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Course Description:

This course aims to introduce students to the fundamental principles of numerical methods and computer programming. It will cover the basic concepts of numerical analysis, approximation methods, and algorithms commonly used in solving numerical problems. Students will also have the opportunity to develop their programming skills through practical exercises.

Course Objectives:

• Understand the fundamental concepts of numerical analysis.
• Be able to apply different numerical methods to solve mathematical problems.
• Acquire programming skills using a language suitable for numerical analysis.
• Know how to evaluate the efficiency and accuracy of the numerical methods used.

Course Content:

1. Basic syntax of a programming language

2. Numerical Integration

   • Trapezoidal Method
   • Simpson's Method

3. Solving Nonlinear Equations

   • Bisection Method
   • Newton-Raphson Method

4. Solving Ordinary Differential Equations

   • Euler's Method
   • Second-Order Runge-Kutta Method
   • Fourth-Order Runge-Kutta Method

5. Solving Linear Systems

   • Jacobi Method
   • Gauss-Seidel Method

Evaluation:

• Practical Exam: 50%
• Final Exam: 50%