This volume is a handbook which contains data dealing with the characteristics of systems with distributed and lumped parameters. Some 200 problems are discussed and, for each problem, all the main characteristics of the solution are listed: standardizing functions, Green's functions, transfer functions or matrices, eigenfunctions and eigenvalues with their asymptotics, roots of characteristic equations, and others. In addition to systems described by a single differential equation, the handbook also includes degenerate multiconnected systems. The volume makes it easier to compare a large number of systems with distributed parameters. It also points the way to the solution of problems in the structural theory of distributed-parameter systems. The book contains three major chapters. Chapter 1 deals with special descriptions combining concrete and general features of distributed parameter systems of selected integro-differential equations. Also presented are the characteristics of simple quantum mechanical systems, and data for other systems. Chapter 2 presents the characteristics of systems of differential or integral equations. Several different multiconnected systems are presented. Chapter 3 describes practical prescriptions for finding and understanding the characteristics of various classes of distributed systems. The work should be useful for researchers whose work involves processes in continuous media, various kinds of field phenomena, problems of mathematical physics, and the control of distributed-parameter systems.

This textbook presents derivations and analytical solution methods for the basic linear partial differential equations that model transport, heat, diffusion, waves, vibration, and steady-state equilibrium (Laplace and Poisson equations). General theorems about solution properties (such as uniqueness and stability) are presented. Solution methods include Dirichlet's principle, separation of variables, Fourier series, and Green's functions. The book includes 61 problems with detailed solutions. The book is suitable for students of undergraduate mathematics, engineering, and science.

This textbook covers the essential theory of random vectors and sequences, an understanding of which is essential for understanding and applying estimation, filtering and tracking algorithms. Requiring only a knowledge of basic probability and of matrix algebra, it begins with a succinct review of probability theory, starting with univariate discrete variables and proceeding step by step to the continuous multivariate case. It then presents multivariate normal (Gaussian) estimation of linear model parameters, random sequences (including convergence, ergodicity, and power spectral density), state space models of linear discrete-time dynamic systems and their response to random inputs, and finally the Kalman filter algorithm. Distinguishing features of this textbook include full coverage of multivariate theory, a modern (Bayesian) approach to estimation and filtering, detailed proofs of key results, and 75 exercises with answers.