Part I. Approximation. Lecture 1. General observations; Decline and fall; The linear sine; Approximation in normed linear spaces; Significant differences; Lecture 2. The space C[0,1]; Existence of best approximations; Uniqueness of best approximations; Convergence in C[0,1]; The Weierstrass approximation theorem; Bernstein polynomials; Comments; Lecture 3. Chebyshev approximation; Uniqueness; Convergence of Chebyshev approximations; Rates of convergence; Part II. Linear and Cubic Splines. Lecture 10. Piecewise linear interpolation; The error in L(f); Approximations in the $\infty$-norm; Hat functions; Integration; Least squares approximation; Implementations issues; Lecture 11. Cubic splines; Derivation of the cubic spline; End conditions; Convergence; Locality; Part III. Eigensystems; Part III. Eigensystems; Part IV. Krylov Sequence Methods; Part V. Iterations, Linear and Nonlinear.
