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.
- Enseignant: narimane aissaoui