April 5 


Matlab Environment
page. 
 Introduction to Matlab.
See the links in the Resources section below. 
 Euler's method for numerical solutions of
ordinary differential equations. 




April 12 

 Euler's method. 
 Discussion of Homework 1. 




April 19 

 Truncation error analysis, order of convergence. 
 RungeKutta second order method. 
 Implicit Trapezoidal method. 
 Discussion of Homework 2. 




April 26 

 Stability, regions of absolute stability. 
 RungeKutta fourth order method. 
 AdamsBashforth and AdamsMoulton methods. 
 Adams predictorcorrector algorithm. 
 Discussion of Homework 3. 




May 3 

 RungeKutta methods for systems. 
 Stability for multistep methods, consistency, convergence. 
 Discussion of Homework 4. 

Midterm Review. 




May 10 

 Two points boundary value problems. 
 Finite difference approximation. 
 Midterm Discussion. 
 Discussion of Homework 5. 




May 17 

 Vector and matrix norms. 
 Iterative methods for the solution of linear systems of
equations. 
 GaussJacobi and Gauss Seidel. 
 Discussion of Homework 6. 




May 24 

 Error analysis for iterative methods. 
 Convergence results for iterative methods. 
 Condition number. 
 QR Decomposition and GramSchmidt process. 
 Discussion of Homework 7. 




May 31 

 Discrete least squares approximation. 
 Construction of the normal equations. 
 Matrix/vector formulation of the discrete least squares problem. 
 Using the QR decomposition to solve normal equations. 
 Discussion of Homework 8. 




June 7 

 Fourier Series. 
 Least squares trigonometric polynomials. 
 Discussion of Homework 8. 
 Final Review. 




June 8 




