February Lectures

Week of February 1-5

Feb 1: error in linear spline interpolation; clamped cubic splines.

Feb 3: least squares approximation; inner products and norms of functions; linear independence
and orthogonality of functions; orthogonal polynomials and least squares approximation.

Tutorial: exercises of discrete and continuous least squares approximation and cubic splines.

Week of February 8-12

Feb 8: the normal equations for polynomial least squares approximation;
orthogonal polynomials and least squares approximation; comments about midterm.

Feb 10: midterm.

Tutorial: constructing sets of orthogonal polynomials; method of undetermined coefficients;
Gram-Schmidt orthogonalization algorithm for functions; three-term recurrence relation algorithm; constructing the least squares polynomial approx.

Week of February 15-19

Reading week: no lectures.

Week of February 22-26

Feb 22: Tchebyshev polynomials; optimal placing of data points in polynomial interpolation.

Feb 24: introduction to numerical integration; midpoint rule and error formula.

Tutorial: comments about midterm; example of Tchebyshev polynomials.