| 1 |
Introduction to Numerical Methods and Error Analysis |
| 2 |
Numerical Solutions of Linear Systems: Direct and Iterative Methods |
| 3 |
Nonlinear Equations: Bisection Method, Newton-Raphson Method |
| 4 |
Polynomial Interpolation and Curve Fitting |
| 5 |
Numerical Differentiation and Integration: Trapezoidal Rule, Simpson’s Rule |
| 6 |
Numerical Solutions of Ordinary Differential Equations (ODEs): Euler, Runge-Kutta Methods |
| 7 |
Midterm Exam |
| 8 |
Stability and Convergence of Numerical Methods |
| 9 |
Finite Difference Methods for Partial Differential Equations (PDEs) |
| 10 |
Numerical Methods for Engineering Optimization |
| 11 |
Application of Numerical Methods in Heat Transfer, Fluid Mechanics, and Structural Analysis |
| 12 |
Case Studies: Numerical Simulations in Engineering Problems |
| 13 |
Advanced Topics: Finite Element Analysis, Computational Fluid Dynamics |
| 14 |
Review and Final Exam Preparation |
