TA Lab · Autumn 2022

Numerical Methods Lab

Independent University, Bangladesh

Autumn 2022 Independent University, Bangladesh 28 students Course repository

Syllabus

Lab sessions implement numerical algorithms from scratch using Python and NumPy, then validate results against SciPy. Focus is on understanding the algorithm, not just using a library.

Learning outcome
Students can implement and analyze core numerical methods, understand their error characteristics, and apply them to scientific computing problems.

Weekly schedule

  1. Lab 01–02 Floating point arithmetic and error analysis
  2. Lab 03–04 Root-finding: bisection, Newton-Raphson
  3. Lab 05–06 Polynomial interpolation and splines
  4. Lab 07–08 Numerical differentiation and integration
  5. Lab 09–10 Linear systems: Gaussian elimination and LU factorization
  6. Lab 11–12 Ordinary differential equations: Euler and Runge-Kutta

Tutorial notebooks

#01 Floating point and machine epsilon .ipynb
#02 Root-finding methods .ipynb
#03 Lagrange and Newton interpolation .ipynb
#04 Numerical integration: trapezoidal and Simpson's rule .ipynb
#05 Solving linear systems .ipynb
#06 ODE solvers: Euler and RK4 .ipynb

Resources & references

  • Numerical Methods for Engineers — Chapra & Canale open
  • SciPy documentation open
  • Course GitHub repository open