Solving Equations: Newton's Method

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Related lectures (29)

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Newton Method: Convergence and Quadratic Care

Covers the Newton method and its convergence properties near the optimal point.

Solving Equations with Newton's Method

Introduces Newton's method for solving non-linear equations iteratively, highlighting its fast convergence but also its potential failure to converge in some cases.

Differential Equations: Solutions and Periodicity

Explores dense sets, Cauchy sequences, periodic solutions, and unique solutions in differential equations.

Advanced Analysis 2: Continuity and Limits

Delves into advanced analysis topics, emphasizing continuity, limits, and uniform continuity.

Higher Order Methods: Iterative Techniques

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

Nonlinear Equations: Convergence and Taylor Polynomials

Explores nonlinear equations, emphasizing convergence and Taylor polynomials for function approximation.

Error Estimation in Numerical Methods

Explores error estimation in numerical methods for solving differential equations, focusing on local truncation error, stability, and Lipschitz continuity.

Resolution Sequence: Defining a Procedure

Explains the systematic procedure for solving flow sheets and stream calculations.

Iterative Methods for Linear Equations

Covers iterative methods for solving linear equations and analyzing convergence, including error control and positive definite matrices.

Nonlinear Equations: Fixed Point Method Convergence

Covers the convergence of fixed point methods for nonlinear equations, including global and local convergence theorems and the order of convergence.