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Lecture
Signal Approximation and Orthogonal Bases
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Orthogonal/Orthonormal Bases and Polynomials
Explores orthogonal and orthonormal bases, Gram-Schmidt process, and orthogonal polynomials in physics.
Orthogonality and Least Squares Methods
Explores orthogonality, norms, and distances in vector spaces for solving linear systems.
Matrix Operations and Orthogonality
Covers matrix operations, scalar product, orthogonality, and bases in vector spaces.
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Covers correlation and cross-correlations in air pollution data analysis, including time series, autocorrelations, Fourier analysis, and power spectrum.
Causal Systems & Transforms: Delay Operator Interpretation
Covers z Variable as a Delay Operator, realizable systems, probability theory, stochastic processes, and Hilbert Spaces.
Signals & Systems I: Cross-Correlation and Convolution
Explores cross-correlation, signal detection, Hilbert spaces, orthogonal approximation, and image compression using DCT.
Orthogonality and Least Squares Method
Covers orthogonal vectors, unit vectors, and the Pythagorean theorem in R^m.
Vector Calculus: Scalars and Vectors
Introduces scalars and vectors, explaining their properties and mathematical operations.
Orthogonality and Scalar Product
Explores orthogonality, scalar product, and orthonormal bases in vector spaces.
Orthogonality and Least Squares Method
Explores orthogonality, dot product properties, vector norms, and angle definitions in vector spaces.
