Nonlinear Equations: Methods and Applications

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Related lectures (28)

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Root Finding Methods: Secant, Newton, and Fixed Point Iteration

Covers numerical methods for finding roots, including secant, Newton, and fixed point iteration techniques.

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.

Root Finding Methods: Secant and Newton's Methods

Covers numerical methods for root finding, focusing on the secant and Newton's methods.

Numerical Analysis: Nonlinear Equations

Explores the numerical analysis of nonlinear equations, focusing on convergence criteria and methods like bisection and fixed-point iteration.

Numerical Methods: Bisection and Multidimensional Arrays

Discusses the bisection method for solving nonlinear equations and its implementation using Python with NumPy and Matplotlib.

Root Finding Methods: Bisection and Secant Techniques

Covers root-finding methods, focusing on the bisection and secant techniques, their implementations, and comparisons of their convergence rates.

Iterative Methods for Nonlinear Equations

Explores iterative methods for solving nonlinear equations, discussing convergence properties and implementation details.

Numerical Methods: Iterative Techniques

Covers open methods, Newton-Raphson, and secant method for iterative solutions in numerical methods.

Fixed Point Theorem: Convergence of Newton's Method

Covers the fixed point theorem and the convergence of Newton's method, emphasizing the importance of function choice and derivative behavior for successful iteration.

Fixed-Point Methods and Newton-Raphson

Covers fixed-point methods and Newton-Raphson, emphasizing their convergence and error control.