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Refinar búsquedaAdvances in Mathematical Finance / SpringerLink (Online service) ; Fu, Michael C ; Jarrow, Robert A ; Yen, Ju-Yi J ; Elliott, Robert J (2007)
Título : Advances in Mathematical Finance Tipo de documento: documento electrónico Autores: SpringerLink (Online service) ; Fu, Michael C ; Jarrow, Robert A ; Yen, Ju-Yi J ; Elliott, Robert J Editorial: Boston, MA : Birkhäuser Boston Fecha de publicación: 2007 Colección: Applied and Numerical Harmonic Analysis, ISSN 2296-5009 Número de páginas: XXVIII, 336 p Il.: online resource ISBN/ISSN/DL: 978-0-8176-4545-8 Idioma : Inglés (eng) Palabras clave: Mathematics Applied mathematics Engineering Economics, Mathematical Actuarial science Economic theory Macroeconomics Sciences Quantitative Finance Applications of Appl.Mathematics/Computational Methods Theory/Quantitative Economics/Mathematical Macroeconomics/Monetary Economics//Financial Economics Clasificación: 51 Matemáticas Resumen: This self-contained volume brings together a collection of chapters by some of the most distinguished researchers and practitioners in the fields of mathematical finance and financial engineering. Presenting state-of-the-art developments in theory and practice, the Festschrift is dedicated to Dilip B. Madan on the occasion of his 60th birthday. Specific topics covered include: * Theory and application of the Variance-Gamma process * Lévy process driven fixed-income and credit-risk models, including CDO pricing * Numerical PDE and Monte Carlo methods * Asset pricing and derivatives valuation and hedging * Itô formulas for fractional Brownian motion * Martingale characterization of asset price bubbles * Utility valuation for credit derivatives and portfolio management Advances in Mathematical Finance is a valuable resource for graduate students, researchers, and practitioners in mathematical finance and financial engineering. Contributors: H. Albrecher, D. C. Brody, P. Carr, E. Eberlein, R. J. Elliott, M. C. Fu, H. Geman, M. Heidari, A. Hirsa, L. P. Hughston, R. A. Jarrow, X. Jin, W. Kluge, S. A. Ladoucette, A. Macrina, D. B. Madan, F. Milne, M. Musiela, P. Protter, W. Schoutens, E. Seneta, K. Shimbo, R. Sircar, J. van der Hoek, M.Yor, T. Zariphopoulou Nota de contenido: Variance-Gamma and Related Stochastic Processes -- The Early Years of the Variance-Gamma Process -- Variance-Gamma and Monte Carlo -- Some Remarkable Properties of Gamma Processes -- A Note About Selberg’s Integrals in Relation with the Beta-Gamma Algebra -- Itô Formulas for Fractional Brownian Motion -- Asset and Option Pricing -- A Tutorial on Zero Volatility and Option Adjusted Spreads -- Asset Price Bubbles in Complete Markets -- Taxation and Transaction Costs in a General Equilibrium Asset Economy -- Calibration of Lévy Term Structure Models -- Pricing of Swaptions in Affine Term Structures with Stochastic Volatility -- Forward Evolution Equations for Knock-Out Options -- Mean Reversion Versus Random Walk in Oil and Natural Gas Prices -- Credit Risk and Investments -- Beyond Hazard Rates: A New Framework for Credit-Risk Modelling -- A Generic One-Factor Lévy Model for Pricing Synthetic CDOs -- Utility Valuation of Credit Derivatives: Single and Two-Name Cases -- Investment and Valuation Under Backward and Forward Dynamic Exponential Utilities in a Stochastic Factor Model En línea: http://dx.doi.org/10.1007/978-0-8176-4545-8 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34548 Advances in Mathematical Finance [documento electrónico] / SpringerLink (Online service) ; Fu, Michael C ; Jarrow, Robert A ; Yen, Ju-Yi J ; Elliott, Robert J . - Boston, MA : Birkhäuser Boston, 2007 . - XXVIII, 336 p : online resource. - (Applied and Numerical Harmonic Analysis, ISSN 2296-5009) .
ISBN : 978-0-8176-4545-8
Idioma : Inglés (eng)
Palabras clave: Mathematics Applied mathematics Engineering Economics, Mathematical Actuarial science Economic theory Macroeconomics Sciences Quantitative Finance Applications of Appl.Mathematics/Computational Methods Theory/Quantitative Economics/Mathematical Macroeconomics/Monetary Economics//Financial Economics Clasificación: 51 Matemáticas Resumen: This self-contained volume brings together a collection of chapters by some of the most distinguished researchers and practitioners in the fields of mathematical finance and financial engineering. Presenting state-of-the-art developments in theory and practice, the Festschrift is dedicated to Dilip B. Madan on the occasion of his 60th birthday. Specific topics covered include: * Theory and application of the Variance-Gamma process * Lévy process driven fixed-income and credit-risk models, including CDO pricing * Numerical PDE and Monte Carlo methods * Asset pricing and derivatives valuation and hedging * Itô formulas for fractional Brownian motion * Martingale characterization of asset price bubbles * Utility valuation for credit derivatives and portfolio management Advances in Mathematical Finance is a valuable resource for graduate students, researchers, and practitioners in mathematical finance and financial engineering. Contributors: H. Albrecher, D. C. Brody, P. Carr, E. Eberlein, R. J. Elliott, M. C. Fu, H. Geman, M. Heidari, A. Hirsa, L. P. Hughston, R. A. Jarrow, X. Jin, W. Kluge, S. A. Ladoucette, A. Macrina, D. B. Madan, F. Milne, M. Musiela, P. Protter, W. Schoutens, E. Seneta, K. Shimbo, R. Sircar, J. van der Hoek, M.Yor, T. Zariphopoulou Nota de contenido: Variance-Gamma and Related Stochastic Processes -- The Early Years of the Variance-Gamma Process -- Variance-Gamma and Monte Carlo -- Some Remarkable Properties of Gamma Processes -- A Note About Selberg’s Integrals in Relation with the Beta-Gamma Algebra -- Itô Formulas for Fractional Brownian Motion -- Asset and Option Pricing -- A Tutorial on Zero Volatility and Option Adjusted Spreads -- Asset Price Bubbles in Complete Markets -- Taxation and Transaction Costs in a General Equilibrium Asset Economy -- Calibration of Lévy Term Structure Models -- Pricing of Swaptions in Affine Term Structures with Stochastic Volatility -- Forward Evolution Equations for Knock-Out Options -- Mean Reversion Versus Random Walk in Oil and Natural Gas Prices -- Credit Risk and Investments -- Beyond Hazard Rates: A New Framework for Credit-Risk Modelling -- A Generic One-Factor Lévy Model for Pricing Synthetic CDOs -- Utility Valuation of Credit Derivatives: Single and Two-Name Cases -- Investment and Valuation Under Backward and Forward Dynamic Exponential Utilities in a Stochastic Factor Model En línea: http://dx.doi.org/10.1007/978-0-8176-4545-8 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34548 Ejemplares
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Título : Approximation Theory : From Taylor Polynomials to Wavelets Tipo de documento: documento electrónico Autores: Christensen, Ole ; SpringerLink (Online service) ; Christensen, Khadija L Editorial: Boston, MA : Birkhäuser Boston Fecha de publicación: 2005 Otro editor: Imprint: Birkhäuser Colección: Applied and Numerical Harmonic Analysis, ISSN 2296-5009 Número de páginas: XI, 156 p. 5 illus Il.: online resource ISBN/ISSN/DL: 978-0-8176-4448-2 Idioma : Inglés (eng) Palabras clave: Mathematics Harmonic analysis Approximation theory Fourier Functional Applied mathematics Engineering Analysis Approximations and Expansions Abstract Applications of Signal, Image Speech Processing Clasificación: 51 Matemáticas Resumen: This concisely written book gives an elementary introduction to a classical area of mathematics—approximation theory—in a way that naturally leads to the modern field of wavelets. The exposition, driven by ideas rather than technical details and proofs, demonstrates the dynamic nature of mathematics and the influence of classical disciplines on many areas of modern mathematics and applications. Key features and topics: * Description of wavelets in words rather than mathematical symbols * Elementary introduction to approximation using polynomials (Weierstrass’ and Taylor’s theorems) * Introduction to infinite series, with emphasis on approximation-theoretic aspects * Introduction to Fourier analysis * Numerous classical, illustrative examples and constructions * Discussion of the role of wavelets in digital signal processing and data compression, such as the FBI’s use of wavelets to store fingerprints * Minimal prerequisites: elementary calculus * Exercises that may be used in undergraduate and graduate courses on infinite series and Fourier series Approximation Theory: From Taylor Polynomials to Wavelets will be an excellent textbook or self-study reference for students and instructors in pure and applied mathematics, mathematical physics, and engineering. Readers will find motivation and background material pointing toward advanced literature and research topics in pure and applied harmonic analysis and related areas Nota de contenido: 1 Approximation with Polynomials -- 1.1 Approximation of a function on an interval -- 1.2 Weierstrass’ theorem -- 1.3 Taylor’s theorem -- 1.4 Exercises -- 2 Infinite Series -- 2.1 Infinite series of numbers -- 2.2 Estimating the sum of an infinite series -- 2.3 Geometric series -- 2.4 Power series -- 2.5 General infinite sums of functions -- 2.6 Uniform convergence -- 2.7 Signal transmission -- 2.8 Exercises -- 3 Fourier Analysis -- 3.1 Fourier series -- 3.2 Fourier’s theorem and approximation -- 3.3 Fourier series and signal analysis -- 3.4 Fourier series and Hilbert spaces -- 3.5 Fourier series in complex form -- 3.6 Parseval’s theorem -- 3.7 Regularity and decay of the Fourier coefficients -- 3.8 Best N-term approximation -- 3.9 The Fourier transform -- 3.10 Exercises -- 4 Wavelets and Applications -- 4.1 About wavelet systems -- 4.2 Wavelets and signal processing -- 4.3 Wavelets and fingerprints -- 4.4 Wavelet packets -- 4.5 Alternatives to wavelets: Gabor systems -- 4.6 Exercises -- 5 Wavelets and their Mathematical Properties -- 5.1 Wavelets and L2 (?) -- 5.2 Multiresolution analysis -- 5.3 The role of the Fourier transform -- 5.4 The Haar wavelet -- 5.5 The role of compact support -- 5.6 Wavelets and singularities -- 5.7 Best N-term approximation -- 5.8 Frames -- 5.9 Gabor systems -- 5.10 Exercises -- Appendix A -- A.1 Definitions and notation -- A.2 Proof of Weierstrass’ theorem -- A.3 Proof of Taylor’s theorem -- A.4 Infinite series -- A.5 Proof of Theorem 3 7 2 -- Appendix B -- B.1 Power series -- B.2 Fourier series for 2?-periodic functions -- List of Symbols -- References En línea: http://dx.doi.org/10.1007/978-0-8176-4448-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35195 Approximation Theory : From Taylor Polynomials to Wavelets [documento electrónico] / Christensen, Ole ; SpringerLink (Online service) ; Christensen, Khadija L . - Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser, 2005 . - XI, 156 p. 5 illus : online resource. - (Applied and Numerical Harmonic Analysis, ISSN 2296-5009) .
ISBN : 978-0-8176-4448-2
Idioma : Inglés (eng)
Palabras clave: Mathematics Harmonic analysis Approximation theory Fourier Functional Applied mathematics Engineering Analysis Approximations and Expansions Abstract Applications of Signal, Image Speech Processing Clasificación: 51 Matemáticas Resumen: This concisely written book gives an elementary introduction to a classical area of mathematics—approximation theory—in a way that naturally leads to the modern field of wavelets. The exposition, driven by ideas rather than technical details and proofs, demonstrates the dynamic nature of mathematics and the influence of classical disciplines on many areas of modern mathematics and applications. Key features and topics: * Description of wavelets in words rather than mathematical symbols * Elementary introduction to approximation using polynomials (Weierstrass’ and Taylor’s theorems) * Introduction to infinite series, with emphasis on approximation-theoretic aspects * Introduction to Fourier analysis * Numerous classical, illustrative examples and constructions * Discussion of the role of wavelets in digital signal processing and data compression, such as the FBI’s use of wavelets to store fingerprints * Minimal prerequisites: elementary calculus * Exercises that may be used in undergraduate and graduate courses on infinite series and Fourier series Approximation Theory: From Taylor Polynomials to Wavelets will be an excellent textbook or self-study reference for students and instructors in pure and applied mathematics, mathematical physics, and engineering. Readers will find motivation and background material pointing toward advanced literature and research topics in pure and applied harmonic analysis and related areas Nota de contenido: 1 Approximation with Polynomials -- 1.1 Approximation of a function on an interval -- 1.2 Weierstrass’ theorem -- 1.3 Taylor’s theorem -- 1.4 Exercises -- 2 Infinite Series -- 2.1 Infinite series of numbers -- 2.2 Estimating the sum of an infinite series -- 2.3 Geometric series -- 2.4 Power series -- 2.5 General infinite sums of functions -- 2.6 Uniform convergence -- 2.7 Signal transmission -- 2.8 Exercises -- 3 Fourier Analysis -- 3.1 Fourier series -- 3.2 Fourier’s theorem and approximation -- 3.3 Fourier series and signal analysis -- 3.4 Fourier series and Hilbert spaces -- 3.5 Fourier series in complex form -- 3.6 Parseval’s theorem -- 3.7 Regularity and decay of the Fourier coefficients -- 3.8 Best N-term approximation -- 3.9 The Fourier transform -- 3.10 Exercises -- 4 Wavelets and Applications -- 4.1 About wavelet systems -- 4.2 Wavelets and signal processing -- 4.3 Wavelets and fingerprints -- 4.4 Wavelet packets -- 4.5 Alternatives to wavelets: Gabor systems -- 4.6 Exercises -- 5 Wavelets and their Mathematical Properties -- 5.1 Wavelets and L2 (?) -- 5.2 Multiresolution analysis -- 5.3 The role of the Fourier transform -- 5.4 The Haar wavelet -- 5.5 The role of compact support -- 5.6 Wavelets and singularities -- 5.7 Best N-term approximation -- 5.8 Frames -- 5.9 Gabor systems -- 5.10 Exercises -- Appendix A -- A.1 Definitions and notation -- A.2 Proof of Weierstrass’ theorem -- A.3 Proof of Taylor’s theorem -- A.4 Infinite series -- A.5 Proof of Theorem 3 7 2 -- Appendix B -- B.1 Power series -- B.2 Fourier series for 2?-periodic functions -- List of Symbols -- References En línea: http://dx.doi.org/10.1007/978-0-8176-4448-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35195 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: Krantz, Steven G ; 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] / Krantz, Steven G ; 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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Título : Four Short Courses on Harmonic Analysis : Wavelets, Frames, Time-Frequency Methods, and Applications to Signal and Image Analysis Tipo de documento: documento electrónico Autores: SpringerLink (Online service) ; Forster, Brigitte ; Massopust, Peter Editorial: Boston, MA : Birkhäuser Boston Fecha de publicación: 2010 Colección: Applied and Numerical Harmonic Analysis, ISSN 2296-5009 Número de páginas: XVIII, 249 p. 36 illus Il.: online resource ISBN/ISSN/DL: 978-0-8176-4891-6 Idioma : Inglés (eng) Palabras clave: Mathematics Harmonic analysis Fourier Physics Analysis Abstract Signal, Image and Speech Processing Theoretical, Mathematical Computational Clasificación: 51 Matemáticas Resumen: This state-of-the-art textbook examines four research directions in harmonic analysis and features some of the latest applications in the field, including cosmic microwave background analysis, human cortex image denoising, and wireless communication. The work is the first one that combines spline theory (from a numerical or approximation-theoretical view), wavelets, frames, and time-frequency methods leading up to a construction of wavelets on manifolds other than Rn. Written by internationally renowned mathematicians, the interdisciplinary chapters are expository by design, enabling the reader to understand the theory behind modern image and signal processing methodologies. The main emphasis throughout the book is on the interdependence of the four modern research directions covered. Each chapter ends with exercises that allow for a more in-depth understanding of the material and are intended to stimulate the reader toward further research. A comprehensive index completes the work. Topics covered: * Frames and bases in mathematics and engineering * Wavelets with composite dilations and their applications * Wavelets on the sphere and their applications * Wiener's Lemma: theme and variations Four Short Courses on Harmonic Analysis is intended as a graduate-level textbook for courses or seminars on harmonic analysis and its applications. The work is also an excellent reference or self-study guide for researchers and practitioners with diverse mathematical backgrounds working in different fields such as pure and applied mathematics, image and signal processing engineering, mathematical physics, and communication theory Nota de contenido: Introduction: Mathematical Aspects of Time-Frequency Analysis -- B-Spline Generated Frames -- Continuous and Discrete Reproducing Systems That Arise from Translations. Theory and Applications of Composite Wavelets -- Wavelets on the Sphere -- Wiener’s Lemma: Theme and Variations. An Introduction to Spectral Invariance and Its Applications En línea: http://dx.doi.org/10.1007/978-0-8176-4891-6 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33549 Four Short Courses on Harmonic Analysis : Wavelets, Frames, Time-Frequency Methods, and Applications to Signal and Image Analysis [documento electrónico] / SpringerLink (Online service) ; Forster, Brigitte ; Massopust, Peter . - Boston, MA : Birkhäuser Boston, 2010 . - XVIII, 249 p. 36 illus : online resource. - (Applied and Numerical Harmonic Analysis, ISSN 2296-5009) .
ISBN : 978-0-8176-4891-6
Idioma : Inglés (eng)
Palabras clave: Mathematics Harmonic analysis Fourier Physics Analysis Abstract Signal, Image and Speech Processing Theoretical, Mathematical Computational Clasificación: 51 Matemáticas Resumen: This state-of-the-art textbook examines four research directions in harmonic analysis and features some of the latest applications in the field, including cosmic microwave background analysis, human cortex image denoising, and wireless communication. The work is the first one that combines spline theory (from a numerical or approximation-theoretical view), wavelets, frames, and time-frequency methods leading up to a construction of wavelets on manifolds other than Rn. Written by internationally renowned mathematicians, the interdisciplinary chapters are expository by design, enabling the reader to understand the theory behind modern image and signal processing methodologies. The main emphasis throughout the book is on the interdependence of the four modern research directions covered. Each chapter ends with exercises that allow for a more in-depth understanding of the material and are intended to stimulate the reader toward further research. A comprehensive index completes the work. Topics covered: * Frames and bases in mathematics and engineering * Wavelets with composite dilations and their applications * Wavelets on the sphere and their applications * Wiener's Lemma: theme and variations Four Short Courses on Harmonic Analysis is intended as a graduate-level textbook for courses or seminars on harmonic analysis and its applications. The work is also an excellent reference or self-study guide for researchers and practitioners with diverse mathematical backgrounds working in different fields such as pure and applied mathematics, image and signal processing engineering, mathematical physics, and communication theory Nota de contenido: Introduction: Mathematical Aspects of Time-Frequency Analysis -- B-Spline Generated Frames -- Continuous and Discrete Reproducing Systems That Arise from Translations. Theory and Applications of Composite Wavelets -- Wavelets on the Sphere -- Wiener’s Lemma: Theme and Variations. An Introduction to Spectral Invariance and Its Applications En línea: http://dx.doi.org/10.1007/978-0-8176-4891-6 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33549 Ejemplares
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Título : Geometric Mechanics on Riemannian Manifolds : Applications to Partial Differential Equations Tipo de documento: documento electrónico Autores: Calin, Ovidiu ; SpringerLink (Online service) ; Chang, Der-Chen Editorial: Boston, MA : Birkhäuser Boston Fecha de publicación: 2005 Colección: Applied and Numerical Harmonic Analysis, ISSN 2296-5009 Número de páginas: XVI, 278 p. 26 illus Il.: online resource ISBN/ISSN/DL: 978-0-8176-4421-5 Idioma : Inglés (eng) Palabras clave: Mathematics Harmonic analysis Fourier Partial differential equations Applied mathematics Engineering Differential geometry Physics Analysis Geometry Equations Mathematical Methods in Abstract Applications of Clasificación: 51 Matemáticas Resumen: Differential geometry techniques have very useful and important applications in partial differential equations and quantum mechanics. This work presents a purely geometric treatment of problems in physics involving quantum harmonic oscillators, quartic oscillators, minimal surfaces, and Schrödinger's, Einstein's and Newton's equations. Historically, problems in these areas were approached using the Fourier transform or path integrals, although in some cases (e.g., the case of quartic oscillators) these methods do not work. New geometric methods are introduced in the work that have the advantage of providing quantitative or at least qualitative descriptions of operators, many of which cannot be treated by other methods. And, conservation laws of the Euler–Lagrange equations are employed to solve the equations of motion qualitatively when quantitative analysis is not possible. Main topics include: Lagrangian formalism on Riemannian manifolds; energy momentum tensor and conservation laws; Hamiltonian formalism; Hamilton–Jacobi theory; harmonic functions, maps, and geodesics; fundamental solutions for heat operators with potential; and a variational approach to mechanical curves. The text is enriched with good examples and exercises at the end of every chapter. Geometric Mechanics on Riemannian Manifolds is a fine text for a course or seminar directed at graduate and advanced undergraduate students interested in elliptic and hyperbolic differential equations, differential geometry, calculus of variations, quantum mechanics, and physics. It is also an ideal resource for pure and applied mathematicians and theoretical physicists working in these areas Nota de contenido: Introductory Chapter -- Laplace Operators on Riemannian Manifolds -- Lagrangian Formalism on Riemannian Manifolds -- Harmonic Maps from a Lagrangian Viewpoint -- Conservation Theorems -- Hamiltonian Formalism -- Hamilton-Jacobi Theory -- Minimal Hypersurfaces -- Radially Symmetric Spaces -- Fundamental Solutions for Heat Operators with Potentials -- Fundamental Solutions for Elliptic Operators -- Mechanical Curves En línea: http://dx.doi.org/10.1007/b138771 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35179 Geometric Mechanics on Riemannian Manifolds : Applications to Partial Differential Equations [documento electrónico] / Calin, Ovidiu ; SpringerLink (Online service) ; Chang, Der-Chen . - Boston, MA : Birkhäuser Boston, 2005 . - XVI, 278 p. 26 illus : online resource. - (Applied and Numerical Harmonic Analysis, ISSN 2296-5009) .
ISBN : 978-0-8176-4421-5
Idioma : Inglés (eng)
Palabras clave: Mathematics Harmonic analysis Fourier Partial differential equations Applied mathematics Engineering Differential geometry Physics Analysis Geometry Equations Mathematical Methods in Abstract Applications of Clasificación: 51 Matemáticas Resumen: Differential geometry techniques have very useful and important applications in partial differential equations and quantum mechanics. This work presents a purely geometric treatment of problems in physics involving quantum harmonic oscillators, quartic oscillators, minimal surfaces, and Schrödinger's, Einstein's and Newton's equations. Historically, problems in these areas were approached using the Fourier transform or path integrals, although in some cases (e.g., the case of quartic oscillators) these methods do not work. New geometric methods are introduced in the work that have the advantage of providing quantitative or at least qualitative descriptions of operators, many of which cannot be treated by other methods. And, conservation laws of the Euler–Lagrange equations are employed to solve the equations of motion qualitatively when quantitative analysis is not possible. Main topics include: Lagrangian formalism on Riemannian manifolds; energy momentum tensor and conservation laws; Hamiltonian formalism; Hamilton–Jacobi theory; harmonic functions, maps, and geodesics; fundamental solutions for heat operators with potential; and a variational approach to mechanical curves. The text is enriched with good examples and exercises at the end of every chapter. Geometric Mechanics on Riemannian Manifolds is a fine text for a course or seminar directed at graduate and advanced undergraduate students interested in elliptic and hyperbolic differential equations, differential geometry, calculus of variations, quantum mechanics, and physics. It is also an ideal resource for pure and applied mathematicians and theoretical physicists working in these areas Nota de contenido: Introductory Chapter -- Laplace Operators on Riemannian Manifolds -- Lagrangian Formalism on Riemannian Manifolds -- Harmonic Maps from a Lagrangian Viewpoint -- Conservation Theorems -- Hamiltonian Formalism -- Hamilton-Jacobi Theory -- Minimal Hypersurfaces -- Radially Symmetric Spaces -- Fundamental Solutions for Heat Operators with Potentials -- Fundamental Solutions for Elliptic Operators -- Mechanical Curves En línea: http://dx.doi.org/10.1007/b138771 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35179 Ejemplares
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