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Contents

• V Full version
• 0 Introduction
• 1 Polynomial interpolation
• 1.1 The interpolation problem
• 1.2 The Lagrange formula
• 1.3 The Newton formula
• 1.4 A useful property of divided differences
• 1.5 Error bounds for polynomial interpolation
• 2 Orthogonal polynomials
• 2.1 Scalar product
• 2.2 Orthogonal polynomials
• 2.3 Three-term recurrence relation
• 2.4 Examples
• 2.5 Least-squares polynomial approximation
• 3 Approximation of linear functionals
• 3.1 Linear functionals
• 3.2 Gaussian quadrature
• 4 Expressing errors in terms of derivatives
• 5 Ordinary differential equations
• 5.1 Introduction
• 5.2 One-step methods
• 5.3 Multi-step methods
• 5.4 Runge-Kutta methods
• 6 Stiff equations
• 6.1 Introduction
• 6.2 Linear stability
• 7 Implementation of ODE methods
• 7.1 Local error estimation
• 7.2 Solving for implicit methods
• 8 Numerical linear algebra
• 8.1 Triangular matrices
• 8.2 LU factorization
• 8.3 A = LU for special A
• 9 Linear least squares