計算數學導論   (91年度 上學期)

Solutions of Equations in One Variable: bisection, fixed-point iteration, Newton's method, special algorithms for polynomials, error analysis and accelerating techniques. Interpolation and Polynomial Approximation: Lagrange type and Hermite type of polynomial interpolations, divided 0differences, spline and parametric curves. Numerical Differentiation and Integration: finite differences, Richardson extrapolation, Newton-Cotes and Gaussian quadrature rules, ideas of adaptivity, numerical methods for multiple and improper integrals. Numerical Solution of IVPs for ODEs: Euler, Runge-Kutta and linear multistep methods, ideas of adaptivity, stability, introduction to stiff problems. Approximation Theory: least squares approximation, Chebyshev and orthogonal polynomials, rational function and trigonometric approximations, fast Fourier transform.

R. L. Burden and J. D. Faires, Numerical Analysis, 7th ed., Brooks/Cole, 2001.

作業 50%，計算習題 30%，期末考 20%