E-Learning Guelma

This course is designed for second-year engineering students in Science and Technology. It aims to provide a solid foundation in vector analysis, series, and Fourier and Laplace transformations, which are essential for various fields of engineering and applied sciences. The course is structured into several chapters, each covering fundamental concepts and their practical applications.

Course Overview:

• Chapter 1: Vector Analysis
  

introduces vector fields, gradient fields, line integrals, conservative vector fields, Green’s theorem, divergence, curl, and their applications in physics and engineering.

• Chapter 2: Series
  

Covers numerical and power series, including convergence criteria, Taylor and Maclaurin series, and their applications in function approximation and differential equations.

• Chapter 3:  Fourier Series
  

Introduces periodic functions, Fourier series expansion, Dirichlet’s conditions, and Parseval’s theorem, with applications in heat transfer.

• Chapter 4: Fourier and Laplace Transforms
  

Discusses Fourier integrals, Fourier transforms and their properties, and Laplace transforms as a powerful tool for solving differential equations in engineering problems.

By the end of this course, students will develop analytical skills and mathematical techniques applicable to real-world engineering challenges. The course emphasizes both theoretical understanding and practical problem-solving to prepare students for advanced studies and professional applications.

The course also includes Tutorials and Laboratory sessions in order to practice solving problems, develop a preliminary understanding of fluid mechanics by engaging students in experiments that expose them to a broad range of diverse fluid phenomena and where students are required to set up and perform experiments, collect data, analyze them and finally report on their findings.

This course is intended for undergraduate engineering students in their 2^nd year. It aims to provide them with the fundamental understanding of fluid mechanics, and its main objectives may be summarized as (1) Providing the basic knowledge of fluid statics, (2) Learning to describe a moving fluid using fields , (3) Implementing the theorems of fluid mechanics, (4) Providing the necessary elements needed to solve perfect & real fluid flow problems, (5) Being able to apply the fundamental hydrostatics equation, (6) Being able to calculate hydrostatic forces applied to a surface, (7) Knowing how to apply Archimedes' principle, (8) Knowing how to apply Bernoulli's theorem and (9) Learning to use the mathematical tools of vector analysis.

Apprendre les notions de base de la résistance des matériaux, les buts et les hypothèses de la RDM, la notion des efforts internes, caractéristiques géométriques des sections, la loi de comportement des matériaux, notion de contraintes admissibles et le dimensionnement des pièces sous sollicitations simples.