| Lec # | Topics |
|---|---|
| 1 | Introduction Content of the Course |
| 2 | Examples of Inverse Problems, Static and Time Dependent |
| 3 | Basic Vector/Matrix Notation Algebraic Formulation |
| 4-6 | Over/Underdetermined Problems Varieties of Least-Squares |
| 7 | Basic Statistics Concepts and Notation |
| 8 | Variances/Covariances Biases of Solutions |
| 9 | Special Case of Eigenvector Solutions |
| 10-11 | Singular Value Decomposition and Singular Vector Solutions |
| 12-13 | Recursive Least-Squares Gauss-Markov Estimation; Recursive Estimation |
| 14 | Time-dependent Models Whole Domain Least-Squares |
| 15-16 | Sequential Methods (Kalman Filter/RTS Smoother) |
| 16-17 | Control Problems Lagrange Multiplier (adjoint) Methods Non-linear Problems |
| 18 | Stationary Processes Numerical Fourier Series/Transforms; Delta Functions |
| 19 | Statistics of Fourier Representations Sampling Periodograms |
| 20 | Convolution Power Density Spectral Estimates |
| 21 | Coherence; Multiple Linear Regression |
| 22 | Filtering, Prediction Problems |
| 23-24 | Special Topics, Spillover |