Taylor Polynominals
ch01 ch02 ch03 ch04
[TKU] 103期中考古題 參考答案
Root Finding 簡要
ch05 ch06
Interpolation 簡要
§ Polynomial interpolation
§ Divided differences
§ Error in polynomial interpolation
§ Interpolation using spline function
Approximation of Functions 簡要
§ The best approximation problem
§ Chebyshev polynomials
§ A near-minimax approximation method
Numerical Integration and Differentiation 簡要
§ The trapezoidal and Simpson rules
§ Error formulas
§ Gaussian numerical integration
§ Numerical differentiation
Solution of Systems of Linear Equations 簡要
§ Systems of linear equations
§ Gaussian elimination
§ Matrix arithmetic
§ The LU factorization
§ Error in solving linear systems
§ Least squares data fitting
§ The eigenvalue problem
§ Iteration methods
§ Nonlinear systems
The Numerical Solution of Differential Equations 簡要
§ Theory of Differential Equations
§ Euler's method
§ Convergence analysis of Euler's method
§ Taylor and Runge-Kutta methods
§ Multistep methods
§ Stability of numerical methods
§ Systems of Differential Equations