| lec # | TOPICS | HANDOUTS |
|---|---|---|
| 1-8 | Root Finding: Solutions of Equations in One Variable (and some Roots of Nonlinear Systems) | Aitken Extrapolations (PDF) Wallis Equation (PDF) 2-D Newton (PDF) Bairstow's Method (PDF) |
| 9-16 | Quadrature: Numerical Integration (and some Lagrange Interpolation) | Quadrature (PDF) Newton-Cotes (PDF) Polynomial Interpolation (PDF) Bernoulli Polynomials (PDF) Bernoulli Numbers (PDF) Some Numerical Fun with Euler/Maclaurin (PDF) Circumference of the Ellipse (PDF) Extrapolation (PDF) Growth of Weeds (PDF) Gauss/Laguerre Quadrature (PDF) |
| 17-23 | ODEs: Initial-Value Problems for Ordinary Differential Equations | Errors vs Evaluations (PDF) ODE via Taylor Series (PDF) Rates of Convergence (PDF) One e = 0.6 Kepler Orbit (PDF) Toward J0 (r) (PDF) |
| 24-31 | Ax=b: Direct Methods for Solving Linear Algebra | Wilkinson's example (PDF) Condition Number (PDF) Ax = b Iterations (PDF) Rates of SOR Convergence (PDF) |
| 32-39 | Ax=λx: Iterative Techniques in Matrix Algebra; Approximating Eigenvalues | Householder Reflections (PDF) Jacobi's Method of Successive 2D Rotations (PDF) Precursor to Problem 36 (PDF) Eigenvalues (PDF) The Geometry of QR (PDF) Eigenvalues of Chain Matrix (PDF) |