Lectures related to Solving the Quintic: Dominant Balance

Explores Legendre polynomials properties and their use in numerical integration.

Covers various methods for solving polynomial equations through examples.

Covers differentiable functions, extreme points, and the Lagrange multiplier method for optimization.

Covers the bisection method for finding function roots within intervals and its geometric interpretation.

Covers methods for solving nonlinear equations, including bisection and Newton-Raphson methods, with a focus on convergence and error criteria.

Explores the inverse power method for ODEs and the significance of Lipschitz continuity.

Covers the integration of simple elements using various techniques to solve integration problems.

Explores the Thomas algorithm for tridiagonal systems and the accuracy of direct methods in numerical computations.