Mathematical analysis: 2
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Berlin
Springer
[2016]
|
| Edition: | Second edition |
| Series: | Universitext
Universitext |
| Subjects: | |
| Online Access: | BTU01 FHR01 FRO01 TUM01 UBM01 UBT01 UBW01 UEI01 UPA01 Volltext Abstract Inhaltsverzeichnis |
| Physical Description: | 1 Online Ressource (XX, 720 Seiten, 42 illus. in color) |
| ISBN: | 9783662489932 |
| DOI: | 10.1007/978-3-662-48993-2 |
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Record in the Search Index
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| adam_text | MATHEMATICAL ANALYSIS II
/ ZORICH, VLADIMIR A.
: 2016
ABSTRACT / INHALTSTEXT
THIS SECOND ENGLISH EDITION OF A VERY POPULAR TWO-VOLUME WORK PRESENTS A
THOROUGH FIRST COURSE IN ANALYSIS, LEADING FROM REAL NUMBERS TO SUCH
ADVANCED TOPICS AS DIFFERENTIAL FORMS ON MANIFOLDS; ASYMPTOTIC METHODS;
FOURIER, LAPLACE, AND LEGENDRE TRANSFORMS; ELLIPTIC FUNCTIONS; AND
DISTRIBUTIONS. ESPECIALLY NOTABLE IN THIS COURSE ARE THE CLEARLY
EXPRESSED ORIENTATION TOWARD THE NATURAL SCIENCES AND THE INFORMAL
EXPLORATION OF THE ESSENCE AND THE ROOTS OF THE BASIC CONCEPTS AND
THEOREMS OF CALCULUS. CLARITY OF EXPOSITION IS MATCHED BY A WEALTH OF
INSTRUCTIVE EXERCISES, PROBLEMS, AND FRESH APPLICATIONS TO AREAS SELDOM
TOUCHED ON IN TEXTBOOKS ON REAL ANALYSIS. THE MAIN DIFFERENCE BETWEEN
THE SECOND AND FIRST ENGLISH EDITIONS IS THE ADDITION OF A SERIES OF
APPENDICES TO EACH VOLUME. THERE ARE SIX OF THEM IN THE FIRST VOLUME AND
FIVE IN THE SECOND. THE SUBJECTS OF THESE APPENDICES ARE DIVERSE.THEY
ARE MEANT TO BE USEFUL TO BOTH STUDENTS (IN MATHEMATICS AND PHYSICS) AND
TEACHERS, WHO MAY BE MOTIVATED BY DIFFERENT GOALS. SOME OF THE
APPENDICES ARE SURVEYS, BOTH PROSPECTIVE AND RETROSPECTIVE. THE FINAL
SURVEY ESTABLISHES IMPORTANT CONCEPTUAL CONNECTIONS BETWEEN ANALYSIS AND
OTHER PARTS OF MATHEMATICS. THIS SECOND VOLUME PRESENTS CLASSICAL
ANALYSIS IN ITS CURRENT FORM AS PART OF A UNIFIED MATHEMATICS. IT SHOWS
HOW ANALYSIS INTERACTS WITH OTHER MODERN FIELDS OF MATHEMATICS SUCH AS
ALGEBRA, DIFFERENTIAL GEOMETRY, DIFFERENTIAL EQUATIONS, COMPLEX
ANALYSIS, AND FUNCTIONAL ANALYSIS. THIS BOOK PROVIDES A FIRM FOUNDATION
FOR ADVANCED WORK IN ANY OF THESE DIRECTIONS. “THE TEXTBOOK OF ZORICH
SEEMS TO ME THE MOST SUCCESSFUL OF THE AVAILABLE COMPREHENSIVE TEXTBOOKS
OF ANALYSIS FOR MATHEMATICIANS AND PHYSICISTS.IT DIFFERS FROM THE
TRADITIONAL EXPOSITION IN TWO MAJOR WAYS: ON THE ONE HAND IN ITS CLOSER
RELATION TO NATURAL-SCIENCE APPLICATIONS (PRIMARILY TO PHYSICS AND
MECHANICS) AND ON THE OTHER HAND IN A GREATER-THAN-USUAL USE OF THE
IDEAS AND METHODS OF MODERN MATHEMATICS, THAT IS, ALGEBRA, GEOMETRY, AND
TOPOLOGY. THE COURSE IS UNUSUALLY RICH IN IDEAS AND SHOWS CLEARLY THE
POWER OF THE IDEAS AND METHODS OF MODERN MATHEMATICS IN THE STUDY OF
PARTICULAR PROBLEMS. ESPECIALLY UNUSUAL IS THE SECOND VOLUME, WHICH
INCLUDES VECTOR ANALYSIS, THE THEORY OF DIFFERENTIAL FORMS ON MANIFOLDS,
AN INTRODUCTION TO THE THEORY OF GENERALIZED FUNCTIONS AND POTENTIAL
THEORY, FOURIER SERIES AND THE FOURIER TRANSFORM, AND THE ELEMENTS OF
THE THEORY OF ASYMPTOTIC EXPANSIONS. AT PRESENT SUCH A WAY OF
STRUCTURING THE COURSE MUST BE CONSIDERED INNOVATIVE.IT WAS NORMAL IN
THE TIME OF GOURSAT, BUT THE TENDENCY TOWARD SPECIALIZED COURSES,
NOTICEABLE OVER THE PAST HALF CENTURY, HAS EMASCULATED THE COURSE OF
ANALYSIS, ALMOST REDUCING IT TO MERE LOGICAL JUSTIFICATIONS. THE NEED TO
RETURN TO MORE SUBSTANTIVE COURSES OF ANALYSIS NOW SEEMS OBVIOUS,
ESPECIALLY IN CONNECTION WITH THE APPLIED CHARACTER OF THE FUTURE
ACTIVITY OF THE MAJORITY OF STUDENTS. ...IN MY OPINION, THIS COURSE IS
THE BEST OF THE EXISTING MODERN COURSES OF ANALYSIS.” FROM A REVIEW BY
V.I.ARNOLD VLADIMIR A. ZORICH IS PROFESSOR OF MATHEMATICS AT MOSCOW
STATE UNIVERSITY. HIS AREAS OF SPECIALIZATION ARE ANALYSIS, CONFORMAL
GEOMETRY, QUASICONFORMAL MAPPINGS, AND MATHEMATICAL ASPECTS OF
THERMODYNAMICS. HE SOLVED THE PROBLEM OF GLOBAL HOMEOMORPHISM FOR SPACE
QUASICONFORMAL MAPPINGS. HE HOLDS A PATENT IN THE TECHNOLOGY OF
MECHANICAL ENGINEERING, AND HE IS ALSO KNOWN BY HIS BOOK MATHEMATICAL
ANALYSIS OF PROBLEMS IN THE NATURAL SCIENCES
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
MATHEMATICAL ANALYSIS II
/ ZORICH, VLADIMIR A.
: 2016
TABLE OF CONTENTS / INHALTSVERZEICHNIS
9 CONTINUOUS MAPPINGS (GENERAL THEORY)
10 DIFFERENTIAL CALCULUS FROM A GENERAL VIEWPOINT
11 MULTIPLE INTEGRALS
12 SURFACES AND DIFFERENTIAL FORMS IN RN
13 LINE AND SURFACE INTEGRALS
14 ELEMENTS OF VECTOR ANALYSIS AND FIELD THEORY
15 INTEGRATION OF DIFFERENTIAL FORMS ON MANIFOLDS
16 UNIFORM CONVERGENCE AND BASIC OPERATIONS OF ANALYSIS
17 INTEGRALS DEPENDING ON A PARAMETER
18 FOURIER SERIES AND THE FOURIER TRANSFORM
19 ASYMPTOTIC EXPANSIONS
TOPICS AND QUESTIONS FOR MIDTERM EXAMINATIONS
EXAMINATION TOPICS
EXAMINATION PROBLEMS (SERIES AND INTEGRALS DEPENDING ON A PARAMETER)
INTERMEDIATE PROBLEMS (INTEGRAL CALCULUS OF SEVERAL VARIABLES)
APPENDICES: A SERIES AS A TOOL (INTRODUCTORY LECTURE)
B CHANGE OF VARIABLES IN MULTIPLE INTEGRALS
C MULTIDIMENSIONAL GEOMETRY AND FUNCTIONS OF A VERY LARGE NUMBER OF
VARIABLES
D OPERATORS OF FIELD THEORY IN CURVILINEAR COORDINATES
E MODERN FORMULA OF NEWTON–LEIBNIZ
REFERENCES
INDEX OF BASIC NOTATION
SUBJECT INDEX
NAME INDEX
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
|
| any_adam_object | 1 |
| author | Zorič, Vladimir A. 1937- |
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| author_role | aut |
| author_sort | Zorič, Vladimir A. 1937- |
| author_variant | v a z va vaz |
| building | Verbundindex |
| bvnumber | BV043484193 |
| classification_rvk | SK 400 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA |
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| dewey-full | 515 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515 |
| dewey-search | 515 |
| dewey-sort | 3515 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-662-48993-2 |
| edition | Second edition |
| format | Electronic eBook |
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| id | DE-604.BV043484193 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:26:57Z |
| institution | BVB |
| isbn | 9783662489932 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-028900945 |
| oclc_num | 969771840 |
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| owner_facet | DE-91 DE-BY-TUM DE-19 DE-BY-UBM DE-20 DE-739 DE-634 DE-898 DE-BY-UBR DE-703 DE-861 DE-824 DE-83 |
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| publishDate | 2016 |
| publishDateSearch | 2016 |
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| publisher | Springer |
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| series2 | Universitext |
| spelling | Zorič, Vladimir A. 1937- Verfasser (DE-588)128567155 aut Matematičeskij analiz Mathematical analysis 2 Vladimir A. Zorich Second edition Berlin Springer [2016] 1 Online Ressource (XX, 720 Seiten, 42 illus. in color) txt rdacontent c rdamedia cr rdacarrier Universitext Mathematics Mathematical analysis Analysis (Mathematics) Physics Analysis Theoretical, Mathematical and Computational Physics Mathematik (DE-604)BV043484169 2 Erscheint auch als Druckausgabe 978-3-662-48991-8 https://doi.org/10.1007/978-3-662-48993-2 Verlag Volltext Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028900945&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=028900945&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Zorič, Vladimir A. 1937- Mathematical analysis Mathematics Mathematical analysis Analysis (Mathematics) Physics Analysis Theoretical, Mathematical and Computational Physics Mathematik |
| title | Mathematical analysis |
| title_alt | Matematičeskij analiz |
| title_auth | Mathematical analysis |
| title_exact_search | Mathematical analysis |
| title_full | Mathematical analysis 2 Vladimir A. Zorich |
| title_fullStr | Mathematical analysis 2 Vladimir A. Zorich |
| title_full_unstemmed | Mathematical analysis 2 Vladimir A. Zorich |
| title_short | Mathematical analysis |
| title_sort | mathematical analysis |
| topic | Mathematics Mathematical analysis Analysis (Mathematics) Physics Analysis Theoretical, Mathematical and Computational Physics Mathematik |
| topic_facet | Mathematics Mathematical analysis Analysis (Mathematics) Physics Analysis Theoretical, Mathematical and Computational Physics Mathematik |
| url | https://doi.org/10.1007/978-3-662-48993-2 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028900945&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=028900945&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV043484169 |
| work_keys_str_mv | AT zoricvladimira matematiceskijanaliz AT zoricvladimira mathematicalanalysis2 |