Notes on Math 514: Numerical Analysis @ University of Wisconsin-Madison Your comments and criticism are greatly welcomed.

Textbook

An Introduction to Numerical Analysis - by Endre Süli

Course Notes (PDF version)

Ch 1: Simple Iteration Method

Ch 2: Solution of Systems of Linear Equations

LU Decomposition

QR Factorization

Norm & Condition Number

Ch 3: Special Matrices

Ch 4: Simultaneous Iteration Method

Ch 5: Eigen-Decomposition

Midterm Review

Ch 6-10: Approximation & Integration

Polynomial Approximation Theory

Polynomial Interpolation & Chebyshev Nodes

Polynomial Projection & Quadrature Method

Integration Rules & Undetermined Coefficients

Review for Approximation & Integration

Ch 12: Numerical ODE

Introduction to Numerical ODE

Euler & Trapezoidal & Runge-Kutta

Linear Multistep Methods & Stability

Review for Numerical ODE

Note: You can download a PDF version of the notes here