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| Preface | |
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| Introduction | |
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| What is 'multiple scattering'? | |
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| Narrowing the scope: previous reviews and omissions | |
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| Acoustic scattering by N obstacles | |
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| Multiple scattering of electromagnetic waves | |
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| Multiple scattering of elastic waves | |
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| Multiple scattering of water waves | |
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| Overview of the book | |
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| Addition theorems in two dimensions | |
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| Introduction | |
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| Cartesian coordinates | |
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| Hobson's theorem | |
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| Wavefunctions | |
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| Addition theorems | |
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| The separation matrices S and S | |
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| Use of rotation matrices | |
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| Two-centre expansions | |
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| Elliptical wavefunctions | |
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| Vector cylindrical wavefunctions | |
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| Multipoles for water waves | |
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| Addition theorems in three dimensions | |
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| Introduction | |
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| Spherical harmonics | |
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| Legendre's addition theorem | |
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| Cartesian coordinates | |
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| Hobson's theorem | |
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| Wavefunctions and the operator Y[Characters not reproducible] | |
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| First derivatives of spherical wavefunctions | |
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| Axisymmetric addition theorems | |
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| A useful lemma | |
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| Composition formula for the operator Y[Characters not reproducible] | |
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| Addition theorem for j[subscript n]Y[Characters not reproducible] | |
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| Addition theorem for h[Characters not reproducible] Y[Characters not reproducible] | |
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| The separation matrices S and S | |
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| Two-centre expansions | |
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| Use of rotation matrices | |
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| Alternative expressions for S(bz) | |
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| Vector spherical wavefunctions | |
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| Multipoles for water waves | |
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| Methods based on separation of variables | |
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| Introduction | |
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| Separation of variables for one circular cylinder | |
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| Notation | |
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| Multipole method for two circular cylinders | |
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| Multipole method for N circular cylinders | |
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| Separation of variables for one sphere | |
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| Multipole method for two spheres | |
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| Multipole method for N spheres | |
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| Electromagnetic waves | |
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| Elastic waves | |
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| Water waves | |
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| Separation of variables in other coordinate systems | |
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| Integral equation methods, I: basic theory and applications | |
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| Introduction | |
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| Wave sources | |
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| Layer potentials | |
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| Explicit formulae in two dimensions | |
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| Explicit formulae in three dimensions | |
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| Green's theorem | |
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| Scattering and radiation problems | |
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| Integral equations: general remarks | |
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| Integral equations: indirect method | |
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| Integral equations: direct method | |
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| Integral equation methods, II: further results and applications | |
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| Introduction | |
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| Transmission problems | |
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| Inhomogeneous obstacles | |
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| Electromagnetic waves | |
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| Elastic waves | |
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| Water waves | |
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| Cracks and other thin scatterers | |
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| Modified integral equations: general remarks | |
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| Modified fundamental solutions | |
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| Combination methods | |
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| Augmentation methods | |
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| Application of exact Green's functions | |
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| Twersky's method | |
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| Fast multipole methods | |
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| Null-field and T-matrix methods | |
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| Introduction | |
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| Radiation problems | |
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| Kupradze's method and related methods | |
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| Scattering problems | |
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| Null-field equations for radiation problems: one obstacle | |
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| Null-field equations for scattering problems: one obstacle | |
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| Infinite sets of functions | |
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| Solution of the null-field equations | |
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| The T-matrix for one obstacle | |
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| The T-matrix for two obstacles | |
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| The T-matrix for N obstacles | |
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| Approximations | |
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| Introduction | |
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| Small scatterers | |
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| Foldy's method | |
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| Point scatterers | |
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| Wide-spacing approximations | |
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| Random arrangements of small scatterers; suspensions | |
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| Appendices | |
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| Legendre functions | |
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| Integrating a product of three spherical harmonics; Gaunt coefficients | |
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| Rotation matrices | |
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| One-dimensional finite-part integrals | |
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| Proof of Theorem 5.4 | |
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| Two-dimensional finite-part integrals | |
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| Maue's formula | |
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| Volume potentials | |
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| Boundary integral equations for G[superscript E] | |
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| References | |
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| Citation index | |
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| Subject index | |