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Título : Complex Analysis 2 : Riemann Surfaces, Several Complex Variables, Abelian Functions, Higher Modular Functions Tipo de documento: documento electrónico Autores: Eberhard Freitag ; SpringerLink (Online service) Editorial: Berlin, Heidelberg : Springer Berlin Heidelberg Fecha de publicación: 2011 Colección: Universitext, ISSN 0172-5939 Número de páginas: XIII, 506 p. 51 illus Il.: online resource ISBN/ISSN/DL: 978-3-642-20554-5 Idioma : Inglés (eng) Palabras clave: Mathematics Functions of complex variables Several Complex Variables and Analytic Spaces a Variable Clasificación: 51 Matemáticas Resumen: The book provides a complete presentation of complex analysis, starting with the theory of Riemann surfaces, including uniformization theory and a detailed treatment of the theory of compact Riemann surfaces, the Riemann-Roch theorem, Abel's theorem and Jacobi's inversion theorem. This motivates a short introduction into the theory of several complex variables, followed by the theory of Abelian functions up to the theta theorem. The last part of the book provides an introduction into the theory of higher modular functions Nota de contenido: Chapter I. Riemann Surfaces -- Chapter II. Harmonic Functions on Riemann Surfaces -- Chapter III. Uniformization -- Chapter IV. Compact Riemann Surfaces -- Appendices to Chapter IV -- Chapter V. Analytic Functions of Several Complex Variables -- Chapter V. Analytic Functions of Several Complex Variable -- Chapter VI. Abelian Functions -- Chapter VII. Modular Forms of Several Variables -- Chapter VIII. Appendix: Algebraic Tools -- References -- Index En línea: http://dx.doi.org/10.1007/978-3-642-20554-5 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33424 Complex Analysis 2 : Riemann Surfaces, Several Complex Variables, Abelian Functions, Higher Modular Functions [documento electrónico] / Eberhard Freitag ; SpringerLink (Online service) . - Berlin, Heidelberg : Springer Berlin Heidelberg, 2011 . - XIII, 506 p. 51 illus : online resource. - (Universitext, ISSN 0172-5939) .
ISBN : 978-3-642-20554-5
Idioma : Inglés (eng)
Palabras clave: Mathematics Functions of complex variables Several Complex Variables and Analytic Spaces a Variable Clasificación: 51 Matemáticas Resumen: The book provides a complete presentation of complex analysis, starting with the theory of Riemann surfaces, including uniformization theory and a detailed treatment of the theory of compact Riemann surfaces, the Riemann-Roch theorem, Abel's theorem and Jacobi's inversion theorem. This motivates a short introduction into the theory of several complex variables, followed by the theory of Abelian functions up to the theta theorem. The last part of the book provides an introduction into the theory of higher modular functions Nota de contenido: Chapter I. Riemann Surfaces -- Chapter II. Harmonic Functions on Riemann Surfaces -- Chapter III. Uniformization -- Chapter IV. Compact Riemann Surfaces -- Appendices to Chapter IV -- Chapter V. Analytic Functions of Several Complex Variables -- Chapter V. Analytic Functions of Several Complex Variable -- Chapter VI. Abelian Functions -- Chapter VII. Modular Forms of Several Variables -- Chapter VIII. Appendix: Algebraic Tools -- References -- Index En línea: http://dx.doi.org/10.1007/978-3-642-20554-5 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33424 Ejemplares
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Título : Complex Variables with Applications Tipo de documento: documento electrónico Autores: S. Ponnusamy ; SpringerLink (Online service) ; Herb Silverman Editorial: Boston, MA : Birkhäuser Boston Fecha de publicación: 2006 Número de páginas: XIV, 514 p Il.: online resource ISBN/ISSN/DL: 978-0-8176-4513-7 Idioma : Inglés (eng) Palabras clave: Mathematics Functions of complex variables Applied mathematics Engineering Geometry Number theory a Complex Variable Applications Several Variables and Analytic Spaces Theory Appl.Mathematics/Computational Methods Clasificación: 51 Matemáticas Resumen: Complex numbers can be viewed in several ways: as an element in a field, as a point in the plane, and as a two-dimensional vector. Examined properly, each perspective provides crucial insight into the interrelations between the complex number system and its parent, the real number system. The authors explore these relationships by adopting both generalization and specialization methods to move from real variables to complex variables, and vice versa, while simultaneously examining their analytic and geometric characteristics, using geometry to illustrate analytic concepts and employing analysis to unravel geometric notions. The engaging exposition is replete with discussions, remarks, questions, and exercises, motivating not only understanding on the part of the reader, but also developing the tools needed to think critically about mathematical problems. This focus involves a careful examination of the methods and assumptions underlying various alternative routes that lead to the same destination. The material includes numerous examples and applications relevant to engineering students, along with some techniques to evaluate various types of integrals. The book may serve as a text for an undergraduate course in complex variables designed for scientists and engineers or for mathematics majors interested in further pursuing the general theory of complex analysis. The only prerequisite is a basic knowledge of advanced calculus. The presentation is also ideally suited for self-study Nota de contenido: Algebraic and Geometric Preliminaries -- Topological and Analytic Preliminaries -- Bilinear Transformations and Mappings -- Elementary Functions -- Analytic Functions -- Power Series -- Complex Integration and Cauchy’s Theorem -- Applications of Cauchy’s Theorem -- Laurent Series and the Residue Theorem -- Harmonic Functions -- Conformal Mapping and the Riemann Mapping Theorem -- Entire and Meromorphic Functions -- Analytic Continuation En línea: http://dx.doi.org/10.1007/978-0-8176-4513-7 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34878 Complex Variables with Applications [documento electrónico] / S. Ponnusamy ; SpringerLink (Online service) ; Herb Silverman . - Boston, MA : Birkhäuser Boston, 2006 . - XIV, 514 p : online resource.
ISBN : 978-0-8176-4513-7
Idioma : Inglés (eng)
Palabras clave: Mathematics Functions of complex variables Applied mathematics Engineering Geometry Number theory a Complex Variable Applications Several Variables and Analytic Spaces Theory Appl.Mathematics/Computational Methods Clasificación: 51 Matemáticas Resumen: Complex numbers can be viewed in several ways: as an element in a field, as a point in the plane, and as a two-dimensional vector. Examined properly, each perspective provides crucial insight into the interrelations between the complex number system and its parent, the real number system. The authors explore these relationships by adopting both generalization and specialization methods to move from real variables to complex variables, and vice versa, while simultaneously examining their analytic and geometric characteristics, using geometry to illustrate analytic concepts and employing analysis to unravel geometric notions. The engaging exposition is replete with discussions, remarks, questions, and exercises, motivating not only understanding on the part of the reader, but also developing the tools needed to think critically about mathematical problems. This focus involves a careful examination of the methods and assumptions underlying various alternative routes that lead to the same destination. The material includes numerous examples and applications relevant to engineering students, along with some techniques to evaluate various types of integrals. The book may serve as a text for an undergraduate course in complex variables designed for scientists and engineers or for mathematics majors interested in further pursuing the general theory of complex analysis. The only prerequisite is a basic knowledge of advanced calculus. The presentation is also ideally suited for self-study Nota de contenido: Algebraic and Geometric Preliminaries -- Topological and Analytic Preliminaries -- Bilinear Transformations and Mappings -- Elementary Functions -- Analytic Functions -- Power Series -- Complex Integration and Cauchy’s Theorem -- Applications of Cauchy’s Theorem -- Laurent Series and the Residue Theorem -- Harmonic Functions -- Conformal Mapping and the Riemann Mapping Theorem -- Entire and Meromorphic Functions -- Analytic Continuation En línea: http://dx.doi.org/10.1007/978-0-8176-4513-7 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34878 Ejemplares
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Título : Holomorphic Function Theory in Several Variables : An Introduction Tipo de documento: documento electrónico Autores: Christine Laurent-Thiébaut ; SpringerLink (Online service) Editorial: London : Springer London Fecha de publicación: 2011 Número de páginas: XIII, 252 p Il.: online resource ISBN/ISSN/DL: 978-0-85729-030-4 Idioma : Inglés (eng) Palabras clave: Mathematics Functions of complex variables Several Complex Variables and Analytic Spaces Clasificación: 51 Matemáticas Resumen: This book provides an introduction to complex analysis in several variables. The viewpoint of integral representation theory together with Grauert's bumping method offers a natural extension of single variable techniques to several variables analysis and leads rapidly to important global results. Applications focus on global extension problems for CR functions, such as the Hartogs-Bochner phenomenon and removable singularities for CR functions. Three appendices on differential manifolds, sheaf theory and functional analysis make the book self-contained. Each chapter begins with a detailed abstract, clearly demonstrating the structure and relations of following chapters. New concepts are clearly defined and theorems and propositions are proved in detail. Historical notes are also provided at the end of each chapter. Clear and succinct, this book will appeal to post-graduate students, young researchers seeking an introduction to holomorphic function theory in several variables and lecturers seeking a concise book on the subject Nota de contenido: Elementary local properties of holomorphic functions of several complex variables -- Currents and complex structures -- The Bochner-Martinelli-Koppelman kernel and formula applications -- Extensions of CR functions -- Extensions of holomorphic and CR functions on manifolds -- Domains of holomorphy and pseudoconvexity -- The Levi problem and the resolution of ? in strictly pseudoconvex domains -- Characterisation of removable singularities of CR functions on a strictly pseudoconvex boundary -- Appendices En línea: http://dx.doi.org/10.1007/978-0-85729-030-4 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33115 Holomorphic Function Theory in Several Variables : An Introduction [documento electrónico] / Christine Laurent-Thiébaut ; SpringerLink (Online service) . - London : Springer London, 2011 . - XIII, 252 p : online resource.
ISBN : 978-0-85729-030-4
Idioma : Inglés (eng)
Palabras clave: Mathematics Functions of complex variables Several Complex Variables and Analytic Spaces Clasificación: 51 Matemáticas Resumen: This book provides an introduction to complex analysis in several variables. The viewpoint of integral representation theory together with Grauert's bumping method offers a natural extension of single variable techniques to several variables analysis and leads rapidly to important global results. Applications focus on global extension problems for CR functions, such as the Hartogs-Bochner phenomenon and removable singularities for CR functions. Three appendices on differential manifolds, sheaf theory and functional analysis make the book self-contained. Each chapter begins with a detailed abstract, clearly demonstrating the structure and relations of following chapters. New concepts are clearly defined and theorems and propositions are proved in detail. Historical notes are also provided at the end of each chapter. Clear and succinct, this book will appeal to post-graduate students, young researchers seeking an introduction to holomorphic function theory in several variables and lecturers seeking a concise book on the subject Nota de contenido: Elementary local properties of holomorphic functions of several complex variables -- Currents and complex structures -- The Bochner-Martinelli-Koppelman kernel and formula applications -- Extensions of CR functions -- Extensions of holomorphic and CR functions on manifolds -- Domains of holomorphy and pseudoconvexity -- The Levi problem and the resolution of ? in strictly pseudoconvex domains -- Characterisation of removable singularities of CR functions on a strictly pseudoconvex boundary -- Appendices En línea: http://dx.doi.org/10.1007/978-0-85729-030-4 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33115 Ejemplares
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Título : Mathematical Analysis : An Introduction to Functions of Several Variables Tipo de documento: documento electrónico Autores: Mariano Giaquinta ; SpringerLink (Online service) ; Giuseppe Modica Editorial: Boston, MA : Birkhäuser Boston Fecha de publicación: 2009 Número de páginas: XII, 348 p. 105 illus Il.: online resource ISBN/ISSN/DL: 978-0-8176-4612-7 Idioma : Inglés (eng) Palabras clave: Mathematics Mathematical analysis Analysis (Mathematics) Measure theory Differential equations Functions of complex variables Calculus variations and Integration Variations Optimal Control; Optimization Several Complex Variables Analytic Spaces Ordinary Equations Clasificación: 51 Matemáticas Resumen: This text introduces basic ideas, structures, and results of differential and integral calculus for functions of several variables. The presentation is engaging and motivates the reader with numerous examples, remarks, illustrations, and exercises. Mathematical Analysis: An Introduction to Functions of Several Variables may be used in the classroom setting for advanced undergraduate and graduate students or as a self-study. It is also a valuable reference for researchers in most mathematical disciplines. An appendix highlights mathematicians and scientists who have made important contributions in the development of theories in the subject. Other books recently published by the authors include: Mathematical Analysis: Functions of One Variable, Mathematical Analysis: Approximation and Discrete Processes, and Mathematical Analysis: Linear and Metric Structures and Continuity, all of which provide the reader with a strong foundation in modern-day analysis. Reviews of previous volumes in Mathematical Analysis: The presentation of the theory is clearly arranged, all theorems have rigorous proofs, and every chapter closes with a summing up of the results and exercises with different requirements. . . . This book is excellently suitable for students in mathematics, physics, engineering, computer science and all students of technological and scientific faculties. —Journal of Analysis and its Applications The exposition requires only a sound knowledge of calculus and the functions of one variable. A key feature this lively yet rigorous and systematic treatment is the historical accounts of ideas and methods of the subject. Ideas in mathematics develop in cultural, historical and economical contexts, thus the authors made brief accounts of those aspects and used a large number of beautiful illustrations. —Zentralblatt MATH Nota de contenido: Differential Calculus -- Integral Calculus -- Curves and Differential Forms -- Holomorphic Functions -- Surfaces and Level Sets -- Systems of Ordinary Differential Equations En línea: http://dx.doi.org/10.1007/978-0-8176-4612-7 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33934 Mathematical Analysis : An Introduction to Functions of Several Variables [documento electrónico] / Mariano Giaquinta ; SpringerLink (Online service) ; Giuseppe Modica . - Boston, MA : Birkhäuser Boston, 2009 . - XII, 348 p. 105 illus : online resource.
ISBN : 978-0-8176-4612-7
Idioma : Inglés (eng)
Palabras clave: Mathematics Mathematical analysis Analysis (Mathematics) Measure theory Differential equations Functions of complex variables Calculus variations and Integration Variations Optimal Control; Optimization Several Complex Variables Analytic Spaces Ordinary Equations Clasificación: 51 Matemáticas Resumen: This text introduces basic ideas, structures, and results of differential and integral calculus for functions of several variables. The presentation is engaging and motivates the reader with numerous examples, remarks, illustrations, and exercises. Mathematical Analysis: An Introduction to Functions of Several Variables may be used in the classroom setting for advanced undergraduate and graduate students or as a self-study. It is also a valuable reference for researchers in most mathematical disciplines. An appendix highlights mathematicians and scientists who have made important contributions in the development of theories in the subject. Other books recently published by the authors include: Mathematical Analysis: Functions of One Variable, Mathematical Analysis: Approximation and Discrete Processes, and Mathematical Analysis: Linear and Metric Structures and Continuity, all of which provide the reader with a strong foundation in modern-day analysis. Reviews of previous volumes in Mathematical Analysis: The presentation of the theory is clearly arranged, all theorems have rigorous proofs, and every chapter closes with a summing up of the results and exercises with different requirements. . . . This book is excellently suitable for students in mathematics, physics, engineering, computer science and all students of technological and scientific faculties. —Journal of Analysis and its Applications The exposition requires only a sound knowledge of calculus and the functions of one variable. A key feature this lively yet rigorous and systematic treatment is the historical accounts of ideas and methods of the subject. Ideas in mathematics develop in cultural, historical and economical contexts, thus the authors made brief accounts of those aspects and used a large number of beautiful illustrations. —Zentralblatt MATH Nota de contenido: Differential Calculus -- Integral Calculus -- Curves and Differential Forms -- Holomorphic Functions -- Surfaces and Level Sets -- Systems of Ordinary Differential Equations En línea: http://dx.doi.org/10.1007/978-0-8176-4612-7 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33934 Ejemplares
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Título : Explorations in Harmonic Analysis : with Applications to Complex Function Theory and the Heisenberg Group Tipo de documento: documento electrónico Autores: Steven G. Krantz ; SpringerLink (Online service) Editorial: Boston, MA : Birkhäuser Boston Fecha de publicación: 2009 Colección: Applied and Numerical Harmonic Analysis, ISSN 2296-5009 Número de páginas: XIV, 362 p Il.: online resource ISBN/ISSN/DL: 978-0-8176-4669-1 Idioma : Inglés (eng) Palabras clave: Mathematics Group theory Harmonic analysis Approximation Fourier Functions of complex variables Mathematical models Abstract Analysis Modeling and Industrial Approximations Expansions Several Complex Variables Analytic Spaces Theory Generalizations Clasificación: 51 Matemáticas Resumen: This self-contained text provides an introduction to modern harmonic analysis in the context in which it is actually applied, in particular, through complex function theory and partial differential equations. It takes the novice mathematical reader from the rudiments of harmonic analysis (Fourier series) to the Fourier transform, pseudodifferential operators, and finally to Heisenberg analysis. Within the textbook, the new ideas on the Heisenberg group are applied to the study of estimates for both the Szegö and Poisson–Szegö integrals on the unit ball in complex space. Thus the main theme of the book is also tied into complex analysis of several variables. With a rigorous but well-paced exposition, this text provides all the necessary background in singular and fractional integrals, as well as Hardy spaces and the function theory of several complex variables, needed to understand Heisenberg analysis. Explorations in Harmonic Analysis is ideal for graduate students in mathematics, physics, and engineering. Prerequisites include a fundamental background in real and complex analysis and some exposure to functional analysis Nota de contenido: Ontology and History of Real Analysis -- The Central Idea: The Hilbert Transform -- Essentials of the Fourier Transform -- Fractional and Singular Integrals -- A Crash Course in Several Complex Variables -- Pseudoconvexity and Domains of Holomorphy -- Canonical Complex Integral Operators -- Hardy Spaces Old and New -- to the Heisenberg Group -- Analysis on the Heisenberg Group -- A Coda on Domains of Finite Type En línea: http://dx.doi.org/10.1007/978-0-8176-4669-1 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33939 Explorations in Harmonic Analysis : with Applications to Complex Function Theory and the Heisenberg Group [documento electrónico] / Steven G. Krantz ; SpringerLink (Online service) . - Boston, MA : Birkhäuser Boston, 2009 . - XIV, 362 p : online resource. - (Applied and Numerical Harmonic Analysis, ISSN 2296-5009) .
ISBN : 978-0-8176-4669-1
Idioma : Inglés (eng)
Palabras clave: Mathematics Group theory Harmonic analysis Approximation Fourier Functions of complex variables Mathematical models Abstract Analysis Modeling and Industrial Approximations Expansions Several Complex Variables Analytic Spaces Theory Generalizations Clasificación: 51 Matemáticas Resumen: This self-contained text provides an introduction to modern harmonic analysis in the context in which it is actually applied, in particular, through complex function theory and partial differential equations. It takes the novice mathematical reader from the rudiments of harmonic analysis (Fourier series) to the Fourier transform, pseudodifferential operators, and finally to Heisenberg analysis. Within the textbook, the new ideas on the Heisenberg group are applied to the study of estimates for both the Szegö and Poisson–Szegö integrals on the unit ball in complex space. Thus the main theme of the book is also tied into complex analysis of several variables. With a rigorous but well-paced exposition, this text provides all the necessary background in singular and fractional integrals, as well as Hardy spaces and the function theory of several complex variables, needed to understand Heisenberg analysis. Explorations in Harmonic Analysis is ideal for graduate students in mathematics, physics, and engineering. Prerequisites include a fundamental background in real and complex analysis and some exposure to functional analysis Nota de contenido: Ontology and History of Real Analysis -- The Central Idea: The Hilbert Transform -- Essentials of the Fourier Transform -- Fractional and Singular Integrals -- A Crash Course in Several Complex Variables -- Pseudoconvexity and Domains of Holomorphy -- Canonical Complex Integral Operators -- Hardy Spaces Old and New -- to the Heisenberg Group -- Analysis on the Heisenberg Group -- A Coda on Domains of Finite Type En línea: http://dx.doi.org/10.1007/978-0-8176-4669-1 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33939 Ejemplares
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