1 | 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 | Interpolation 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 |