Lecture Notes

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)