Numerical Analysis

Feras Awad, 24/2/2026

This collection of GeoGebra applets is designed to bridge the gap between theoretical numerical methods and practical computational visualization. By transforming static algorithms into interactive simulations, this book provides a dynamic environment to explore error analysis, root-finding iterations, polynomial interpolation, and the precision of numerical integration.

Tabla de Contenidos

  1. Mathematical Preliminaries & Error Analysis
    1. Horner's Method for Polynomial Evaluation
    2. Taylor Polynomial
  2. Solutions of Equations in One Variable
    1. Bisection Method
    2. Fixed-Point Method
    3. Newton's Method
    4. Secant Method
    5. False Position (Regula Falsi) Method
  3. Interpolation and Polynomial Approximation
    1. Interpolating Polynomials
    2. Divided Differences & Interpolation
  4. Numerical Differentiation and Integration
    1. Approximating First Derivative
    2. Numerical Integration Methods
    3. Area Approximation using Monte-Carlo Method
    4. Monte-Carlo Integration

1.

Mathematical Preliminaries & Error Analysis

Taylor Polynomial

  • 1. Horner's Method for Polynomial Evaluation
  • 2. Taylor Polynomial

1.1.

Horner's Method for Polynomial Evaluation

Horner's Method
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1.2.

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2.

Solutions of Equations in One Variable

Bisection Method Fixed-Point Method Newton's Method Secant Method False-Position Method

  • 1. Bisection Method
  • 2. Fixed-Point Method
  • 3. Newton's Method
  • 4. Secant Method
  • 5. False Position (Regula Falsi) Method

2.1.

Bisection Method

Bisection Method
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2.2.

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2.3.

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2.4.

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2.5.

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3.

Interpolation and Polynomial Approximation

Lagrange Interpolating Polynomial Newton Divided Difference Method

  • 1. Interpolating Polynomials
  • 2. Divided Differences & Interpolation

3.1.

Interpolating Polynomials

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3.2.

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4.

Numerical Differentiation and Integration

  • 1. Approximating First Derivative
  • 2. Numerical Integration Methods
  • 3. Area Approximation using Monte-Carlo Method
  • 4. Monte-Carlo Integration

4.1.

Approximating First Derivative

Approximating the 1st Order Derivative using Data Table
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4.2.

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4.3.

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4.4.

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Información