Introduction to calculus and classical analysis:
Gespeichert in:
1. Verfasser: | |
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Format: | Elektronisch E-Book |
Sprache: | English |
Veröffentlicht: |
Cham
Springer
[2016]
|
Ausgabe: | Fourth edition |
Schriftenreihe: | Undergraduate texts in mathematics
|
Schlagworte: | |
Online-Zugang: | BTU01 FHR01 FRO01 TUM01 UBM01 UBT01 UBW01 UEI01 UPA01 Volltext Abstract Inhaltsverzeichnis |
Beschreibung: | 1 Online Ressource (XIII, 427 Seiten, 69 illus., 1 illus. in color) |
ISBN: | 9783319284002 |
ISSN: | 0172-6056 |
DOI: | 10.1007/978-3-319-28400-2 |
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adam_text | INTRODUCTION TO CALCULUS AND CLASSICAL ANALYSIS
/ HIJAB, OMAR
: 2016
ABSTRACT / INHALTSTEXT
THIS COMPLETELY SELF-CONTAINED TEXT IS INTENDED EITHER FOR A COURSE IN
HONORS CALCULUS OR FOR AN INTRODUCTION TO ANALYSIS. BEGINNING WITH THE
REAL NUMBER AXIOMS, AND INVOLVING RIGOROUS ANALYSIS, COMPUTATIONAL
DEXTERITY, AND A BREADTH OF APPLICATIONS, IT IS IDEAL FOR UNDERGRADUATE
MATH MAJORS. THIS FOURTH EDITION INCLUDES AN ADDITIONAL CHAPTER ON THE
FUNDAMENTAL THEOREMS IN THEIR FULL LEBESGUE GENERALITY, BASED ON THE
SUNRISE LEMMA. KEY FEATURES OF THIS TEXT INCLUDE: • APPLICATIONS FROM
SEVERAL PARTS OF ANALYSIS, E.G., CONVEXITY, THE CANTOR SET, CONTINUED
FRACTIONS, THE AGM, THE THETA AND ZETA FUNCTIONS, TRANSCENDENTAL
NUMBERS, THE BESSEL AND GAMMA FUNCTIONS, AND MANY MORE; • A HEAVY
EMPHASIS ON COMPUTATIONAL PROBLEMS, FROM THE HIGH-SCHOOL QUADRATIC
FORMULA TO THE FORMULA FOR THE DERIVATIVE OF THE ZETA FUNCTION AT ZERO;
• TRADITIONALLY TRANSCENDENTALLY PRESENTED MATERIAL, SUCH AS INFINITE
PRODUCTS, THE BERNOULLI SERIES, AND THE ZETA FUNCTIONAL EQUATION, IS
DEVELOPED OVER THE REALS; • A SELF-CONTAINED TREATMENT OF THE
FUNDAMENTAL THEOREMS OF CALCULUS IN THE GENERAL CASE USING THE SUNRISE
LEMMA; • THE INTEGRAL IS DEFINED AS THE AREA UNDER THE GRAPH, WHILE
THE AREA IS DEFINED FOR EVERY SUBSET OF THE PLANE; • 450 PROBLEMS WITH
ALL THE SOLUTIONS PRESENTED AT THE BACK OF THE TEXT. REVIEWS: CHAPTER 5
IS…AN ASTONISHING TOUR DE FORCE… —STEVEN G. KRANTZ, AMERICAN
MATH. MONTHLY FOR A TREATMENT…[OF INFINITE PRODUCTS AND BERNOULLI
SERIES] THAT IS VERY CLOSE TO EULER’S AND EVEN MORE ELEMENTARY…
—V. S. VARADARAJAN, BULLETIN AMS THIS IS A VERY INTRIGUING, DECIDEDLY
UNUSUAL, AND VERY SATISFYING TREATMENT OF CALCULUS AND INTRODUCTORY
ANALYSIS. IT S FULL OF QUIRKY LITTLE APPROACHES TO STANDARD TOPICS THAT
MAKE ONE WONDER OVER AND OVER AGAIN, WHY IS IT NEVER DONE LIKE THIS?
—JOHN ALLEN PAULOS, AUTHOR OF INNUMERACY AND A MATHEMATICIAN READS THE
NEWSPAPER
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
INTRODUCTION TO CALCULUS AND CLASSICAL ANALYSIS
/ HIJAB, OMAR
: 2016
TABLE OF CONTENTS / INHALTSVERZEICHNIS
PREFACE
A NOTE TO THE READER
1. THE SET OF REAL NUMBERS
2. CONTINUITY
3. DIFFERENTIATION.-4. INTEGRATION
5. APPLICATIONS
6. GENERALIZATIONS
A. SOLUTIONS
REFERENCES
INDEX
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
|
any_adam_object | 1 |
author | Hijab, Omar |
author_GND | (DE-588)115519351 |
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author_sort | Hijab, Omar |
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dewey-raw | 511.4 |
dewey-search | 511.4 |
dewey-sort | 3511.4 |
dewey-tens | 510 - Mathematics |
discipline | Mathematik |
doi_str_mv | 10.1007/978-3-319-28400-2 |
edition | Fourth edition |
format | Electronic eBook |
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spelling | Hijab, Omar Verfasser (DE-588)115519351 aut Introduction to calculus and classical analysis Omar Hijab Fourth edition Cham Springer [2016] © 2016 1 Online Ressource (XIII, 427 Seiten, 69 illus., 1 illus. in color) txt rdacontent c rdamedia cr rdacarrier Undergraduate texts in mathematics 0172-6056 Mathematics Approximation theory Sequences (Mathematics) Special functions Combinatorics Approximations and Expansions Sequences, Series, Summability Special Functions Mathematik Functions, special Analysis (DE-588)4001865-9 gnd rswk-swf Infinitesimalrechnung (DE-588)4072798-1 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Infinitesimalrechnung (DE-588)4072798-1 s DE-604 Analysis (DE-588)4001865-9 s Erscheint auch als Druckausgabe 978-3-319-28399-9 https://doi.org/10.1007/978-3-319-28400-2 Verlag Volltext Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028840950&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Abstract Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028840950&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
spellingShingle | Hijab, Omar Introduction to calculus and classical analysis Mathematics Approximation theory Sequences (Mathematics) Special functions Combinatorics Approximations and Expansions Sequences, Series, Summability Special Functions Mathematik Functions, special Analysis (DE-588)4001865-9 gnd Infinitesimalrechnung (DE-588)4072798-1 gnd |
subject_GND | (DE-588)4001865-9 (DE-588)4072798-1 (DE-588)4123623-3 |
title | Introduction to calculus and classical analysis |
title_auth | Introduction to calculus and classical analysis |
title_exact_search | Introduction to calculus and classical analysis |
title_full | Introduction to calculus and classical analysis Omar Hijab |
title_fullStr | Introduction to calculus and classical analysis Omar Hijab |
title_full_unstemmed | Introduction to calculus and classical analysis Omar Hijab |
title_short | Introduction to calculus and classical analysis |
title_sort | introduction to calculus and classical analysis |
topic | Mathematics Approximation theory Sequences (Mathematics) Special functions Combinatorics Approximations and Expansions Sequences, Series, Summability Special Functions Mathematik Functions, special Analysis (DE-588)4001865-9 gnd Infinitesimalrechnung (DE-588)4072798-1 gnd |
topic_facet | Mathematics Approximation theory Sequences (Mathematics) Special functions Combinatorics Approximations and Expansions Sequences, Series, Summability Special Functions Mathematik Functions, special Analysis Infinitesimalrechnung Lehrbuch |
url | https://doi.org/10.1007/978-3-319-28400-2 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028840950&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028840950&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
work_keys_str_mv | AT hijabomar introductiontocalculusandclassicalanalysis |