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Error (floating point arithmetic, definition and source error, truncation and round-off, propagation error, stability, convergence).
Non-linear equations
Numerical solving for systems of linear equations
Interpolation (Taylor series, definitions, divided differences, Newton interpolation, Lagrange interpolation, errors on polynomial interpolation, Chebyshev interpolation, Hermite interpolation, Spline interpolation).
Approximations (Weierstrass theorem, Taylor's theorem, least-squares approximations, minimax approximation, near-minimax approximations).
Numerical differentiation (basic concepts, differentiation with interpolation, Richardson extrapolation).
Numerical integration (basic concepts, trapezoidal rules, Simpson rules, Newton-Cotes integration formulas, Gaussian Quadrature, automatic numerical integration, Romberg integration).
Numerical methods for differential equations

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