K. Atkinson, * An Introduction
to Numerical Analysis,*,Wiley, 1989 (second edition),
referred to as [A].

D. Kincaid and W. Cheney: *Mathematics of Scientific Computing*,
AMS, 2002 (third edition), referred to as [KC].

A. Quarteroni, R. Sacco, and F. Saleri,
*Numerical Mathematics,*
Springer, 2004 (second edition), referred to as [QRS]

J. Stoer and R. Bulirsch: *Introduction to Numerical Analysis*,
Springer, 2002, (third edition) referred to as [SB].

1.1 Weierstrass approximation theorem, Lagrange and Newton forms of the interpolating polynomial. [A: 4.1, 3.1, 3.2], [KC: 6.1, 6.2], [QSS: 8.1, 8.2], [SB: 2.1.1, 2.1.3] 1.2 Polynomial interpolation error, divided differences for repeated points, [A: 3.2, 3.6], [KC: 6.2, 6.3], [QSS: 8.5], [SB: 2.1.4, 2.1.5] 1.3 Interpolation of moments, Runge example. [A: 3.5], [KC: 6.1], [QSS: 8.1], [SB: 2.1.4] 1.4 Piecewise polynomial approximation: C^0 and C^1 piecewise polynomial approximation and error estimates; construction of basis functions. [A: 3.7], [KC: 6.4], [QSS: 8.3] 1.5 Piecewise Polynomial Approximation: cubic spline approximation, basis functions, and error estimates [A:3.7], [KC: 6.5, 6.6], [QSS: 8.7], [SB: 2.4.1, 2.4.2, 2.4.3, 2.4.4, 2.4.5] 1.6 Trigonometric interpolation; fast Fourier transform [A:3.8], [KC: 6.12, 6.13], [QSS: 10.9], [SB: 2.3.1, 2.3.2] 1.7 Piecewise polynomial approximation in higher dimensions [KC: 6.10], [QSS: 8.6]

2.1 Numerical differentiation [A: 5.7], [KC: 7.1], [QSS: 10.10] 2.2 Basic and composite rules for numerical integration [A: 5.1, 5.2], [KC: 7.2], [QSS: 9.1, 9.2, 9.3, 9.4], [SB: 3.1, 3.2] 2.3 Extrapolation and Romberg integration [A: 5.4], [KC: 7.4], [QSS: 9.6], [SB: 3.4, 3.5] 2.4 Orthogonal polynomials and Gaussian quadrature [A: 4.4, 5.3], [KC: 6.8, 7.3], [QSS: 10.1, 10.2, 10.3, 10.4, 10.5, 10.6], [SB: 3.6] 2.5 Orthogonal polynomials and Gaussian quadrature (continued) 2.6 Adaptive quadrature [A: 5.5], [KC: 7.5], [QSS: 9.7] 2.7 Singular integrals [A: 5.6], [QSS: 9.8], [SB: 3.7]

3.1 The initial value problem for ordinary differential equations [A: 6.1], [KC: 8.1], [QSS: 11.1], [SB: 7.0,7.1] 3.2 Euler and general Taylor series methods [A: 6.2], [KC: 8.2], [QSS: 11.1, 11.2, 11.3], [SB: 7.2.1, 7.2.2, 7.2.3, 7.2.4] 3.3 Runge-Kutta methods [A: 6.10], [KC: 8.3], [QSS: 11.8], [SB: 7.2.1, 7.2.2, 7.2.3, 7.2.4] 3.4 Estimation of local error and adaptive methods [A: 6.10], [QSS: 11.8.2], [SB: 7.2.5] 3.5 Linear multistep methods (derivation, order, consistency, local truncation error) [A: 6.3, 6.4, 6.5], [KC: 8.4], [QSS: 11.5, 11.6], [SB: 7.2.6, 7.2.7] 3.6 Convergence of linear multistep methods [A: 6.8], [KC: 8.5], [QSS: 11.4, 11.6], [SB: 7.2.7, 7.2.8, 7.2.9, 7.2.10, 7.2.11] 3.7 Stability of linear multistep methods [A: 6.8], [KC: 8.5], [QSS: 11.6], [SB: 7.2.9, 7.2.11, 7.2.12, 7.2.16] 3.8 Stability of linear multistep methods (continued) 3.9 Predictor-corrector methods [A: 6.6, 6.7], [QSS: 11.7], [SB: 7.2.6] 3.10 First order systems of odes [KC: 8.6], [QSS: 11.9] 3.11 Stiff systems of odes [A: 6.9], [QSS: 11.10], [SB: 7.2.16] 3.12 The discontinuous Galerkin method