Newton's Method for Dynamical Systems

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Explores the method of undetermined coefficients for solving non-homogeneous linear differential equations with constant coefficients.

Higher Order Methods: Iterative Techniques

Covers higher order methods for solving equations iteratively, including fixed point methods and Newton's method.

Lipschitz continuous Hessian and Newton's method

Explores the convergence of Newton's method and the CG algorithm for solving linear equations.

Newton's Method: Optimization Techniques

Explores optimization techniques like gradient descent, line search, and Newton's method for efficient problem-solving.

Numerical Analysis: Introduction to Computational Methods

Covers the basics of numerical analysis and computational methods using Python, focusing on algorithms and practical applications in mathematics.

Numerical Analysis: Newton's Method

Explores Newton's method for finding roots of nonlinear equations and its interpretation as a second-order method.

Dynamical Systems: Maps and Stability

Explores one-dimensional maps, periodic solutions, and bifurcations in dynamical systems.

State-space Modeling

Introduces the state-space approach to modeling dynamical systems and its utility for high-speed solution of differential equations and computer algorithms.

Linear Systems: Iterative Methods

Covers iterative methods for solving linear systems, including Jacobi and Gauss-Seidel methods.

Direct and Iterative Methods for Linear Equations

Explores direct and iterative methods for solving linear equations, emphasizing symmetric matrices and computational cost.