- Polynomial approximation:
Weierstrass Theorem and Bernstein's
polynomials, best uniform approximations, least-squares
approximations, orthogonal polynomials.
- Polynomial interpolation:
Lagrange interpolation, remainder,
Peano kernals, iterated linear interpolation, convergence of
Lagrange interpolation polynomials.
- Numerical quadrature:
degree of precision, method of undetermined
coefficients, interpolatory quadrature, Newton-Cotes formulas,
Peano kernals, Gaussian quadrature.
- Numerical solution of ordinary differential equations:
Euler's method, linear multistep methods, one step methods, Runge-Kutta methods.