NUMERICAL ANALYSIS 9041   >  SUBJECT CONTENT IN OUTLINE

linear systems

1. Computer arithmetic, approximation and errors.
   
2. Gaussian Elimination.
   
3. LU Factorization.
   
4. Norms and Stability.
   
5. Iterative Methods.
   
6. Jacobi Method.
   
7. Gauss-Seidel Method.
   
8. Relaxation methods.
   

interpolation

1. Lagrange Interpolation.
   
2. Newton's Dividend Differences.
   
3. Hermite Interpolation.
   

Numerical Differentiation and Integration

1. Numerical Differentiation.
   
2. Newton - Cotes Formulas for Numerical Integration. 
   
3. Trapezoid Rule.
   
4. Simpson's Rule.
   
5. Composite Newton - Cotes Formulas.
   
6. Error Estimates.
   

Non linear equations and systems

1. Bisection Method.
   
2. Regula Falsi Method.
   
3. General iterative method.
   
4. Newton-Raphson Method.
   
5. Secant Method.
   
6. Newton-Raphson Method for non linear systems.
   
7. Complex Newton-Raphson Method.
   

least squares

1. Least Squares Method and the Normal Equations.