Linear Transformations: Matrices and Bases

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Explores advanced Matplotlib functions for precise function representation and visualization of scalar fields in 2D and 3D.

Explores eigenvalues, eigenvectors, and methods for solving linear systems with a focus on rounding errors and preconditioning matrices.

Explores the diagonalizability of matrices based on eigenvalue multiplicities and eigenvectors.

Explores dynamic systems, focusing on control mechanisms and stability analysis through practical examples and mathematical modeling.

Explores derivability and function composition with examples.

Explores the use of optics in machine learning, focusing on large-scale random matrix multiplication through multiple scattering of light.

Covers the fundamental theorem of calculus, immediate integration, and properties of derivatives, with examples of integration by substitution.

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