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  • 🎯 Module Objective

    🎯 Module Objective – Numerical Analysis 2

    By the end of this module, students will be able to apply fundamental numerical methods to approximate the solutions of mathematical problems that cannot be solved analytically. They will learn to model, analyze, and solve numerical problems arising from scientific, engineering, or computing contexts.

    The module is organized into three chapters, each with specific learning outcomes.

    📘 Chapter 1: Polynomial Interpolation and Approximation

    • Explain the principles of interpolation based on discrete data.
    • Apply classical interpolation methods:
      • Use the Lagrange interpolation method,
      • Build interpolants using the Newton method,
      • Implement Hermite interpolation.
    • Construct appropriate polynomial approximations for experimental data.
    • Formulate least squares approximations.
    • Analyze interpolation and approximation errors.

    📗 Chapter 2: Numerical Integration and Differentiation

    • Approximate derivatives and integrals of functions using basic numerical methods.
    • Apply standard numerical integration techniques:
      • Use the rectangle method,
      • Implement the trapezoidal rule,
      • Apply Simpson’s rule.
    • Use two- and three-point differentiation formulas to approximate derivatives.
    • Evaluate the order of accuracy of numerical formulas.
    • Estimate approximation errors in numerical integration and differentiation.

    📙 Chapter 3: Solving Ordinary Differential Equations (ODEs)

    • Solve simple ODEs using appropriate numerical methods.
    • Implement numerical schemes such as:
    • Study the convergence and stability of numerical schemes.
    • Analyze the validity and limitations of each method.