18.330 | Spring 2004 | Undergraduate

Introduction to Numerical Analysis

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)

Course Info

As Taught In
Spring 2004