NUMERICAL ANALYSIS 3008 > SUBJECT CONTENT IN OUTLINE
linear systems
- Computer arithmetic, approximation and errors.
- Gaussian Elimination.
- LU Factorization.
- Norms and Stability.
- Iterative Methods.
- Jacobi Method.
- Gauss-Seidel Method.
- Relaxation methods.
interpolation
- Lagrange Interpolation.
- Newton's Dividend Differences.
- Hermite Interpolation.
Numerical Differentiation and Integration
- Numerical Differentiation.
- Newton - Cotes Formulas for Numerical Integration.
- Trapezoid Rule.
- Simpson's Rule.
- Composite Newton - Cotes Formulas.
- Error Estimates.
Non linear equations and systems
- Bisection Method.
- Regula Falsi Method.
- General iterative method.
- Newton-Raphson Method.
- Secant Method.
- Newton-Raphson Method for non linear systems.
- Complex Newton-Raphson Method.
least squares
- Least Squares Method and the Normal Equations.
ordinary differential equations
- Initial Value Problems.
- Existence, Uniqueness and Continuity of Solutions. Euler, Taylor and Runge-Kutta Methods.
- Multistep Methods.
- Predictor-Corrector Method.
- Systems of Differential Equations.
- Higher Order Differential Equations.
- Boundary value problems, Finite differences and Finite Elements Methods.