Lecture Notes on
"Numerical Methods for Polynomial Interpolation"

1. Introduction to numerical analysis and MATLAB programming
• Matlab 6: computations, visualization, programming
• Errors of numerical approximations: round-off and truncation
• Convergence and stability of iterative methods (root finding)
  
  
2. Polynomial interpolation and approximation (curve fitting)
• Lagrange interpolating polynomials
• Newton divided difference polynomials
• Linear and cubic splines
• Least squares approximations and orthogonal polynomials
  
  
3. Numerical differentiation and integration
• Forward, backward and central differences for derivatives
• Difference formulas from interpolating polynomials
• Recursive difference formulas from Richardson extrapolation
• Trapezoidal, Simpson's and midpoint integration formulas
• Recursive integration formulas from Romberg integration