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.

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.

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.

Course Overview
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.

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

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