Professor's Notes
These lecture notes are provided for students in MAT342 Numerical Analysis. The are based on the presentation in Cheney and Kincaid. They guide but do not necessarily correspond exactly to the classroom presentation.
Mathematical preliminaries
- Introduction
- Review of Taylor Series
- Representation of Numbers in Different Bases
- Floating Point Representation
Solving linear systems
- Naive Gaussian Elimination
- Gaussian Elimination with Scaled Partial Pivoting
- Tridiagonal and Banded Systems
Solving nonlinear equations (root-finding)
Interpolation and numerical differentiation
- Polynomial Interpolation
- Errors In Polynomial Interpolation
- Estimating Derivatives and Richardson Extrapolation
Numerical integration
- Numerical Integration and the Trapezoid Rule
- Romberg Algorithm
- Simpson's Rule and Adaptive Simpson's Rule
- Gaussian Quadrature
Initial value problems
- Taylor Series Methods
- Runge-Kutta Methods
- Stability
- Adaptive Runge-Kutta Method
- Multistep Methods
- Methods for First and Higher Order Systems