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.