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Welcome to this comprehensive lecture series on Computational Methods in Engineering — a step-by-step guide for students, researchers, and engineers who want to master numerical techniques and MATLAB-based problem solving.

This course covers everything you need to understand numerical modeling, simulation, and computational analysis used in modern engineering applications — from solving equations to modeling differential systems.

1. Systems of Equations & Eigenvalues
2. Interpolation, Differentiation & Integration
3. Ordinary Differential Equations (ODEs)
4. Partial Differential Equations (PDEs)
5. Application Examples


🧩 Course Modules:

Module I – Systems of Equations & Eigenvalues
• Floating point & truncation errors
• Gauss, LU, Cholesky, and iterative solvers
• Eigenvalue computation: Power, Inverse, QR, Rayleigh methods
• Nonlinear systems & optimization

Module II – Interpolation, Differentiation & Integration
• Lagrange, Newton, Hermite, and Spline methods
• Regression & Curve Fitting (Linear/Nonlinear, PCA)
• Numerical Integration – Simpson, Gauss, Romberg

Module III – Ordinary Differential Equations (ODEs)
• Euler, Runge–Kutta, Predictor–Corrector, and BDF methods
• Boundary value problems – Shooting, Finite Difference, FEM, FVM

Module IV – Partial Differential Equations (PDEs)
• Laplace, Poisson, Advection, Diffusion, and Wave equations
• Explicit, Implicit & Crank–Nicolson methods

Module V – Applications in Engineering
• Heat transfer, vibrations, circuits, and advection–diffusion modeling
• Real-world MATLAB examples and open-ended projects

💻 Software Used:

MATLAB (with coding demonstrations and assignments)

Numerical analysis workflows for engineers

🎯 Learning Outcomes:

Build strong foundations in Numerical Methods

Solve real engineering problems using MATLAB

Develop computational thinking for research & design