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Lecture notes on the mathematics of acoustics /
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 dev...
| Clasificación: | Libro Electrónico |
|---|---|
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
London :
Imperial College Press,
©2005.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 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 Series3.4 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 Condition6.4 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 AeroacousticsChapter 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 ProcessingChapter 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.