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Author Wright, Matthew M C
Title Lecture Notes On The Mathematics Of Acoustics
Imprint Singapore : World Scientific Publishing Company, 2004
©2005
book jacket
Descript 1 online resource (308 pages)
text txt rdacontent
computer c rdamedia
online resource cr rdacarrier
Note Intro -- Preface -- Contents -- Part I Mathematical Methods -- Chapter 1 Vector Calculus -- 1.1 Motivation -- 1.2 Scalars and Vectors -- 1.3 Vector and Scalar Functions -- 1.4 Curves and Surfaces in 3-D Space -- 1.5 Curvilinear Coordinate Systems -- 1.6 Integrals -- 1.7 Integral Theorems -- 1.8 Suffix Notation -- Problems -- Chapter 2 Functions of a Complex Variable -- 2.1 Complex Numbers -- 2.2 Functions of a Complex Variable -- 2.3 Contour Integration -- 2.4 Power Series Expansions -- 2.5 Residue Theory -- 2.6 Analytic Continuation -- Problems -- Chapter 3 Integral Transforms -- 3.1 The Laplace Transform -- 3.2 The Inversion Theorem -- 3.3 Fourier Series -- 3.4 The Fourier Transform -- 3.5 The Heat Conduction Equation -- 3.6 The Wave Equation -- Problems -- Chapter 4 Asymptotic Expansion of Integrals -- 4.1 Introduction -- 4.2 Two Elementary Methods -- 4.3 Method of Laplace -- 4.4 Method of Stationary Phase -- 4.5 Method of Steepest Descents -- Further Reading -- Problems -- Part II Wave Motion -- Chapter 5 The Wiener-Hopf Technique -- 5.1 Introduction -- 5.2 Rigid Screen Diffraction -- 5.3 The General Wiener-Hopf Equation -- 5.4 A Systematic Decomposition Procedure -- 5.5 Summary -- References -- Chapter 6 Waveguides -- 6.1 Basic Theory -- 6.2 Eigenfunction Expansions -- 6.3 An Abrupt Change in Boundary Condition -- 6.4 Complex Variable Methods -- Further Reading -- Problems -- Chapter 7 Wavefield Decomposition -- 7.1 Introduction -- 7.2 Wavefields -- 7.3 Two-Dimensional Representation -- 7.4 Extension to Three Dimensions -- 7.5 Angular Representation -- 7.6 Solution to Original Problem -- References -- Problems -- Chapter 8 Acoustics of Rigid-Porous Materials -- 8.1 Introduction -- 8.2 Wave Equations -- 8.3 Impedance -- 8.4 Analysis for a Single Slit -- 8.5 Analysis for a Bulk Absorber -- 8.6 Comparisons with Data and Nonlinear Aspects
8.7 Conclusions -- Acknowledgements -- References -- Part III Aeroacoustics -- Chapter 9 Generalised Functions in Aeroacoustics -- 9.1 Introduction -- 9.2 Application in Aeroacoustics -- 9.3 Fourier Transforms -- Further Reading -- Problems -- Chapter 10 Monopoles, Dipoles, and Quadrupoles -- 10.1 Introduction -- 10.2 The Three-Dimensional Wave Equation -- 10.3 The Three-Dimensional Convected Wave Equation -- 10.4 The Two-Dimensional Wave Equation -- 10.5 The Two-Dimensional Convected Wave Equation -- 10.6 Conclusion -- References -- Problems -- Chapter 11 Corrugated Pipe Flow -- 11.1 The Problem -- 11.2 Pipe Flow -- 11.3 Cummings's Corrugated Model -- 11.4 Further Thoughts -- Part IV Signal Processing -- Chapter 12 Digital Filters -- 12.1 Mathematical Overview -- 12.2 Fourier Transform -- 12.3 Impulse Response and Frequency Response -- 12.4 Convolution Principle -- 12.5 Dirac Delta Functions and Sifting Property -- 12.6 Laplace Transform Analysis -- 12.7 Digital Filters -- 12.8 Summary -- Further Reading -- Chapter 13 Measurement of Linear Time-Invariant Systems -- 13.1 Introduction -- 13.2 Estimating Statistics Using Fourier Methods -- 13.3 Maximum Length Sequences -- 13.4 Practical -- Further Reading -- Chapter 14 Numerical Optimisation -- 14.1 Introduction -- 14.2 Genetic Algorithms -- 14.3 Adaptive Filtering -- References -- Index
This book aims to give a thorough grounding in the mathematical tools necessary for research in acoustics. Twelve authors, all highly-respected researchers in the field of acoustics, provide a comprehensive introduction to mathematical analysis and its applications in acoustics, through material developed for a summer school in mathematics for acoustics researchers funded by the UK Engineering and Physical Sciences Research Council.Mathematical Methods, Wave Motion, Aeroacoustics and Signal Processing are covered in fourteen chapters by authors including Keith Attenborough (Hull), John Chapman (Keele), Trevor Cox (Salford), Chris Linton and Maureen McIver (Loughborough), and Nigel Peake (Cambridge). There are worked examples, exercises and suggestions for further reading where appropriate. This book is suitable for advanced undergraduate and graduate courses in acoustics and will form an important reference source for researchers in the field
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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2020. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries
Link Print version: Wright, Matthew M C Lecture Notes On The Mathematics Of Acoustics Singapore : World Scientific Publishing Company,c2004 9781860944963
Subject Sound -- Mathematics -- Congresses.;Sound
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