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Numerical Methods

Solving Linear Systems
Gaussian elimination - Review of a direct method to solve linear equations
Jacobi method - Iterative methods to solve linear equations.
Gauss–Seidel method
Conjugate gradient method
Nonlinear Equations
Bisection method
Newton's method
Secant method
Polynomial Interpolation
Polynomial interpolation
Lagrange polynomial
Newton polynomial
Runge's phenomenon
Polynomial Interpolation
optional
Stone–Weierstrass theorem
Bernstein polynomial
Numerical Integration
Numerical integration - Overview
Trapezoidal rule
Simpson's rule
Romberg's method
Gaussian quadrature
Monte Carlo integration
Solving Ordinary Differential Equations
Numerical methods for ordinary differential equations - Overview
Euler method
Backward Euler method (Implicit Euler method)
Heun's method
Runge–Kutta_methods
Solving Partial Differential Equations
Partial differential equation#Numerical solutions
Finite difference method#Example: The heat equation
Crank-Nicolson method
Courant–Friedrichs–Lewy condition - Hyperbolic PDE