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Título : Distributions : Theory and Applications Tipo de documento: documento electrónico Autores: J.J. Duistermaat ; SpringerLink (Online service) ; Kolk, J.A.C Editorial: Boston : Birkhäuser Boston Fecha de publicación: 2010 Colección: Cornerstones Número de páginas: XVI, 445 p. 41 illus Il.: online resource ISBN/ISSN/DL: 978-0-8176-4675-2 Idioma : Inglés (eng) Palabras clave: Mathematics Approximation theory Fourier analysis Functional Differential equations Partial differential Applied mathematics Engineering Analysis Approximations and Expansions Applications of Equations Ordinary Clasificación: 51 Matemáticas Resumen: This textbook is an application-oriented introduction to the theory of distributions, a powerful tool used in mathematical analysis. The treatment emphasizes applications that relate distributions to linear partial differential equations and Fourier analysis problems found in mechanics, optics, quantum mechanics, quantum field theory, and signal analysis. Throughout the book, methods are developed to deal with formal calculations involving functions, series, and integrals that cannot be mathematically justified within the classical framework. Key features: • Many examples, exercises, hints, and solutions guide the reader throughout the text. • Includes an introduction to distributions, differentiation, convergence, convolution, the Fourier transform, and spaces of distributions having special properties. • Original proofs, which may be difficult to locate elsewhere, are given for many well-known results. • The Fourier transform is transparently treated and applied to provide a new proof of the Kernel Theorem, which in turn is used to efficiently derive numerous important results. • The systematic use of pullback and pushforward introduces concise notation. • Emphasizes the role of symmetry in obtaining short arguments and investigates distributions that are invariant under the actions of various groups of transformations. Distributions: Theory and Applications is aimed at advanced undergraduates and graduate students in mathematics, theoretical physics, and engineering, who will find this textbook a welcome introduction to the subject, requiring only a minimal mathematical background. The work may also serve as an excellent self-study guide for researchers who use distributions in various fields Nota de contenido: Motivation -- Test Functions -- Distributions -- Differentiation of Distributions -- Convergence of Distributions -- Taylor Expansion in Several Variables -- Localization -- Distributions with Compact Support -- Multiplication by Functions -- Transposition: Pullback and Pushforward -- Convolution of Distributions -- Fundamental Solutions -- Fractional Integration and Differentiation -- Fourier Transform -- Distribution Kernels -- Fourier Series -- Fundamental Solutions and Fourier Transform -- Supports and Fourier Transform -- Sobolev Spaces -- Appendix: Integration -- Solutions to Selected Problems En línea: http://dx.doi.org/10.1007/978-0-8176-4675-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33536 Distributions : Theory and Applications [documento electrónico] / J.J. Duistermaat ; SpringerLink (Online service) ; Kolk, J.A.C . - Boston : Birkhäuser Boston, 2010 . - XVI, 445 p. 41 illus : online resource. - (Cornerstones) .
ISBN : 978-0-8176-4675-2
Idioma : Inglés (eng)
Palabras clave: Mathematics Approximation theory Fourier analysis Functional Differential equations Partial differential Applied mathematics Engineering Analysis Approximations and Expansions Applications of Equations Ordinary Clasificación: 51 Matemáticas Resumen: This textbook is an application-oriented introduction to the theory of distributions, a powerful tool used in mathematical analysis. The treatment emphasizes applications that relate distributions to linear partial differential equations and Fourier analysis problems found in mechanics, optics, quantum mechanics, quantum field theory, and signal analysis. Throughout the book, methods are developed to deal with formal calculations involving functions, series, and integrals that cannot be mathematically justified within the classical framework. Key features: • Many examples, exercises, hints, and solutions guide the reader throughout the text. • Includes an introduction to distributions, differentiation, convergence, convolution, the Fourier transform, and spaces of distributions having special properties. • Original proofs, which may be difficult to locate elsewhere, are given for many well-known results. • The Fourier transform is transparently treated and applied to provide a new proof of the Kernel Theorem, which in turn is used to efficiently derive numerous important results. • The systematic use of pullback and pushforward introduces concise notation. • Emphasizes the role of symmetry in obtaining short arguments and investigates distributions that are invariant under the actions of various groups of transformations. Distributions: Theory and Applications is aimed at advanced undergraduates and graduate students in mathematics, theoretical physics, and engineering, who will find this textbook a welcome introduction to the subject, requiring only a minimal mathematical background. The work may also serve as an excellent self-study guide for researchers who use distributions in various fields Nota de contenido: Motivation -- Test Functions -- Distributions -- Differentiation of Distributions -- Convergence of Distributions -- Taylor Expansion in Several Variables -- Localization -- Distributions with Compact Support -- Multiplication by Functions -- Transposition: Pullback and Pushforward -- Convolution of Distributions -- Fundamental Solutions -- Fractional Integration and Differentiation -- Fourier Transform -- Distribution Kernels -- Fourier Series -- Fundamental Solutions and Fourier Transform -- Supports and Fourier Transform -- Sobolev Spaces -- Appendix: Integration -- Solutions to Selected Problems En línea: http://dx.doi.org/10.1007/978-0-8176-4675-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33536 Ejemplares
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Título : Geometric Integration Theory Tipo de documento: documento electrónico Autores: Krantz, Steven ; SpringerLink (Online service) ; Parks, Harold Editorial: Boston : Birkhäuser Boston Fecha de publicación: 2008 Colección: Cornerstones Número de páginas: XVI, 340 p. 33 illus Il.: online resource ISBN/ISSN/DL: 978-0-8176-4679-0 Idioma : Inglés (eng) Palabras clave: Mathematics Integral equations transforms Operational calculus Measure theory Geometry Convex geometry Discrete Differential and Integration Equations Transforms, Calculus Clasificación: 51 Matemáticas Resumen: This textbook introduces geometric measure theory through the notion of currents. Currents—continuous linear functionals on spaces of differential forms—are a natural language in which to formulate various types of extremal problems arising in geometry, and can be used to study generalized versions of the Plateau problem and related questions in geometric analysis. Key features of Geometric Integration Theory: * Includes topics on the deformation theorem, the area and coarea formulas, the compactness theorem, the slicing theorem and applications to minimal surfaces * Applies techniques to complex geometry, partial differential equations, harmonic analysis, differential geometry, and many other parts of mathematics * Provides considerable background material for the student Motivating key ideas with examples and figures, Geometric Integration Theory is a comprehensive introduction ideal for use in the classroom and for self-study. The exposition demands minimal background, is self-contained and accessible, and thus is ideal for graduate students and researchers Nota de contenido: Basics -- Carathéodory’s Construction and Lower-Dimensional Measures -- Invariant Measures and the Construction of Haar Measure. -- Covering Theorems and the Differentiation of Integrals -- Analytical Tools: The Area Formula, the Coarea Formula, and Poincaré Inequalities. -- The Calculus of Differential Forms and Stokes’s Theorem -- to Currents -- Currents and the Calculus of Variations -- Regularity of Mass-Minimizing Currents En línea: http://dx.doi.org/10.1007/978-0-8176-4679-0 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34276 Geometric Integration Theory [documento electrónico] / Krantz, Steven ; SpringerLink (Online service) ; Parks, Harold . - Boston : Birkhäuser Boston, 2008 . - XVI, 340 p. 33 illus : online resource. - (Cornerstones) .
ISBN : 978-0-8176-4679-0
Idioma : Inglés (eng)
Palabras clave: Mathematics Integral equations transforms Operational calculus Measure theory Geometry Convex geometry Discrete Differential and Integration Equations Transforms, Calculus Clasificación: 51 Matemáticas Resumen: This textbook introduces geometric measure theory through the notion of currents. Currents—continuous linear functionals on spaces of differential forms—are a natural language in which to formulate various types of extremal problems arising in geometry, and can be used to study generalized versions of the Plateau problem and related questions in geometric analysis. Key features of Geometric Integration Theory: * Includes topics on the deformation theorem, the area and coarea formulas, the compactness theorem, the slicing theorem and applications to minimal surfaces * Applies techniques to complex geometry, partial differential equations, harmonic analysis, differential geometry, and many other parts of mathematics * Provides considerable background material for the student Motivating key ideas with examples and figures, Geometric Integration Theory is a comprehensive introduction ideal for use in the classroom and for self-study. The exposition demands minimal background, is self-contained and accessible, and thus is ideal for graduate students and researchers Nota de contenido: Basics -- Carathéodory’s Construction and Lower-Dimensional Measures -- Invariant Measures and the Construction of Haar Measure. -- Covering Theorems and the Differentiation of Integrals -- Analytical Tools: The Area Formula, the Coarea Formula, and Poincaré Inequalities. -- The Calculus of Differential Forms and Stokes’s Theorem -- to Currents -- Currents and the Calculus of Variations -- Regularity of Mass-Minimizing Currents En línea: http://dx.doi.org/10.1007/978-0-8176-4679-0 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34276 Ejemplares
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Título : Partial Differential Equations : Second Edition Tipo de documento: documento electrónico Autores: DiBenedetto, Emmanuele ; SpringerLink (Online service) Editorial: Boston : Birkhäuser Boston Fecha de publicación: 2010 Colección: Cornerstones Número de páginas: XX, 389 p. 19 illus Il.: online resource ISBN/ISSN/DL: 978-0-8176-4552-6 Idioma : Inglés (eng) Palabras clave: Mathematics Mathematical analysis Analysis (Mathematics) Difference equations Functional Fourier Integral Partial differential Calculus of variations Differential Equations and Variations Optimal Control; Optimization Clasificación: 51 Matemáticas Resumen: This self-contained textbook offers an elementary introduction to partial differential equations (PDEs), primarily focusing on linear equations, but also providing a perspective on nonlinear equations, through Hamilton--Jacobi equations, elliptic equations with measurable coefficients and DeGiorgi classes. The exposition is complemented by examples, problems, and solutions that enhance understanding and explore related directions. Large parts of this revised second edition have been streamlined and rewritten to incorporate years of classroom feedback, correct misprints, and improve clarity. The work can serve as a text for advanced undergraduates and graduate students in mathematics, physics, engineering, and the natural sciences, as well as an excellent reference for applied mathematicians and mathematical physicists. The newly added three last chapters, on first order non-linear PDEs (Chapter 8), quasilinear elliptic equations with measurable coefficients (Chapter 9) and DeGiorgi classes (Chapter 10), point to issues and directions at the forefront of current investigations. Reviews of the first edition: The author's intent is to present an elementary introduction to PDEs... In contrast to other elementary textbooks on PDEs . . . much more material is presented on the three basic equations: Laplace's equation, the heat and wave equations. . . . The presentation is clear and well organized. . . . The text is complemented by numerous exercises and hints to proofs. ---Mathematical Reviews This is a well-written, self-contained, elementary introduction to linear, partial differential equations. ---Zentralblatt MATH Nota de contenido: Preliminaries -- Quasi-Linear Equations and the Cauchy#x2013;Kowalewski Theorem -- The Laplace Equation -- Boundary Value Problems by Double-Layer Potentials -- Integral Equations and Eigenvalue Problems -- The Heat Equation -- The Wave Equation -- Quasi-Linear Equations of First-Order -- Non-Linear Equations of First-Order -- Linear Elliptic Equations with Measurable Coefficients -- DeGiorgi Classes En línea: http://dx.doi.org/10.1007/978-0-8176-4552-6 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33531 Partial Differential Equations : Second Edition [documento electrónico] / DiBenedetto, Emmanuele ; SpringerLink (Online service) . - Boston : Birkhäuser Boston, 2010 . - XX, 389 p. 19 illus : online resource. - (Cornerstones) .
ISBN : 978-0-8176-4552-6
Idioma : Inglés (eng)
Palabras clave: Mathematics Mathematical analysis Analysis (Mathematics) Difference equations Functional Fourier Integral Partial differential Calculus of variations Differential Equations and Variations Optimal Control; Optimization Clasificación: 51 Matemáticas Resumen: This self-contained textbook offers an elementary introduction to partial differential equations (PDEs), primarily focusing on linear equations, but also providing a perspective on nonlinear equations, through Hamilton--Jacobi equations, elliptic equations with measurable coefficients and DeGiorgi classes. The exposition is complemented by examples, problems, and solutions that enhance understanding and explore related directions. Large parts of this revised second edition have been streamlined and rewritten to incorporate years of classroom feedback, correct misprints, and improve clarity. The work can serve as a text for advanced undergraduates and graduate students in mathematics, physics, engineering, and the natural sciences, as well as an excellent reference for applied mathematicians and mathematical physicists. The newly added three last chapters, on first order non-linear PDEs (Chapter 8), quasilinear elliptic equations with measurable coefficients (Chapter 9) and DeGiorgi classes (Chapter 10), point to issues and directions at the forefront of current investigations. Reviews of the first edition: The author's intent is to present an elementary introduction to PDEs... In contrast to other elementary textbooks on PDEs . . . much more material is presented on the three basic equations: Laplace's equation, the heat and wave equations. . . . The presentation is clear and well organized. . . . The text is complemented by numerous exercises and hints to proofs. ---Mathematical Reviews This is a well-written, self-contained, elementary introduction to linear, partial differential equations. ---Zentralblatt MATH Nota de contenido: Preliminaries -- Quasi-Linear Equations and the Cauchy#x2013;Kowalewski Theorem -- The Laplace Equation -- Boundary Value Problems by Double-Layer Potentials -- Integral Equations and Eigenvalue Problems -- The Heat Equation -- The Wave Equation -- Quasi-Linear Equations of First-Order -- Non-Linear Equations of First-Order -- Linear Elliptic Equations with Measurable Coefficients -- DeGiorgi Classes En línea: http://dx.doi.org/10.1007/978-0-8176-4552-6 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33531 Ejemplares
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