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1. Introduction to numerical methods, mathematical models, error definitions, Taylor series.
2. Bisection and false position methods for finding roots of equations
3. Simple fixed point iteration, Newton-Raphson and secant methods for finding roots of equations
4. Solutions of linear systems of equations, Gauss elimination method
5. LU Decomposition and matrix inversion, Gauss-Seidel iterative method
6. Curve fitting, least-squares regression, interpolation
7. 1st MIDTERM
8. Numerical integration, Trapezoidal rule, Simpson’s rules
9. Gauss quadrature rule, numerical differentiation
10. Numerical solution of ODE’s by Euler’s method and Heun’s method
11. 2nd Midterm
12. Numerical solution of ODE’s by Runge-Kutta methods
13. Partial Differential Equations, finite difference method
14. Partial Differential Equations, finite element method |