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Methods of applied mathematics with a MATLAB overview

Author: Jon H Davis
Publisher: Boston : Birkhäuser, ©2004.
Series: Applied and numerical harmonic analysis.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:

Organized around the applications of Fourier analysis, this title covers both classical applications in partial differential equations and boundary value problems, as well as the concepts and methods  Read more...

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Additional Physical Format: Online version:
Davis, Jon H., 1943-
Methods of applied mathematics with a MATLAB overview.
Boston : Birkhäuser, ©2004
(OCoLC)696254882
Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Jon H Davis
ISBN: 0817643311 9780817643317 3764343311 9783764343316
OCLC Number: 52418165
Description: xii, 721 pages : illustrations ; 24 cm.
Contents: 2 Fourier Series 5 --
2.2 Inner Products and Fourier Expansions 14 --
2.3 Convergence of Fourier Series 24 --
2.4 Pointwise and Uniform Convergence of Fourier Series 37 --
2.5 Gibb's Phenomenon and Summation Methods 43 --
2.6 Summation Methods 46 --
2.7 Fourier Series Properties 51 --
2.8 Periodic Solutions of Differential Equations 64 --
2.9 Impedance Methods and Periodic Solutions 69 --
2.10 Power Spectrum and Parseval's Theorem 70 --
3 Elementary Boundary Value Problems 79 --
3.2 The One-Dimensional Diffusion Equation 80 --
3.3 The Wave Equation 86 --
3.4 The Potential Equation 91 --
3.5 Discrete Models of Boundary Value Problems 95 --
3.6 Separation of Variables 103 --
3.7 Half-Range Expansions and Symmetries 120 --
4 Sturm-Liouville Theory and Boundary Value Problems 163 --
4.2 Selfadjoint Eigenvalue Problems 170 --
4.3 Sturm-Liouville Problems 180 --
4.4 Power Series and Singular Sturm-Liouville Problems 199 --
4.5 Cylindrical Problems and Bessel's Equation 211 --
4.6 Multidimensional Problems and Forced Systems 225 --
4.7 Finite Differences and Numerical Methods 250 --
4.8 Variational Models and Finite Element Methods 258 --
4.9 Computational Finite Element Methods 272 --
5 Functions of a Complex Variable 279 --
5.1 Complex Variables and Analytic Functions 279 --
5.2 Domains of Definition of Complex Functions 287 --
5.3 Integrals and Cauchy's Theorem 294 --
5.4 Cauchy's Integral Formula, Taylor Series, and Residues 301 --
5.5 Complex Variables and Fluid Flows 316 --
5.6 Conformal Mappings and the Principle of the Argument 327 --
6 Laplace Transforms 345 --
6.3 Mechanical Properties of Laplace Transforms 350 --
6.4 Elementary Transforms and Fourier Series Calculations 358 --
6.5 Elementary Applications to Differential Equations 368 --
6.6 Convolutions, Impulse Responses, and Weighting Patterns 376 --
6.7 Vector Differential Equations 391 --
6.8 Impedance Methods 404 --
7 Fourier Transforms 411 --
7.3 Formal Properties of Fourier Transforms 423 --
7.4 Convolutions and Parseval's Theorem 433 --
7.5 Comments on the Inversion Theorem 447 --
7.6 Fourier Inversion by Contour Integration 458 --
7.7 The Laplace Transform Inversion Integral 478 --
7.8 An Introduction to Generalized Functions 493 --
7.9 Fourier Transforms, Differential Equations and Circuits 504 --
7.10 Transform Solutions of Boundary Value Problems 513 --
7.11 Band-limited Functions and Communications 529 --
8 Discrete Variable Transforms 543 --
8.1 Some Discrete Variable Models 543 --
8.2 Z-Transforms 551 --
8.3 Z-Transform Properties 554 --
8.4 z-Transform Inversion Integral 562 --
8.5 Discrete Fourier Transforms 577 --
8.6 Discrete Fourier Transform Properties 581 --
8.7 Some Applications of Discrete Transform Methods 597 --
8.8 Finite and Fast Fourier Transforms 610 --
8.9 Finite Fourier Properties 613 --
8.10 Fast Finite Transform Algorithm 620 --
8.11 Computing The FFT 626 --
9.1 Local Waveform Analysis 635 --
9.2 Uncertainty Principle 636 --
9.3 Short-Time Fourier Transforms 641 --
9.4 Function Shifts and Scalings 645 --
9.5 Orthonormal Shifts 647 --
9.6 Multi-Resolution Analysis and Wavelets 648 --
9.7 On Wavelet Applications 661 --
9.8 Two-Sided Transforms 663 --
9.9 Walsh Functions 668 --
9.10 Geometrically Based Transforms 672 --
A Linear Algebra Overview 685 --
A.1 Vector spaces 685 --
A.2 Linear Mappings 687 --
A.3 Inner Products 688 --
A.4 Linear Functionals and Dual Spaces 689 --
A.5 Canonical Forms 689 --
B Software Resources 693 --
B.1 Computational and Visualization Software 693 --
B.2 MATLAB Data Structures 694 --
B.3 MATLAB Operators and Syntax 696 --
B.4 MATLAB Programming Structures 698 --
B.5 MATLAB Programs and Scripts 699 --
B.6 Common Idioms 700 --
B.7 Graphics 702 --
B.8 Toolboxes and Enhancemants 709 --
C Transform Tables 711 --
C.1 Laplace Transforms 711 --
C.2 Fourier Transforms 713 --
C.3 Z Transforms 714 --
C.4 Discrete Fourier Transforms 715.
Series Title: Applied and numerical harmonic analysis.
Responsibility: Jon H. Davis.
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