Numerical Analysis

Introduction
Polynomial interpolation
	The interpolation problem
	The Lagrange formula
	The Newton formula
	A useful property of divided differences
	Error bounds for polynomial interpolation
Orthogonal polynomials
	Scalar product
	Orthogonal polynomials
	Three-term recurrence relation
	Examples
	Least-squares polynomial approximation
Approximation of linear functionals
	Linear functionals
	Gaussian quadrature
Expressing errors in terms of derivatives
Ordinary differential equations
	Introduction
	One-step methods
	Multi-step methods
	Runge-Kutta methods
Stiff equations
	Introduction
	Linear stability
Implementation of ODE methods
	Local error estimation
	Solving for implicit methods
Numerical linear algebra
	Triangular matrices
	LU factorization
	A = LU for special A
Linear least squares