This book presents important recent developments in mathematical and computational methods used in impedance imaging and the theory of composite materials. By augmenting the theory with interesting practical examples and numerical illustrations, the exposition brings simplicity to the advanced material. An introductory chapter covers the necessary basics. An extensive bibliography and open problems at the end of each chapter enhance the text.

1 Introduction 2 Layer Potentials and Transmission Problems 3 Uniqueness for Inverse Conductivity Problems 4 Generalized Isotropic and Anisotropic Polarization Tensors 5 Full Asymptotic Formula for the Potentials 6 Near-Boundary Conductivity Inclusions 7 Impedance Imaging of Conductivity Inclusions 8 Effective Properties of Electrical Composites 9 Transmission Problem for Elastostatics 10 Elastic Moment Tensor 11 Full Asymptotic Expansions of the Displacement Field 12 Imaging of Elastic Inclusions 13 Effective Properties of Elastic Composites

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