課程概述 Round-off error; algorithms and convergence; the bisection method; the fixed-point iteration; the Newton method; accelerating convergence; the Muller method; Lagrange interpolation; Newton divided differences; Hermite interpolation; cubic spline interpolation; numerical differentiation; Richardson extrapolation; numerical integration; composite numerical integration; Romberg integration; Gaussian quadrature; adaptive quadrature method; initial value problem; the Euler method; higher-order Taylor method; the Runge-Kutta methods and so on.

To introduce modern approximation techniques; to explain how, why, and when they can be expected to work; and to provide a foundation for further study of numerical analysis and scientific computing.

R. L. Burden, J. D. Faires and A. M. Burden, Numerical Analysis 10th Edition, 2018