Lectures related to Ordinary Differential Equations: Definitions and Solutions

Explores polynomial equations, their degree, solutions, and domain definition.

Covers the definitions and notations related to functions.

Explores surjections in linear algebra, demonstrating their importance in mapping elements between sets.

Explains quadrature formulas for digital integration and achieving accurate results.

Covers limited order 1 and 2 development, focusing on linearity and polynomial approximation.

Introduces d-dimensional charts on manifolds and the concept of an atlas.

Covers integral closures, focusing on Eisenstein primes and their properties.

Covers the normalization process of plane algebraic curves, focusing on irreducible polynomials and affine curves.

Explores error analysis and limitations in interpolation on evenly distributed nodes.

Explores characteristic polynomials, similarity of matrices, and eigenvalues in linear transformations.