Auxiliary results from linear algebra: matrices, eigenvalues, reduction to diagonal form, singular value decomposition, method of least squares. Multiple linear regression and correlation. Empirical orthogonal functions (EOF). Objective analysis: polynomial fitting, objective interpolation. Time series, spatial fields: a) deterministic theory: linear systems, Fourier transform, discrete sampling, aliasing, digital filters; b) stochastic theory in frequency domain as well as in the domain of wave numbers: linear systems with stochastic input, power spectra and cross-spectra of stationary stochastic processes, linear model with noise; d) wavelets.
Exercises will comprise the implementation of various methods on computer. These will be used to analyze real or artificial (computer generated) data.
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