Introduction to Mathematical Analysis / / by Igor Kriz, Aleš Pultr

• Autore: Kriz Igor
• Pubblicazione: Basel : , : Springer Basel : , : Imprint : Birkhäuser, , 2013
• Edizione: 1st ed. 2013.
• Descrizione fisica: 1 online resource (517 p.)
• Disciplina: 515
• Soggetto topico: Functions of real variables; Matrix theory; Algebra; Measure theory; Functions of complex variables; Differential equations; Sequences (Mathematics); Real Functions; Linear and Multilinear Algebras, Matrix Theory; Measure and Integration; Functions of a Complex Variable; Ordinary Differential Equations; Sequences, Series, Summability
• Persona (resp. second.): PultrAleš
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references (pages 501) and indexes.
• Nota di contenuto: 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. .
• Sommario/riassunto: 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, the Lebesgue 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.
• Titolo autorizzato: Introduction to Mathematical Analysis
• ISBN: 9783034806367; 3034806361
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910768190003321
• Lo trovi qui: Univ. Federico II