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Differential Equations with Maple / Jon H. Davis / Bâle (CHE) ; Boston, MA : Birkhäuser (2001)
Titre : Differential Equations with Maple : An Interactive Approach Type de document : document électronique Auteurs : Jon H. Davis ; SpringerLink (Online service) Editeur : Bâle (CHE) ; Boston, MA : Birkhäuser Année de publication : 2001 Importance : XVII, 411 p Présentation : online resource ISBN/ISSN/EAN : 978-1-4612-1376-5 Langues : Anglais (eng) Tags : Mathematics Computer-aided engineering Mathematical analysis Analysis Differential equations Applied mathematics Engineering mathematics Ordinary Differential Equations Computer-Aided Engineering (CAD CAE) and Design Applications of Mathematics Résumé : Differential equations is a subject of wide applicability, and knowledge of dif Differential equations is a subject of wide applicability, and knowledge of dif ferential ferential equations equations topics topics permeates permeates all all areas areas of of study study in in engineering engineering and and applied applied mathematics. mathematics. Some Some differential differential equations equations are are susceptible susceptible to to analytic analytic means means of of so so lution, lution, while while others others require require the the generation generation of of numerical numerical solution solution trajectories trajectories to to see see the the behavior behavior of of the the system system under under study. study. For For both both situations, situations, the the software software package package Maple Maple can can be be used used to to advantage. advantage. To To the the student student Making Making effective effective use use of of differential differential equations equations requires requires facility facility in in recognizing recognizing and and solving solving standard standard "tractable" "tractable" problems, problems, as as well well as as having having the the background background in in the the subject subject to to make make use use of of tools tools for for dealing dealing with with situations situations that that are are not not amenable amenable to to simple simple analytic analytic approaches. approaches Note de contenu : I Maple Use and Programming -- 1 Introduction to Maple -- II Differential Equations -- 2 Introduction to Differential Equations -- 3 First Order Equations -- 4 Introduction to Numerical Methods -- 5 Higher Order Differential Equations -- 6 Laplace Transform Methods -- 7 Systems of Equations -- 8 Stability -- 9 Periodic Problems -- 10 Impedances and Differential Equations -- 11 Partial Differential Equations -- III Maple Application Topics -- 12 Introduction to Maple Applications -- 13 Plotting With Maple -- 14 Maple and Laplace Transforms -- 15 Maple Linear Algebra Applications -- 16 Runge-Kutta Designs -- 17 Maple Packages -- IV Appendices -- A Review Problems -- B Laplace Transform Table -- References Permalink : https://genes.bibli.fr/index.php?lvl=notice_display&id=126998 Differential Equations with Maple : An Interactive Approach [document électronique] / Jon H. Davis ; SpringerLink (Online service) . - Bâle (CHE) ; Boston, MA : Birkhäuser, 2001 . - XVII, 411 p : online resource.
ISBN : 978-1-4612-1376-5
Langues : Anglais (eng)
Tags : Mathematics Computer-aided engineering Mathematical analysis Analysis Differential equations Applied mathematics Engineering mathematics Ordinary Differential Equations Computer-Aided Engineering (CAD CAE) and Design Applications of Mathematics Résumé : Differential equations is a subject of wide applicability, and knowledge of dif Differential equations is a subject of wide applicability, and knowledge of dif ferential ferential equations equations topics topics permeates permeates all all areas areas of of study study in in engineering engineering and and applied applied mathematics. mathematics. Some Some differential differential equations equations are are susceptible susceptible to to analytic analytic means means of of so so lution, lution, while while others others require require the the generation generation of of numerical numerical solution solution trajectories trajectories to to see see the the behavior behavior of of the the system system under under study. study. For For both both situations, situations, the the software software package package Maple Maple can can be be used used to to advantage. advantage. To To the the student student Making Making effective effective use use of of differential differential equations equations requires requires facility facility in in recognizing recognizing and and solving solving standard standard "tractable" "tractable" problems, problems, as as well well as as having having the the background background in in the the subject subject to to make make use use of of tools tools for for dealing dealing with with situations situations that that are are not not amenable amenable to to simple simple analytic analytic approaches. approaches Note de contenu : I Maple Use and Programming -- 1 Introduction to Maple -- II Differential Equations -- 2 Introduction to Differential Equations -- 3 First Order Equations -- 4 Introduction to Numerical Methods -- 5 Higher Order Differential Equations -- 6 Laplace Transform Methods -- 7 Systems of Equations -- 8 Stability -- 9 Periodic Problems -- 10 Impedances and Differential Equations -- 11 Partial Differential Equations -- III Maple Application Topics -- 12 Introduction to Maple Applications -- 13 Plotting With Maple -- 14 Maple and Laplace Transforms -- 15 Maple Linear Algebra Applications -- 16 Runge-Kutta Designs -- 17 Maple Packages -- IV Appendices -- A Review Problems -- B Laplace Transform Table -- References Permalink : https://genes.bibli.fr/index.php?lvl=notice_display&id=126998 Foundations of Deterministic and Stochastic Control / Jon H. Davis / Bâle (CHE) ; Boston, MA : Birkhäuser (2002)
Titre : Foundations of Deterministic and Stochastic Control Type de document : document électronique Auteurs : Jon H. Davis ; SpringerLink (Online service) Editeur : Bâle (CHE) ; Boston, MA : Birkhäuser Année de publication : 2002 Collection : Systems & Control: Foundations & Applications, ISSN 2324-9749 Importance : XIV, 426 p Présentation : online resource ISBN/ISSN/EAN : 978-1-4612-0071-0 Langues : Anglais (eng) Tags : Mathematics Partial differential equations System theory Probabilities Control engineering Electrical engineering Probability Theory and Stochastic Processes Control Systems Theory Partial Differential Equations Communications Engineering Networks Résumé : Control theory has applications to a number of areas in engineering and communication theory. This introductory text on the subject is fairly self-contained, and consists of a wide range of topics that include realization problems, linear-quadratic optimal control, stability theory, stochastic modeling and recursive estimation algorithms in communications and control, and distributed system modeling. In the early chapters methods based on Wiener--Hopf integral equations are utilized. The fundamentals of both linear control systems as well as stochastic control are presented in a unique way so that the methods generalize to a useful class of distributed parameter and nonlinear system models. The control of distributed parameter systems (systems governed by PDEs) is based on the framework of linear quadratic Gaussian optimization problems. Additionally, the important notion of state space modeling of distributed systems is examined. Basic results due to Gohberg and Krein on convolution are given and many results are illustrated with some examples that carry throughout the text. The standard linear regulator problem is studied in the continuous and discrete time cases, followed by a discussion of (dual) filtering problems. Later chapters treat the stationary regulator and filtering problems using a Wiener--Hopf approach. This leads to spectral factorization problems and useful iterative algorithms that follow naturally from the methods employed. The interplay between time and frequency domain approaches is emphasized. "Foundations of Deterministic and Stochastic Control" is geared primarily towards advanced mathematics and engineering students in various disciplines Note de contenu : 1 State Space Realizations -- 1.1 Linear Models -- 1.2 Realizations -- 1.3 Constructing Time Invariant Realizations -- 1.4 An Active Suspension Model -- 1.5 A Model Identification Problem -- 1.6 Simulating Recursive Identification -- 1.7 Discrete Time Models -- Problems -- 2 Least Squares Control -- 2.1 Minimum Energy Transfers -- 2.2 The Output Regulator -- 2.3 Linear Regulator Tracking Problems -- 2.4 Dynamic Programming -- Problems -- 3 Stability Theory -- 3.1 Introduction -- 3.2 Introduction to Lyapunov Theory -- 3.3 Definitions -- 3.4 Classical Lyapunov Theorems -- 3.5 The Invariance Approach -- 3.6 Input-Output Stability -- Problems -- 4 Random Variables and Processes -- 4.1 Introduction -- 4.2 Random Variables -- 4.3 Sample Spaces and Probabilities -- 4.4 Densities -- 4.5 Expectations, Inner Products and Variances -- 4.6 Linear Minimum Variance Estimates -- 4.7 Gramians and Covariance Matrices -- 4.8 Random Processes -- 4.9 Gaussian Variables -- Problems -- 5 Kalman-Bucy Filters -- 5.1 The Model -- 5.2 Estimation Criterion -- 5.3 The One Step Predictor -- Problems -- 6 Continuous Time Models -- 6.1 Introduction -- 6.2 Stochastic Integrals -- 6.3 Stochastic Differential Equations -- 6.4 Linear Models -- 6.5 Second Order Results -- 6.6 Continuous White Noise -- 6.7 Continuous Time Kalman-Bucy Filters -- Problems -- 7 The Separation Theorem -- 7.1 Stochastic Dynamic Programming -- 7.2 Dynamic Programming Algorithm -- 7.3 Discrete Time Stochastic Regulator -- 7.4 Continuous Time -- 7.5 The Time Invariant Case -- 7.6 Active Suspension -- Problems -- 8 Luenberger Observers -- 8.1 Full State Observers -- 8.2 Reduced Order Observers -- Problems -- 9 Nonlinear and Finite State Problems -- 9.1 Introduction -- 9.2 Finite State Machines -- 9.3 Finite Markov Processes -- 9.4 Hidden Markov Models -- Problems -- 10 Wiener-Hopf Methods -- 10.1 Wiener Filters -- 10.2 Spectral Factorization -- 10.3 The Scalar Case - Spectral Factorization -- 10.4 Discrete Time Factorization -- 10.5 Factorization in The Vector Case -- 10.6 Finite Dimensional Symmetric Problems -- 10.7 Spectral Factors and Optimal Gains -- 10.8 Linear Regulators and The Projection Theorem -- Problems -- 11 Distributed System Regulators -- 11.1 Open Loop Unstable Distributed Regulators -- 11.2 The ?Wiener-Hopf? Condition -- 11.3 Optimal Feedback Gains -- 11.4 Matched Filter Evasion -- Problems -- 12 Filters Without Riccati Equations -- 12.1 Introduction -- 12.2 Basic Problem Formulation -- 12.3 Spectral Factors -- 12.4 Closed Loop Stability -- 12.5 Realizing The Optimal Filter -- Problems -- 13 Newton?s Method for Riccati Equations -- 13.1 Newton?s Method -- 13.2 Continuous Time Riccati Equations -- 13.3 Discrete Time Riccati Equations -- 13.4 Convergence of Newton?s Method -- 14 Numerical Spectral Factorization -- 14.1 Introduction -- 14.2 An Intuitive Algorithm Derivation -- 14.3 A Convergence Proof for the Continuous Time Algorithm -- 14.4 Implementation -- 14.5 The Discrete Case -- 14.6 Numerical Comments -- A Hilbert and Banach Spaces and Operators -- A.1 Banach and Hilbert Spaces -- A.2 Quotient Spaces -- A.3 Dual Spaces -- A.4 Bounded Linear Operators -- A.5 Induced Norms -- A.6 The Banach Space G(X, Y) -- A.7 Adjoint Mappings -- A.8 Orthogonal Complements -- A.9 Projection Theorem -- A.10 Abstract Linear Equations -- A.11 Linear Equations and Adjoints -- A.12 Minimum Miss Distance Problems -- A.13 Minimum Norm Problems -- A.14 Fredholm Operators -- A.15 Banach Algebras -- A.15.1 Inverses and Spectra -- A.15.2 Ideals, Transforms, and Spectra -- A.15.3 Functional Calculus -- B Measure Theoretic Probability -- B.1 Measure Theory -- B.2 Random variables -- B.3 Integrals and Expectation -- B.4 Derivatives and Densities -- B.5 Conditional Probabilities and Expectations -- B.5.1 Conditional Probability -- B.5.2 Conditional Expectations -- References Permalink : https://genes.bibli.fr/index.php?lvl=notice_display&id=126854 Foundations of Deterministic and Stochastic Control [document électronique] / Jon H. Davis ; SpringerLink (Online service) . - Bâle (CHE) ; Boston, MA : Birkhäuser, 2002 . - XIV, 426 p : online resource. - (Systems & Control: Foundations & Applications, ISSN 2324-9749) .
ISBN : 978-1-4612-0071-0
Langues : Anglais (eng)
Tags : Mathematics Partial differential equations System theory Probabilities Control engineering Electrical engineering Probability Theory and Stochastic Processes Control Systems Theory Partial Differential Equations Communications Engineering Networks Résumé : Control theory has applications to a number of areas in engineering and communication theory. This introductory text on the subject is fairly self-contained, and consists of a wide range of topics that include realization problems, linear-quadratic optimal control, stability theory, stochastic modeling and recursive estimation algorithms in communications and control, and distributed system modeling. In the early chapters methods based on Wiener--Hopf integral equations are utilized. The fundamentals of both linear control systems as well as stochastic control are presented in a unique way so that the methods generalize to a useful class of distributed parameter and nonlinear system models. The control of distributed parameter systems (systems governed by PDEs) is based on the framework of linear quadratic Gaussian optimization problems. Additionally, the important notion of state space modeling of distributed systems is examined. Basic results due to Gohberg and Krein on convolution are given and many results are illustrated with some examples that carry throughout the text. The standard linear regulator problem is studied in the continuous and discrete time cases, followed by a discussion of (dual) filtering problems. Later chapters treat the stationary regulator and filtering problems using a Wiener--Hopf approach. This leads to spectral factorization problems and useful iterative algorithms that follow naturally from the methods employed. The interplay between time and frequency domain approaches is emphasized. "Foundations of Deterministic and Stochastic Control" is geared primarily towards advanced mathematics and engineering students in various disciplines Note de contenu : 1 State Space Realizations -- 1.1 Linear Models -- 1.2 Realizations -- 1.3 Constructing Time Invariant Realizations -- 1.4 An Active Suspension Model -- 1.5 A Model Identification Problem -- 1.6 Simulating Recursive Identification -- 1.7 Discrete Time Models -- Problems -- 2 Least Squares Control -- 2.1 Minimum Energy Transfers -- 2.2 The Output Regulator -- 2.3 Linear Regulator Tracking Problems -- 2.4 Dynamic Programming -- Problems -- 3 Stability Theory -- 3.1 Introduction -- 3.2 Introduction to Lyapunov Theory -- 3.3 Definitions -- 3.4 Classical Lyapunov Theorems -- 3.5 The Invariance Approach -- 3.6 Input-Output Stability -- Problems -- 4 Random Variables and Processes -- 4.1 Introduction -- 4.2 Random Variables -- 4.3 Sample Spaces and Probabilities -- 4.4 Densities -- 4.5 Expectations, Inner Products and Variances -- 4.6 Linear Minimum Variance Estimates -- 4.7 Gramians and Covariance Matrices -- 4.8 Random Processes -- 4.9 Gaussian Variables -- Problems -- 5 Kalman-Bucy Filters -- 5.1 The Model -- 5.2 Estimation Criterion -- 5.3 The One Step Predictor -- Problems -- 6 Continuous Time Models -- 6.1 Introduction -- 6.2 Stochastic Integrals -- 6.3 Stochastic Differential Equations -- 6.4 Linear Models -- 6.5 Second Order Results -- 6.6 Continuous White Noise -- 6.7 Continuous Time Kalman-Bucy Filters -- Problems -- 7 The Separation Theorem -- 7.1 Stochastic Dynamic Programming -- 7.2 Dynamic Programming Algorithm -- 7.3 Discrete Time Stochastic Regulator -- 7.4 Continuous Time -- 7.5 The Time Invariant Case -- 7.6 Active Suspension -- Problems -- 8 Luenberger Observers -- 8.1 Full State Observers -- 8.2 Reduced Order Observers -- Problems -- 9 Nonlinear and Finite State Problems -- 9.1 Introduction -- 9.2 Finite State Machines -- 9.3 Finite Markov Processes -- 9.4 Hidden Markov Models -- Problems -- 10 Wiener-Hopf Methods -- 10.1 Wiener Filters -- 10.2 Spectral Factorization -- 10.3 The Scalar Case - Spectral Factorization -- 10.4 Discrete Time Factorization -- 10.5 Factorization in The Vector Case -- 10.6 Finite Dimensional Symmetric Problems -- 10.7 Spectral Factors and Optimal Gains -- 10.8 Linear Regulators and The Projection Theorem -- Problems -- 11 Distributed System Regulators -- 11.1 Open Loop Unstable Distributed Regulators -- 11.2 The ?Wiener-Hopf? Condition -- 11.3 Optimal Feedback Gains -- 11.4 Matched Filter Evasion -- Problems -- 12 Filters Without Riccati Equations -- 12.1 Introduction -- 12.2 Basic Problem Formulation -- 12.3 Spectral Factors -- 12.4 Closed Loop Stability -- 12.5 Realizing The Optimal Filter -- Problems -- 13 Newton?s Method for Riccati Equations -- 13.1 Newton?s Method -- 13.2 Continuous Time Riccati Equations -- 13.3 Discrete Time Riccati Equations -- 13.4 Convergence of Newton?s Method -- 14 Numerical Spectral Factorization -- 14.1 Introduction -- 14.2 An Intuitive Algorithm Derivation -- 14.3 A Convergence Proof for the Continuous Time Algorithm -- 14.4 Implementation -- 14.5 The Discrete Case -- 14.6 Numerical Comments -- A Hilbert and Banach Spaces and Operators -- A.1 Banach and Hilbert Spaces -- A.2 Quotient Spaces -- A.3 Dual Spaces -- A.4 Bounded Linear Operators -- A.5 Induced Norms -- A.6 The Banach Space G(X, Y) -- A.7 Adjoint Mappings -- A.8 Orthogonal Complements -- A.9 Projection Theorem -- A.10 Abstract Linear Equations -- A.11 Linear Equations and Adjoints -- A.12 Minimum Miss Distance Problems -- A.13 Minimum Norm Problems -- A.14 Fredholm Operators -- A.15 Banach Algebras -- A.15.1 Inverses and Spectra -- A.15.2 Ideals, Transforms, and Spectra -- A.15.3 Functional Calculus -- B Measure Theoretic Probability -- B.1 Measure Theory -- B.2 Random variables -- B.3 Integrals and Expectation -- B.4 Derivatives and Densities -- B.5 Conditional Probabilities and Expectations -- B.5.1 Conditional Probability -- B.5.2 Conditional Expectations -- References Permalink : https://genes.bibli.fr/index.php?lvl=notice_display&id=126854 Methods of Applied Mathematics with a MATLAB Overview / Jon H. Davis / Bâle (CHE) ; Boston, MA : Birkhäuser (2004)
Titre : Methods of Applied Mathematics with a MATLAB Overview Type de document : document électronique Auteurs : Jon H. Davis ; SpringerLink (Online service) Editeur : Bâle (CHE) ; Boston, MA : Birkhäuser Année de publication : 2004 Collection : Applied and Numerical Harmonic Analysis, ISSN 2296-5009 Importance : XIII, 721 p Présentation : online resource ISBN/ISSN/EAN : 978-0-8176-8198-2 Langues : Anglais (eng) Tags : Mathematics Harmonic analysis Fourier analysis Functions of complex variables Applied mathematics Engineering mathematics Computer mathematics Physics Fourier Analysis Computational Mathematics and Numerical Analysis Theoretical Mathematical and Computational Physics Applications of Mathematics Abstract Harmonic Analysis Functions of a Complex Variable Résumé : Broadly organized around the applications of Fourier analysis, Methods of Applied Mathematics with a MATLAB Overview covers both classical applications in partial differential equations and boundary value problems, as well as the concepts and methods associated to the Laplace, Fourier, and discrete transforms. Transform inversion problems are also examined, along with the necessary background in complex variables. A final chapter treats wavelets, short-time Fourier analysis, and geometrically-based transforms. The computer program MATLAB is emphasized throughout, and an introduction to MATLAB is provided in an appendix. Rich in examples, illustrations, and exercises of varying difficulty, this text can be used for a one- or two-semester course and is ideal for students in pure and applied mathematics, physics, and engineering Note de contenu : 1 Introduction -- 1.1 An Overview -- 1.2 Topics by Chapter -- 1.3 Applying Mathematics -- References -- 2 Fourier Series -- 2.1 Introduction -- 2.2 Inner Products and Fourier Expansions -- 2.3 Convergence of Fourier Series -- 2.4 Pointwise and Uniform Convergence of Fourier Series -- 2.5 Gibb?s Phenomenon and Summation Methods -- 2.6 Summation Methods -- 2.7 Fourier Series Properties -- 2.8 Periodic Solutions of Differential Equations -- 2.9 Impedance Methods and Periodic Solutions -- 2.10 Power Spectrum and Parseval?s Theorem -- References -- 3 Elementary Boundary Value Problems -- 3.1 Introduction -- 3.2 The One-Dimensional Diffusion Equation -- 3.3 The Wave Equation -- 3.4 The Potential Equation -- 3.5 Discrete Models of Boundary Value Problems -- 3.6 Separation of Variables -- 3.7 Half-Range Expansions and Symmetries -- 3.8 Some Matters of Detail -- References -- 4 Sturm-Liouville Theory and Boundary Value Problems -- 4.1 Further Boundary Value Problems -- 4.2 Selfadjoint Eigenvalue Problems -- 4.3 Sturm-Liouville Problems -- 4.4 Power Series and Singular Sturm-Liouville Problems -- 4.5 Cylindrical Problems and Bessel?s Equation -- 4.6 Multidimensional Problems and Forced Systems -- 4.7 Finite Differences and Numerical Methods -- 4.8 Variational Models and Finite Element Methods -- 4.9 Computational Finite Element Methods -- References -- 5 Functions of a Complex Variable -- 5.1 Complex Variables and Analytic Functions -- 5.2 Domains of Definition of Complex Functions -- 5.3 Integrals and Cauchy?s Theorem -- 5.4 Cauchy?s Integral Formula, Taylor Series, and Residues -- 5.5 Complex Variables and Fluid Flows -- 5.6 Conformal Mappings and the Principle of the Argument -- References -- 6 Laplace Transforms -- 6.1 Introduction -- 6.2 Definitions of the Laplace Transform -- 6.3 Mechanical Properties of Laplace Transforms -- 6.4 Elementary Transforms and Fourier Series Calculations -- 6.5 Elementary Applications to Differential Equations -- 6.6 Convolutions, Impulse Responses, and Weighting Patterns -- 6.7 Vector Differential Equations -- 6.8 Impedance Methods -- References -- 7. Fourier Transforms -- 7.1 Introduction -- 7.2 Basic Fourier Transforms -- 7.3 Formal Properties of Fourier Transforms -- 7.4 Convolutions and Parseval?s Theorem -- 7.5 Comments on the Inversion Theorem -- 7.6 Fourier Inversion by Contour Integration -- 7.7 The Laplace Transform Inversion Integral -- 7.8 An Introduction to Generalized Functions -- 7.9 Fourier Transforms, Differential Equations and Circuits -- 7.10 Transform Solutions of Boundary Value Problems -- 7.11 Band-limited Functions and Communications -- References -- 8 Discrete Variable Transforms -- 8.1 Some Discrete Variable Models -- 8.2 Z-Transforms -- 8.3 Z-Transform Properties -- 8.4 z-Transform Inversion Integral -- 8.5 Discrete Fourier Transforms -- 8.6 Discrete Fourier Transform Properties -- 8.7 Some Applications of Discrete Transform Methods -- 8.8 Finite and Fast Fourier Transforms -- 8.9 Finite Fourier Properties -- 8.10 Fast Finite Transform Algorithm -- 8.11 Computing The 1-1.1 -- References -- 9 Additional Topics -- 9.1 Local Waveform Analysis -- 9.2 Uncertainty Principle -- 9.3 Short-Time Fourier Transforms -- 9.4 Function Shifts and Scalings -- 9.5 Orthonormal Shifts -- 9.6 Multi-Resolution Analysis and Wavelets -- 9.7 On Wavelet Applications -- 9.8 Two-Sided Transforms -- 9.9 Walsh Functions -- 9.10 Geometrically Based Transforms -- References -- A Linear Algebra Overview -- A.1 Vector spaces -- A.2 Linear Mappings -- A.3 Inner Products -- A.4 Linear Functionals and Dual Spaces -- A.5 Canonical Forms -- References -- B Software Resources -- B.1 Computational and Visualization Software -- B.2 MATLAB Data Structures -- B.3 MATLAB Operators and Syntax -- B.4 MATLAB Programming Structures -- B.5 MATLAB Programs and Scripts -- B.6 Common Idioms -- B.7 Graphics -- B.8 Toolboxes and Enhancemants -- References -- C Transform Tables -- C.1 Laplace Transforms -- C.2 Fourier Transforms -- C.3 Z Transforms -- C.4 Discrete Fourier Transforms Permalink : https://genes.bibli.fr/index.php?lvl=notice_display&id=126697 Methods of Applied Mathematics with a MATLAB Overview [document électronique] / Jon H. Davis ; SpringerLink (Online service) . - Bâle (CHE) ; Boston, MA : Birkhäuser, 2004 . - XIII, 721 p : online resource. - (Applied and Numerical Harmonic Analysis, ISSN 2296-5009) .
ISBN : 978-0-8176-8198-2
Langues : Anglais (eng)
Tags : Mathematics Harmonic analysis Fourier analysis Functions of complex variables Applied mathematics Engineering mathematics Computer mathematics Physics Fourier Analysis Computational Mathematics and Numerical Analysis Theoretical Mathematical and Computational Physics Applications of Mathematics Abstract Harmonic Analysis Functions of a Complex Variable Résumé : Broadly organized around the applications of Fourier analysis, Methods of Applied Mathematics with a MATLAB Overview covers both classical applications in partial differential equations and boundary value problems, as well as the concepts and methods associated to the Laplace, Fourier, and discrete transforms. Transform inversion problems are also examined, along with the necessary background in complex variables. A final chapter treats wavelets, short-time Fourier analysis, and geometrically-based transforms. The computer program MATLAB is emphasized throughout, and an introduction to MATLAB is provided in an appendix. Rich in examples, illustrations, and exercises of varying difficulty, this text can be used for a one- or two-semester course and is ideal for students in pure and applied mathematics, physics, and engineering Note de contenu : 1 Introduction -- 1.1 An Overview -- 1.2 Topics by Chapter -- 1.3 Applying Mathematics -- References -- 2 Fourier Series -- 2.1 Introduction -- 2.2 Inner Products and Fourier Expansions -- 2.3 Convergence of Fourier Series -- 2.4 Pointwise and Uniform Convergence of Fourier Series -- 2.5 Gibb?s Phenomenon and Summation Methods -- 2.6 Summation Methods -- 2.7 Fourier Series Properties -- 2.8 Periodic Solutions of Differential Equations -- 2.9 Impedance Methods and Periodic Solutions -- 2.10 Power Spectrum and Parseval?s Theorem -- References -- 3 Elementary Boundary Value Problems -- 3.1 Introduction -- 3.2 The One-Dimensional Diffusion Equation -- 3.3 The Wave Equation -- 3.4 The Potential Equation -- 3.5 Discrete Models of Boundary Value Problems -- 3.6 Separation of Variables -- 3.7 Half-Range Expansions and Symmetries -- 3.8 Some Matters of Detail -- References -- 4 Sturm-Liouville Theory and Boundary Value Problems -- 4.1 Further Boundary Value Problems -- 4.2 Selfadjoint Eigenvalue Problems -- 4.3 Sturm-Liouville Problems -- 4.4 Power Series and Singular Sturm-Liouville Problems -- 4.5 Cylindrical Problems and Bessel?s Equation -- 4.6 Multidimensional Problems and Forced Systems -- 4.7 Finite Differences and Numerical Methods -- 4.8 Variational Models and Finite Element Methods -- 4.9 Computational Finite Element Methods -- References -- 5 Functions of a Complex Variable -- 5.1 Complex Variables and Analytic Functions -- 5.2 Domains of Definition of Complex Functions -- 5.3 Integrals and Cauchy?s Theorem -- 5.4 Cauchy?s Integral Formula, Taylor Series, and Residues -- 5.5 Complex Variables and Fluid Flows -- 5.6 Conformal Mappings and the Principle of the Argument -- References -- 6 Laplace Transforms -- 6.1 Introduction -- 6.2 Definitions of the Laplace Transform -- 6.3 Mechanical Properties of Laplace Transforms -- 6.4 Elementary Transforms and Fourier Series Calculations -- 6.5 Elementary Applications to Differential Equations -- 6.6 Convolutions, Impulse Responses, and Weighting Patterns -- 6.7 Vector Differential Equations -- 6.8 Impedance Methods -- References -- 7. Fourier Transforms -- 7.1 Introduction -- 7.2 Basic Fourier Transforms -- 7.3 Formal Properties of Fourier Transforms -- 7.4 Convolutions and Parseval?s Theorem -- 7.5 Comments on the Inversion Theorem -- 7.6 Fourier Inversion by Contour Integration -- 7.7 The Laplace Transform Inversion Integral -- 7.8 An Introduction to Generalized Functions -- 7.9 Fourier Transforms, Differential Equations and Circuits -- 7.10 Transform Solutions of Boundary Value Problems -- 7.11 Band-limited Functions and Communications -- References -- 8 Discrete Variable Transforms -- 8.1 Some Discrete Variable Models -- 8.2 Z-Transforms -- 8.3 Z-Transform Properties -- 8.4 z-Transform Inversion Integral -- 8.5 Discrete Fourier Transforms -- 8.6 Discrete Fourier Transform Properties -- 8.7 Some Applications of Discrete Transform Methods -- 8.8 Finite and Fast Fourier Transforms -- 8.9 Finite Fourier Properties -- 8.10 Fast Finite Transform Algorithm -- 8.11 Computing The 1-1.1 -- References -- 9 Additional Topics -- 9.1 Local Waveform Analysis -- 9.2 Uncertainty Principle -- 9.3 Short-Time Fourier Transforms -- 9.4 Function Shifts and Scalings -- 9.5 Orthonormal Shifts -- 9.6 Multi-Resolution Analysis and Wavelets -- 9.7 On Wavelet Applications -- 9.8 Two-Sided Transforms -- 9.9 Walsh Functions -- 9.10 Geometrically Based Transforms -- References -- A Linear Algebra Overview -- A.1 Vector spaces -- A.2 Linear Mappings -- A.3 Inner Products -- A.4 Linear Functionals and Dual Spaces -- A.5 Canonical Forms -- References -- B Software Resources -- B.1 Computational and Visualization Software -- B.2 MATLAB Data Structures -- B.3 MATLAB Operators and Syntax -- B.4 MATLAB Programming Structures -- B.5 MATLAB Programs and Scripts -- B.6 Common Idioms -- B.7 Graphics -- B.8 Toolboxes and Enhancemants -- References -- C Transform Tables -- C.1 Laplace Transforms -- C.2 Fourier Transforms -- C.3 Z Transforms -- C.4 Discrete Fourier Transforms Permalink : https://genes.bibli.fr/index.php?lvl=notice_display&id=126697 Methods of Applied Mathematics with a Software Overview / Jon H. Davis / Bâle (CHE) ; Boston, MA : Birkhäuser (2016)
Titre : Methods of Applied Mathematics with a Software Overview Type de document : document électronique Auteurs : Jon H. Davis ; SpringerLink (Online service) Editeur : Bâle (CHE) ; Boston, MA : Birkhäuser Année de publication : 2016 Collection : Applied and Numerical Harmonic Analysis, ISSN 2296-5009 Importance : XVII, 781 p. 240 illus., 108 illus. in color Présentation : online resource ISBN/ISSN/EAN : 978-3-319-43370-7 Langues : Anglais (eng) Tags : Mathematics Harmonic analysis Fourier analysis Functions of complex variables Applied mathematics Engineering mathematics Computer mathematics Physics Fourier Analysis Computational Mathematics and Numerical Analysis Mathematical and Computational Physics Applications of Mathematics Abstract Harmonic Analysis Functions of a Complex Variable Résumé : This textbook, now in its second edition, provides students with a firm grasp of the fundamental notions and techniques of applied mathematics as well as the software skills to implement them. The text emphasizes the computational aspects of problem solving as well as the limitations and implicit assumptions inherent in the formal methods. Readers are also given a sense of the wide variety of problems in which the presented techniques are useful. Broadly organized around the theme of applied Fourier analysis, the treatment covers classical applications in partial differential equations and boundary value problems, and a substantial number of topics associated with Laplace, Fourier, and discrete transform theories. Some advanced topics are explored in the final chapters such as short-time Fourier analysis and geometrically based transforms applicable to boundary value problems. The topics covered are useful in a variety of applied fields such as continuum mechanics, mathematical physics, control theory, and signal processing. Replete with helpful examples, illustrations, and exercises of varying difficulty, this text can be used for a one- or two-semester course and is ideal for students in pure and applied mathematics, physics, and engineering. Key features of the software overview: Now relies solely on the free software tools Octave, Maxima, and Python. Appendix introduces all of these tools at a level suitable to those with some programming experience Provides references to sources of further learning. Code snippets incorporated throughout the text. All graphics and illustrations generated using these tools. Praise for the first edition: ?The author mixed in a remarkable way theoretical results and applications illustrating the results. Flexibility of presentation (increasing and decreasing level of rigor, accessibility) is a key feature...The book contains extensive examples, presented in an intuitive way with high quality figures (some of them quite spectacular)?? ? Mathematica ?...Davis's book has many novel features being quite different from most other textbooks on applied mathematics.... Mainly it has a clear and consistent exposition with a strong focus on mathematical fundamentals and useful techniques. It has numerous extensive examples, illustrations, comments, and a very modern graphical presentation of results. ??The book has style. Every theorem and mathematical result has a wonderful appealing comment.? ? Studies in Informatics and Control Note de contenu : Introduction. Fourier Series -- Elementary Boundary Value Problems -- Strum-Liouville Theory and Boundary Value Problems -- Functions of a Complex Variable -- Laplace Transforms -- Fourier Transforms -- Discrete Variable Transforms -- Additional Topics -- Linear Algebra Overview -- Software Resources -- Transform Tables Permalink : https://genes.bibli.fr/index.php?lvl=notice_display&id=124288 Methods of Applied Mathematics with a Software Overview [document électronique] / Jon H. Davis ; SpringerLink (Online service) . - Bâle (CHE) ; Boston, MA : Birkhäuser, 2016 . - XVII, 781 p. 240 illus., 108 illus. in color : online resource. - (Applied and Numerical Harmonic Analysis, ISSN 2296-5009) .
ISBN : 978-3-319-43370-7
Langues : Anglais (eng)
Tags : Mathematics Harmonic analysis Fourier analysis Functions of complex variables Applied mathematics Engineering mathematics Computer mathematics Physics Fourier Analysis Computational Mathematics and Numerical Analysis Mathematical and Computational Physics Applications of Mathematics Abstract Harmonic Analysis Functions of a Complex Variable Résumé : This textbook, now in its second edition, provides students with a firm grasp of the fundamental notions and techniques of applied mathematics as well as the software skills to implement them. The text emphasizes the computational aspects of problem solving as well as the limitations and implicit assumptions inherent in the formal methods. Readers are also given a sense of the wide variety of problems in which the presented techniques are useful. Broadly organized around the theme of applied Fourier analysis, the treatment covers classical applications in partial differential equations and boundary value problems, and a substantial number of topics associated with Laplace, Fourier, and discrete transform theories. Some advanced topics are explored in the final chapters such as short-time Fourier analysis and geometrically based transforms applicable to boundary value problems. The topics covered are useful in a variety of applied fields such as continuum mechanics, mathematical physics, control theory, and signal processing. Replete with helpful examples, illustrations, and exercises of varying difficulty, this text can be used for a one- or two-semester course and is ideal for students in pure and applied mathematics, physics, and engineering. Key features of the software overview: Now relies solely on the free software tools Octave, Maxima, and Python. Appendix introduces all of these tools at a level suitable to those with some programming experience Provides references to sources of further learning. Code snippets incorporated throughout the text. All graphics and illustrations generated using these tools. Praise for the first edition: ?The author mixed in a remarkable way theoretical results and applications illustrating the results. Flexibility of presentation (increasing and decreasing level of rigor, accessibility) is a key feature...The book contains extensive examples, presented in an intuitive way with high quality figures (some of them quite spectacular)?? ? Mathematica ?...Davis's book has many novel features being quite different from most other textbooks on applied mathematics.... Mainly it has a clear and consistent exposition with a strong focus on mathematical fundamentals and useful techniques. It has numerous extensive examples, illustrations, comments, and a very modern graphical presentation of results. ??The book has style. Every theorem and mathematical result has a wonderful appealing comment.? ? Studies in Informatics and Control Note de contenu : Introduction. Fourier Series -- Elementary Boundary Value Problems -- Strum-Liouville Theory and Boundary Value Problems -- Functions of a Complex Variable -- Laplace Transforms -- Fourier Transforms -- Discrete Variable Transforms -- Additional Topics -- Linear Algebra Overview -- Software Resources -- Transform Tables Permalink : https://genes.bibli.fr/index.php?lvl=notice_display&id=124288