdamedia nc rdacarrier Auf der letzten Seite: "This new printing contains a large number of corrections and a short author biography as well as a list of selected publications of the author" 1981 Analyse mathématique Analyse mathématique ram Mathematical analysis Analysis (DE-588)4001865-9 gnd rswk-swf Analysis (DE-588)4001865-9 s DE-604 Nachdruck von Stromberg, Karl R. Introduction to classical real analysis Belmont, California : Wadsworth, 1981 Erscheint auch als Online-Ausgabe 978-1-4704-2725-2 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028773398&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
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| subject_GND | (DE-588)4001865-9 |
| title | An introduction to classical real analysis |
| title_auth | An introduction to classical real analysis |
| title_exact_search | An introduction to classical real analysis |
| title_full | An introduction to classical real analysis Karl R. Stromberg |
| title_fullStr | An introduction to classical real analysis Karl R. Stromberg |
| title_full_unstemmed | An introduction to classical real analysis Karl R. Stromberg |
| title_short | An introduction to classical real analysis |
| title_sort | an introduction to classical real analysis |
| topic | Analyse mathématique Analyse mathématique ram Mathematical analysis Analysis (DE-588)4001865-9 gnd |
| topic_facet | Analyse mathématique Mathematical analysis Analysis |
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