Lectures related to Numerical Analysis: Nonlinear Equations

Introduces Mathematica basics, including graphics creation, list manipulation, and function definition.

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 convergence of Newton's method and its applications in numerical analysis.

Discusses ordinary differential equations, focusing on initial conditions and methods for finding solutions.

Covers Fourier series, periodic functions, and Fourier transforms.

Covers the progressive Euler method for numerical integration of ODEs, including Cauchy problems and Runge-Kutta methods.