January Lectures

Week of January 4-8

Jan 4: course introduction; interpolation.

Jan 6: polynomial approximation and interpolation; Weierstrass theorem;
polynomial interpolation using monomial basis; Vandermonde matrix.

Tutorial: exercises of polynomial interpolation with monomial basis
and with Lagrange basis; comments on MATLAB.

Week of January 11-15

Jan 11: Lagrange interpolation; existence and uniqueness of interpolant.

Jan 13: no lecture (snow storm)

Tutorial: university closed (snow storm).

Week of January 18-22

Jan 18: error in polynomial interpolation; Newton divided differences (start).

Jan 20: Newton divided differences; Evaluating a polynomial (Horner's rule);
polynomial interpolation with derivative data.

Tutorial: exercises of polynomial interpolation with Newton divided differences,
and introduction to Hermite polynomial interpolation.

Week of January 25-29

Jan 25: polynomial interpolation with derivative data; osculating polynomial interpolation;
Hermite polynomial interpolation: monomial, Lagrange and Newton's bases.

Jan 27: pitfalls with polynomial interpolation; piecewise polynomials and splines;
linear spline interpolation (Lagrange form).

Tutorial: cubic spline interpolation -- choice of end-conditions.