Introduction to mathematical analysis:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Basel [u.a.]
Birkhäuser
2013
|
| Schlagworte: | |
| Online-Zugang: | BTU01 TUM01 UBA01 UBM01 UBT01 UBW01 UPA01 Volltext Inhaltsverzeichnis Abstract |
| Beschreibung: | 1 Online-Ressource |
| ISBN: | 9783034806350 9783034806367 |
| DOI: | 10.1007/978-3-0348-0636-7 |
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Datensatz im Suchindex
| _version_ | 1804150721704099840 |
|---|---|
| adam_text | INTRODUCTION TO MATHEMATICAL ANALYSIS
/ KRIZ, IGOR
: 2013
TABLE OF CONTENTS / INHALTSVERZEICHNIS
PREFACE
INTRODUCTION
PART 1. A RIGOROUS APPROACH TO ADVANCED CALCULUS
1. PRELIMINARIES
2. METRIC AND TOPOLOGICAL SPACES I
3. MULTIVARIABLE DIFFERENTIAL CALCULUS
4. INTEGRATION I: MULTIVARIABLE RIEMANN INTEGRAL AND BASIC IDEAS TOWARD
THE LEBESGUE INTEGRAL
5. INTEGRATION II: MEASURABLE FUNCTIONS, MEASURE AND THE TECHNIQUES OF
LEBESGUE INTEGRATION
6. SYSTEMS OF ORDINARY DIFFERENTIAL EQUATIONS
7. SYSTEM OF LINEAR DIFFERENTIAL EQUATIONS
8. LINE INTEGRALS AND GREEN S THEOREM
PART 2. ANALYSIS AND GEOMETRY
9. AN INTRODUCTION TO COMPLEX ANALYSIS
10. METRIC AND TOPOLOGICAL SPACES II
11. MULTILINEAR ALGEBRA
12. SMOOTH MANIFOLDS, DIFFERENTIAL FORMS AND STOKES THEOREM
13. CALCULUS OF VARIATIONS AND THE GEODESIC EQUATION
14. TENSOR CALCULUS AND RIEMANNIAN GEOMETRY
15. HILBERT SPACES I: DEFINITIONS AND BASIC PROPERTIES
16. HILBERT SPACES II: EXAMPLES AND APPLICATIONS
APPENDIX A. LINEAR ALGEBRA I: VECTOR SPACES
APPENDIX B. LINEAR ALGEBRA II: MORE ABOUT MATRICES
BIBLIOGRAPHY
INDEX OF SYMBOLS
INDEX.
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
INTRODUCTION TO MATHEMATICAL ANALYSIS
/ KRIZ, IGOR
: 2013
ABSTRACT / INHALTSTEXT
THE BOOK BEGINS AT AN UNDERGRADUATE STUDENT LEVEL, ASSUMING ONLY BASIC
KNOWLEDGE OF CALCULUS IN ONE VARIABLE. IT RIGOROUSLY TREATS TOPICS SUCH
AS MULTIVARIABLE DIFFERENTIAL CALCULUS, THELEBESGUE INTEGRAL, VECTOR
CALCULUS AND DIFFERENTIAL EQUATIONS. AFTER HAVING CREATED A SOLID
FOUNDATION OF TOPOLOGY AND LINEAR ALGEBRA, THE TEXT LATER EXPANDS INTO
MORE ADVANCED TOPICS SUCH AS COMPLEX ANALYSIS, DIFFERENTIAL FORMS,
CALCULUS OF VARIATIONS, DIFFERENTIAL GEOMETRY AND EVEN FUNCTIONAL
ANALYSIS. OVERALL, THIS TEXT PROVIDES A UNIQUE AND WELL-ROUNDED
INTRODUCTION TO THE HIGHLY DEVELOPED AND MULTI-FACETED SUBJECT OF
MATHEMATICAL ANALYSIS AS UNDERSTOOD BY MATHEMATICIANS TODAY
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
|
| any_adam_object | 1 |
| author | Kriz, Igor Pultr, Aleš 1938- |
| author_GND | (DE-588)1017468141 |
| author_facet | Kriz, Igor Pultr, Aleš 1938- |
| author_role | aut aut |
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| dewey-full | 515.8 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.8 |
| dewey-search | 515.8 |
| dewey-sort | 3515.8 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-0348-0636-7 |
| format | Electronic eBook |
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| title_auth | Introduction to mathematical analysis |
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