E-Book, Englisch, 721 Seiten, eBook
Davis Methods of Applied Mathematics with a MATLAB Overview
Erscheinungsjahr 2012
ISBN: 978-0-8176-8198-2
Verlag: Birkhäuser Boston
Format: PDF
Kopierschutz: 1 - PDF Watermark
E-Book, Englisch, 721 Seiten, eBook
Reihe: Applied and Numerical Harmonic Analysis
ISBN: 978-0-8176-8198-2
Verlag: Birkhäuser Boston
Format: PDF
Kopierschutz: 1 - PDF Watermark
Zielgruppe
Research
Autoren/Hrsg.
Weitere Infos & Material
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 LaplaceTransforms.- 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 andVisualization 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.