Introduction to Numerical Analysis

Lecture Notes

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)