| Preface | p. xi |
| Introduction | p. 1 |
| What is 'multiple scattering'? | p. 1 |
| Narrowing the scope: previous reviews and omissions | p. 10 |
| Acoustic scattering by N obstacles | p. 11 |
| Multiple scattering of electromagnetic waves | p. 16 |
| Multiple scattering of elastic waves | p. 19 |
| Multiple scattering of water waves | p. 23 |
| Overview of the book | p. 27 |
| Addition theorems in two dimensions | p. 29 |
| Introduction | p. 29 |
| Cartesian coordinates | p. 30 |
| Hobson's theorem | p. 31 |
| Wavefunctions | p. 34 |
| Addition theorems | p. 36 |
| The separation matrices S and S | p. 40 |
| Use of rotation matrices | p. 43 |
| Two-centre expansions | p. 44 |
| Elliptical wavefunctions | p. 46 |
| Vector cylindrical wavefunctions | p. 53 |
| Multipoles for water waves | p. 54 |
| Addition theorems in three dimensions | p. 62 |
| Introduction | p. 62 |
| Spherical harmonics | p. 62 |
| Legendre's addition theorem | p. 65 |
| Cartesian coordinates | p. 66 |
| Hobson's theorem | p. 67 |
| Wavefunctions and the operator Y[Characters not reproducible] | p. 69 |
| First derivatives of spherical wavefunctions | p. 73 |
| Axisymmetric addition theorems | p. 75 |
| A useful lemma | p. 81 |
| Composition formula for the operator Y[Characters not reproducible] | p. 83 |
| Addition theorem for j[subscript n]Y[Characters not reproducible] | p. 87 |
| Addition theorem for h[Characters not reproducible] Y[Characters not reproducible] | p. 89 |
| The separation matrices S and S | p. 91 |
| Two-centre expansions | p. 95 |
| Use of rotation matrices | p. 98 |
| Alternative expressions for S(bz) | p. 99 |
| Vector spherical wavefunctions | p. 106 |
| Multipoles for water waves | p. 107 |
| Methods based on separation of variables | p. 122 |
| Introduction | p. 122 |
| Separation of variables for one circular cylinder | p. 122 |
| Notation | p. 125 |
| Multipole method for two circular cylinders | p. 126 |
| Multipole method for N circular cylinders | p. 128 |
| Separation of variables for one sphere | p. 132 |
| Multipole method for two spheres | p. 135 |
| Multipole method for N spheres | p. 138 |
| Electromagnetic waves | p. 140 |
| Elastic waves | p. 141 |
| Water waves | p. 143 |
| Separation of variables in other coordinate systems | p. 148 |
| Integral equation methods, I: basic theory and applications | p. 152 |
| Introduction | p. 152 |
| Wave sources | p. 153 |
| Layer potentials | p. 154 |
| Explicit formulae in two dimensions | p. 159 |
| Explicit formulae in three dimensions | p. 162 |
| Green's theorem | p. 164 |
| Scattering and radiation problems | p. 166 |
| Integral equations: general remarks | p. 168 |
| Integral equations: indirect method | p. 169 |
| Integral equations: direct method | p. 172 |
| Integral equation methods, II: further results and applications | p. 179 |
| Introduction | p. 179 |
| Transmission problems | p. 179 |
| Inhomogeneous obstacles | p. 180 |
| Electromagnetic waves | p. 187 |
| Elastic waves | p. 196 |
| Water waves | p. 203 |
| Cracks and other thin scatterers | p. 206 |
| Modified integral equations: general remarks | p. 209 |
| Modified fundamental solutions | p. 209 |
| Combination methods | p. 217 |
| Augmentation methods | p. 219 |
| Application of exact Green's functions | p. 222 |
| Twersky's method | p. 229 |
| Fast multipole methods | p. 235 |
| Null-field and T-matrix methods | p. 242 |
| Introduction | p. 242 |
| Radiation problems | p. 242 |
| Kupradze's method and related methods | p. 243 |
| Scattering problems | p. 246 |
| Null-field equations for radiation problems: one obstacle | p. 247 |
| Null-field equations for scattering problems: one obstacle | p. 249 |
| Infinite sets of functions | p. 251 |
| Solution of the null-field equations | p. 257 |
| The T-matrix for one obstacle | p. 268 |
| The T-matrix for two obstacles | p. 274 |
| The T-matrix for N obstacles | p. 281 |
| Approximations | p. 284 |
| Introduction | p. 284 |
| Small scatterers | p. 284 |
| Foldy's method | p. 297 |
| Point scatterers | p. 304 |
| Wide-spacing approximations | p. 306 |
| Random arrangements of small scatterers; suspensions | p. 312 |
| Appendices | p. 323 |
| Legendre functions | p. 323 |
| Integrating a product of three spherical harmonics; Gaunt coefficients | p. 325 |
| Rotation matrices | p. 329 |
| One-dimensional finite-part integrals | p. 333 |
| Proof of Theorem 5.4 | p. 339 |
| Two-dimensional finite-part integrals | p. 343 |
| Maue's formula | p. 350 |
| Volume potentials | p. 351 |
| Boundary integral equations for G[superscript E] | p. 355 |
| References | p. 357 |
| Citation index | p. 421 |
| Subject index | p. 433 |
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