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Numerical methods

Course Description: Numerical solution of nonlinear equations and associated errors, rate of convergence, solution of systems of equations by direct and iterative methods and associated errors, interpolation and polynomial approximation and associated errors, numerical differentiation and integration and associated errors, introduction to numerical solutions of ordinary differential equations.
Credit hours: 3
Prerequisites: MATH107
Objectives of the course :

1. Calculating the roots of nonlinear equations using Newton's method, the secant method, the fixed-point iteration method, and others.

2. Different types of interpolation techniques.

3. Numerical calculation of definite integrals and numerical differentiation of functions.

4. The ability to solve initial value problems using Euler, Taylor, and Runge-Kutta methods.

5. Solving systems of linear equations using iterative methods and matrix methods.

6. Understanding the concept of numerical computation errors, and the necessity of analyzing and predicting them.

Course outputs :

1. Finding the roots of nonlinear equations using various numerical methods.

2. Description of different interpolation methods.

3. Finding numerical differentiation and integration of functions.

4. Description of Matrix Analysis, its Properties, and Criteria.

5. Estimating errors arising from numerical computation.

6. Estimating error bounds in integration and differentiation formulas.

7. Constructing polynomial interpolations for functions using various methods, including Lagrange interpolation and divided differences.

8. Solve initial value problems using Euler's method, Taylor series method, and Runge-Kutta methods.

Additional information:
  • Last updated: 2026-05-17

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