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.

Numerical Methods, 4th edition, J. Douglas Faires/Richard Burden
2013, 2003, 1998 Brooks/Cole, Cengage Learning

Numerical Methods, 4th edition, J. Douglas Faires/Richard Burden
2013, 2003, 1998 Brooks/Cole, Cengage Learning