Recently, there has appeared a new type of evaluating partial differential equations with Volterra integral operators in various practical areas. Such equations possess new physical and mathematical properties. This monograph systematically discusses application of the finite element methods to numerical solution of integrodifferential equations. It will be useful for numerical analysts, mathematicians, physicists and engineers. Advanced undergraduates and graduate students should also find it beneficial I. Extended Kalman Filtering for Nonlinear Systems. Extended Kalman Filters 1: Continuous and Discrete Linearizations / T. E. Bullock and M. J. Moorman. Extended Kalman Filters 2: Standard, Modified and Ideal / T. E. Bullock and M. J. Moorman. Extended Kalman Filters 3: A Mathematical Analysis of Bias / M. J. Moorman and T. E. Bullock -- II. Initialization of Kalman Filtering. Fisher Initialization in the Presence of Ill-Conditioned Measurements / D. Catlin. Initializing the Kalman Filter with Incompletely Specified Initial Conditions / V. Gomez and A. Maravall -- III. Adaptive Kalman Filtering in Irregular Environments. Robust Adaptive Kalman Filtering / A. R. Moghaddamjoo and R. L. Kirlin. On-line Estimation of Signal and Noise Parameters and the Adaptive Kalman Filtering / P. J. Wojcik. Suboptimal Kalman Filtering for Linear Systems with Non-Gaussian Noise / H. Wu and G. Chen -- IV. Set-valued and Distributed Kalman Filtering. Set-valued Kalman Filtering / D. Morrell and W. C. Stirling. Distributed Filtering Using Set Models for Systems with Non-Gaussian Noise / L. Hong -- V. Stability Analysis and Numerical Approximation of Kalman Filtering. Robust Stability Analysis of Kalman Filter under Parametric and Noise Uncertainties / B. S. Chen and S. C. Peng. Numerical Approximations and Other Structural Issues in Practical Implementations of Kalman Filtering / T. H. Kerr