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Lecture
LED Drivers: Microcontrollers Understanding
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Gram-Schmidt Algorithm: Orthogonalization and QR Factorization
Introduces the Gram-Schmidt algorithm, QR factorization, and the method of least squares.
Linear Models: Least Squares and QR Factorization
Covers least squares, QR factorization, linear models, and regression analysis with applications to experimental data.
Homogeneous Solutions: Linear Independence
Explores finding particular solutions for homogeneous differential equations, emphasizing linear independence and variation of constants.
Linear Regression: Least Squares and Normal Equations
Explores linear regression through least squares and normal equations, emphasizing the importance of minimizing errors for accurate predictions.
Linear Regression and Logistic Regression
Covers linear and logistic regression for regression and classification tasks, focusing on loss functions and model training.
Linear Transformations: Polynomials and Bases
Covers linear transformations between polynomial spaces and explores examples of linear independence and bases.
PCA: Directions of Largest Variance
Covers PCA, finding directions of largest variance, data dimensionality reduction, and limitations of PCA.
Linear Algebra: Linear Dependence and Independence
Explores linear dependence and independence of vectors in geometric spaces.
Coordinate Systems and Applications
Covers the definition and use of coordinate systems and applications in bases and linear equations.
Linear Regression: Statistical Inference and Regularization
Covers the probabilistic model for linear regression and the importance of regularization techniques.