chapter 1 Some Preliminaries from Analysis and the Theory of Wave Processes -- Integrands, and Series in Residues -- chapter 1 2. Convolution Integral Equations and the Wiener–Hopf Method -- chapter 1 5. Fredholm Theory for Integral Equations of the Second Kind -- chapter 1 6. Fredholm Integral Equations of the First Kind -- chapter 1 8. Hyper-Singular Integrals and Integral Equations -- chapter 2 Integral Equations of Diffraction Theory for Obstacles in Unbounded Medium -- Layers -- chapter Helpful remarks -- chapter Arbitrary 3D obstacle: Acoustically hard boundary -- chapter 2 5. Application: Scattering Diagram for Obstacles of Canonical Shape -- chapter Helpful remarks -- chapter mCylyA y -y OyBl -- chapter 3 Wave Fields in a Layer of Constant Thickness -- Homogeneous and Inhomogeneous Waves -- chapter Helpful remarks -- chapter 3 5. Application: Efficient Calculation of Wave Fields in a Layer of Constant Thickness -- chapter 4 Analytical Methods for Simply Connected Bounded Domains -- chapter 4 5. Exact Explicit Results for Some Polygons -- chapter y1-4bxa -- chapter y 7-12 c1-6x -- chapter y 13-24 c 1-12 x -- chapter 5 Integral Equations in Diffraction by Linear Obstacles -- chapter Helpful remarks -- chapter 6 Short-Wave Asymptotic Methods on the Basis of Multiple Integrals -- Fields by One-Dimensional Quadratures -- chapter 6 2. High-Frequency Wave Fields in Elastic Half-Space -- chapter Helpful remarks -- chapter 6 4. High-Frequency Diffraction with Re-Reflections -- chapter ak /p -- chapter xxnLLyy -- chapter 7 Inverse Problems of the Short-Wave Diffraction -- chapter 7 2. Reducing Inverse Problem of the Short-Wave Diffraction to Minkowski Problem -- chapter 7 4. Exact Explicit Inversion of the Basic Operator in the Case of Axial Symmetry -- chapter Helpful remarks -- chapter A 8q6420 90 180 270 q, degrees -- chapter 123 7. Reconstruction of Nonconvex Obstacles in the High-Frequency Range: 3D Case -- chapter xnqnSqnS -- chapter 8 Ill-Posed Equations of Inverse Diffraction Problems for Arbitrary Boundary -- First Kind: General Properties -- chapter xbaOxxOx -- chapter x 1 -1 1xO -1 -- chapter g(y) -5 -4 -3 -2 0 120 ° 240 ° -- chapter xxxx -- chapter 9 Numerical Methods for Irregular Operator Equations -- Improvement of the Convergence -- chapter 9 3. Integral Equations of the Physical Diffraction Theory in the Case of Nonconvex Obstacles -- chapter A 6a422100 ° 60 ° ° ° 15° 30° 45°.