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  • 🎯 Course Plan

    🎯 Course Plan – Numerical Analysis 2

    This course introduces students to advanced computational methods for numerical approximation. It focuses on polynomial interpolation, numerical differentiation and integration, and the resolution of differential equations using iterative and numerical techniques.

    📘 Chapter 1: Interpolation and Polynomial Approximation

    • Identify the conditions for existence and uniqueness of the interpolation polynomial.
    • Compute the divided differences of a given data set.
    • Apply Newton’s interpolation method to a set of data points.
    • Analyze the advantages of Chebyshev interpolation compared to the Runge phenomenon.
    • Implement Hermite interpolation for data including derivatives.
    • Formulate a least-squares polynomial approximation.

    📗 Chapter 2: Numerical Differentiation and Integration

    • Use two-point formulas for numerical differentiation.
    • Derive formulas for higher-order derivatives.
    • Apply numerical methods to estimate definite integrals:
      • ◽ Implement the rectangle (midpoint) rule.
      • ◽ Compare the accuracy of the trapezoidal and rectangle rules.
      • ◽ Evaluate the performance of Simpson’s rule on practical examples.

    📙 Chapter 3: Solving Ordinary Differential Equations (ODEs)

    • Locate a root of an equation using graphical or numerical analysis.
    • Implement the bisection (dichotomy) method to solve a nonlinear equation.
    • Solve equations using Newton’s method (Newton–Raphson).