User:Moacyr.alvim/Books/Numerical Methods

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
 * Finite difference method
 * Crank-Nicolson method
 * Courant–Friedrichs–Lewy condition - Hyperbolic PDE