1. Basic concepts, discretization, and error analysis.
2. Numerical solution of algebraic equations: bisection method, regula falsi method, fixed-point iteration, and Newton–Raphson method.
3. Numerical solution of linear systems: Gaussian elimination, LU factorization, Jacobi, Gauss–Seidel, and successive over-relaxation (SOR) methods.
4. Numerical computation of eigenvalues and eigenvectors.
5. Interpolation, approximation, and curve fitting to data: Lagrange and Newton polynomials, spline functions, linear regression, and the method of least squares.
6. Numerical differentiation: forward, backward, and central difference schemes.
7. Numerical integration: rectangle and trapezoidal rules, Simpson’s rules, and Romberg integration.
8. Numerical solution of ordinary differential equations (ODEs):
   (1) Initial value problems: Euler methods, Runge–Kutta methods, multistep methods, predictor–corrector methods.
   (2) Boundary value problems: shooting method and finite difference method.

Learning Outcomes

The course serves as a fundamental introduction to Numerical Analysis.
Its content aims to present the basic numerical methods for solving algebraic and differential equations, numerical differentiation and integration of functions, as well as data processing and analysis.

The knowledge acquired is essential for the solution of a wide range of Civil Engineering problems.
The laboratory component of the course includes the implementation of numerical methods using an appropriate programming language or suitable computational software.

Upon successful completion of the course, the student will be able to:

• Solve a variety of problems using numerical methods.
• Select the most appropriate numerical method for a given problem.
• Use an appropriate programming language or computational software to implement numerical methods.