Numerical Analysis

Feras Awad, Feb 24, 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.

Table of Contents

  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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