Numerical methods usually get taught as formulas to memorize or as code to copy, rarely both together. This course walks the full path for each technique: the mathematics behind it, a hand worked example, the algorithm, then the MATLAB implementation with visualization and error analysis.

This Course Offers

• Root finding methods including Bisection, Regula Falsi, Newton Raphson, and Secant, with stopping criteria and convergence analysis
• Systems of linear equations covering Gaussian Elimination, LU Decomposition, Gauss Jacobi, and Gauss Seidel, plus convergence concepts
• Interpolation through Lagrange and Newton's Divided Difference, with polynomial construction and numerical examples
• Numerical differentiation using forward, backward, and central difference, and integration with Trapezoidal and Simpson's rules including error analysis
• ODE solving with Euler, RK2, and RK4 methods, complete with graphical visualization of numerical solutions

Why We Love This Course

1. It refuses to separate theory from code. Every method goes through mathematical derivation, hand calculation, algorithm, and MATLAB implementation in sequence.
2. The emphasis on error and convergence is what makes numerical work trustworthy, and it runs through every section rather than being mentioned once.
3. Dr. Muhammad Sarmad Arshad Khan brings a PhD in computational mathematics and over 15 years of university teaching experience, so the explanations come from someone who has taught this repeatedly.
4. GNU Octave works as a free alternative if you do not have MATLAB, which removes a common barrier.

Numerical methods sit underneath simulation, modeling, and machine learning, so understanding them properly pays off well beyond one course. Do you want to memorize formulas for an exam, or actually implement and analyze them? Enrollment is open, and no programming experience is needed.

• This course is perfect for engineering, mathematics, and computer science students at BS, MS, or PhD level.
• It suits data science, AI, and scientific computing students who need numerical foundations.
• Researchers beginning numerical computing, and anyone preparing for university examinations in numerical analysis, will find the structured progression useful.

• Basic knowledge of calculus and linear algebra is expected.
• MATLAB or free GNU Octave needs to be installed to run the code examples.
• No programming experience is required, since implementations are built step by step.

Interested in exploring more lessons? Check out our full course library to continue building your skills and advancing your learning journey.