Real mathematical analysis
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| Format: | Elektronisch E-Book |
| Sprache: | English |
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Cham [u.a.]
Springer
2015
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| Ausgabe: | 2. ed. |
| Schriftenreihe: | Undergraduate texts in mathematics
|
| Schlagworte: | |
| Online-Zugang: | DE-634 DE-861 DE-91 DE-19 DE-703 DE-20 DE-739 Volltext Inhaltsverzeichnis Abstract |
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Datensatz im Suchindex
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| adam_text | REAL MATHEMATICAL ANALYSIS
/ PUGH, CHARLES C.
: 2015
TABLE OF CONTENTS / INHALTSVERZEICHNIS
REAL NUMBERS
A TASTE OF TOPOLOGY
FUNCTIONS OF A REAL VARIABLE
FUNCTION SPACES
MULTIVARIABLE CALCULUS
LEBESGUE THEORY
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
REAL MATHEMATICAL ANALYSIS
/ PUGH, CHARLES C.
: 2015
ABSTRACT / INHALTSTEXT
BASED ON AN HONORS COURSE TAUGHT BY THE AUTHOR AT UC BERKELEY, THIS
INTRODUCTION TO UNDERGRADUATE REAL ANALYSIS GIVES A DIFFERENT EMPHASIS
BY STRESSING THE IMPORTANCE OF PICTURES AND HARD PROBLEMS. TOPICS
INCLUDE: A NATURAL CONSTRUCTION OF THE REAL NUMBERS, FOUR-DIMENSIONAL
VISUALIZATION, BASIC POINT-SET TOPOLOGY, FUNCTION SPACES, MULTIVARIABLE
CALCULUS VIA DIFFERENTIAL FORMS (LEADING TO A SIMPLE PROOF OF THE
BROUWER FIXED POINT THEOREM), AND A PICTORIAL TREATMENT OF LEBESGUE
THEORY. OVER 150 DETAILED ILLUSTRATIONS ELUCIDATE ABSTRACT CONCEPTS AND
SALIENT POINTS IN PROOFS. THE EXPOSITION IS INFORMAL AND RELAXED, WITH
MANY HELPFUL ASIDES, EXAMPLES, SOME JOKES, AND OCCASIONAL COMMENTS FROM
MATHEMATICIANS, SUCH AS LITTLEWOOD, DIEUDONNE, AND OSSERMAN. THIS BOOK
THUS SUCCEEDS IN BEING MORE COMPREHENSIVE, MORE COMPREHENSIBLE, AND MORE
ENJOYABLE, THAN STANDARD INTRODUCTIONS TO ANALYSIS. NEW TO THE SECOND
EDITION OF REAL MATHEMATICAL ANALYSIS IS A PRESENTATION OF LEBESGUE
INTEGRATION DONE ALMOST ENTIRELY USING THE UNDERGRAPH APPROACH OF
BURKILL. PAYOFFS INCLUDE: CONCISE PICTURE PROOFS OF THE MONOTONE AND
DOMINATED CONVERGENCE THEOREMS, A ONE-LINE/ONE-PICTURE PROOF OF FUBINI S
THEOREM FROM CAVALIERI’S PRINCIPLE, AND, IN MANY CASES, THE ABILITY TO
SEE AN INTEGRAL RESULT FROM MEASURE THEORY. THE PRESENTATION INCLUDES
VITALI’S COVERING LEMMA, DENSITY POINTS — WHICH ARE RARELY TREATED
IN BOOKS AT THIS LEVEL — AND THE ALMOST EVERYWHERE DIFFERENTIABILITY
OF MONOTONE FUNCTIONS. SEVERAL NEW EXERCISES NOW JOIN A COLLECTION OF
OVER 500 EXERCISES THAT POSE INTERESTING CHALLENGES AND INTRODUCE
SPECIAL TOPICS TO THE STUDENT KEEN ON MASTERING THIS BEAUTIFUL SUBJECT
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
|
| any_adam_object | 1 |
| author | Pugh, Charles Chapman 1940- |
| author_GND | (DE-588)123790255 |
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| bvnumber | BV042730461 |
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| callnumber-raw | QA300 |
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| callnumber-subject | QA - Mathematics |
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| dewey-ones | 515 - Analysis |
| dewey-raw | 515.42 515 |
| dewey-search | 515.42 515 |
| dewey-sort | 3515.42 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-319-17771-7 |
| edition | 2. ed. |
| format | Electronic eBook |
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| indexdate | 2024-12-24T04:32:06Z |
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| spellingShingle | Pugh, Charles Chapman 1940- Real mathematical analysis Mathematics Sequences (Mathematics) Measure and Integration Real Functions Sequences, Series, Summability Reelle Analysis Mathematik Mathematical analysis Reelle Analysis (DE-588)4627581-2 gnd |
| subject_GND | (DE-588)4627581-2 (DE-588)4151278-9 |
| title | Real mathematical analysis |
| title_auth | Real mathematical analysis |
| title_exact_search | Real mathematical analysis |
| title_full | Real mathematical analysis Charles C. Pugh |
| title_fullStr | Real mathematical analysis Charles C. Pugh |
| title_full_unstemmed | Real mathematical analysis Charles C. Pugh |
| title_short | Real mathematical analysis |
| title_sort | real mathematical analysis |
| topic | Mathematics Sequences (Mathematics) Measure and Integration Real Functions Sequences, Series, Summability Reelle Analysis Mathematik Mathematical analysis Reelle Analysis (DE-588)4627581-2 gnd |
| topic_facet | Mathematics Sequences (Mathematics) Measure and Integration Real Functions Sequences, Series, Summability Reelle Analysis Mathematik Mathematical analysis Einführung |
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