Coordinate systems and types. Motions of the Earth. Concept and types of datum. Wobbles of spin axes of the Earth. Terrestrial coordinate systems. Celestial coordinate systems. Orbital coordinate systems. Transformations between the terrestrial and the celestial systems. Transformations between the terrestrial and the orbital systems. Structure and mission of IERS (International Earth Rotational Service). ITRF (International Terrestrial Reference Frame) and ICRF (International Celestial Reference Frame). Datum transformations in 1D (Dimension), 2D, 3D and 4D. Concept and types of the time.
Mathematical modeling. Rank defect and generalized inverse. Observation and condition equation models. Observation equation model with constraints. Mixed model. Mixed model with constraints. Transformations in 2D using all mathematical models. Relationship among the all mathematical model. Recursive parameter estimation for all mathematic models. Kalman filtering. Collocation, prediction and filtering. Analyzing the results of the all mathematic models.
Number systems and base conversions. Data representation in computer. Errors on the numerical computation. Matrices. Generalized matrix inverse. Solution of linear equation systems. Solution of symmetric linear equation systems. Series, Taylor series and Least squares method. Solution of a non-linear equation. Solution of a non-linear equations system. Finite differences. Interpolation and extrapolation. Numerical differentiation and integral.