| 1 | Preliminaries of Computing
- Basic concepts: round-off errors, floating point arithmetic, Convergence. |
| 2 | Numerical solution of Nonlinear Equations:
- Bisection method
- fixed-point iteration |
| 3 | Numerical solution of Nonlinear Equations:
- Newton’s method
- The Secant Method |
| 4 | Interpolation and Polynomial Approximation
a) Lagrange Polynomial
b) Divided Differences
c) Hermite Interpolation |
| 5 | Direct Methods for Solving Linear Systems |
| 6 | IterativeTechniques for Solving Linear Systems:
The Jacobi and Gauss-Siedel Iterative Techniques |
| 7 | Interpolation and Polynomial Approximation:
Interpolation and the Lagrange Polynomial
Data Approximation and Neville’s Method |
| 8 | Midterm exam |
| 9 | nterpolation and Polynomial Approximation:
Divided Differences
Hermite Interpolation |
| 10 | Numerical Differentiation
Three-Point Formulas, Five-Point Formulas, |
| 11 | Numerical Integration
TheTrapezoidal Rule,Simpson’s Rule .Composite Numerical Integration. |
| 12 | Initial-Value Problems for Ordinary Differential Equations:
Euler’s Method, Higher-Order Taylor Methods, Runge-Kutta Methods |
| 13 | Approximation Theory:
Discrete Least Squares Approximation.
Rational Function Approximation. |
| 14 | Revision |
