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by David V. Ingerman

 * About the book


 * Summary
 * Summary


 * Background
 * Basic definitions and background
 * Harmonic functions
 * On random processes
 * Special matrices and determinants
 * Electrical networks
 * The inverse problems


 * Three classical problems
 * On the inverse problem of Calderon
 * "Can One Hear the Shape of a Drum?"
 * On inhomogeneous string of Krein


 * Embedded graphs
 * Medial graphs
 * Dual graphs and harmonic conjugates
 * Determining genus of a graph
 * The new spectral theorem


 * The layered case
 * Fourier coordinates
 * Stieltjes continued fractions
 * Blaschke products
 * Pick-Nevanlinna interpolation
 * Cauchy matrices
 * Solution of the inverse problem


 * The square root of minus Laplacian
 * The case of the unit disc
 * Zolotarev problem
 * One more graph example


 * Discrete and continuous models
 * Kernel of Dirichlet-to-Neumann map
 * Riemann mapping theorem
 * Hilbert transfrom
 * Schrodinger equation
 * Variation diminition property
 * Spectral properties


 * Notation
 * Notation


 * Acknowledgements
 * Acknowledgements


 * About the author
 * About the author


 * Bibliography
 * Bibliography