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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),...

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 Dirichlets principle, separation of variables, Fourier series, and Greens functions. The book includes 61 problems with detailed solutions. The book is suitable for students of undergraduate mathematics, engineering, and science.