Numerical Methods for Engineering

This course introduces the study and analysis of numerical methods essential for engineering sciences. It combines lectures and tutorials using Python, with practical applications to highlight the importance of numerical simulation, from theory to practice.

Course Content

• Function Interpolation and Approximation
  • Lagrange interpolation, Newton’s divided difference formulas
  • Error formulas
  • Uniform and least squares approximation
  • Cubic spline functions
• Numerical Integration and Differentiation
  • Composite methods (Newton-Cotes, Gauss)
  • Error analysis
  • Numerical differentiation and error formulas
  • Application to partial differential equations (finite difference methods)
• Numerical Solution of Differential Equations
  • One-step methods (Euler, Crank-Nicholson, Runge-Kutta)
  • Multi-step methods (Adams and variants)
  • Step-size adjustment, stability, and convergence
  • Shooting method for boundary value problems