Course Description

The Engineering Mathematics course provides students with a comprehensive foundation in essential mathematical concepts crucial to various engineering disciplines. Beginning with Fourier Series and Fourier Integral, students learn fundamental tools for analyzing periodic functions and decomposing signals into their frequency components, essential for applications in telecommunications and signal processing. The course progresses to explore Partial Differential Equations (PDEs), focusing on methods for solving these equations and their applications in modeling physical phenomena such as heat conduction and wave propagation across engineering domains. Complex Analysis forms a significant part of the course, introducing students to functions of a complex variable and their applications in fluid dynamics, electromagnetism, and beyond. Topics include analytical functions, integral calculus in the complex plane, series expansions, and the residue theorem, equipping students with advanced mathematical techniques essential for solving complex engineering problems.

In the Engineering Mathematics course, students are introduced to foundational concepts that underpin a wide array of engineering disciplines. The course begins with Fourier Series and Fourier Integral, essential tools for analyzing periodic functions and understanding the decomposition of signals into their frequency components. Moving forward, the study explores Partial Differential Equations (PDEs), focusing on their application in modeling physical phenomena such as heat conduction and wave propagation. Additionally, Complex Analysis, or the theory of functions of a complex variable, is introduced, providing insights into the behavior of functions in the complex plane and their applications in engineering, including fluid dynamics and electromagnetism. These topics collectively lay the groundwork for advanced mathematical techniques crucial for solving practical engineering problems.

2- Fourier Series and Integral

In this section, Fourier Series and Fourier Integral are pivotal topics explored for their applications across various engineering disciplines. Fourier Series enable the representation of periodic functions as a sum of sinusoidal functions, essential for analyzing signals and waveforms in fields such as telecommunications and signal processing. Fourier Integral extends this concept to non-periodic functions, providing a continuous spectrum representation that finds applications in solving differential equations and analyzing complex systems in physics and engineering. Mastery of these concepts equips students with essential tools for tackling advanced engineering problems and understanding the fundamental principles of signal analysis and system dynamics.

3- Partial Differential Equations and its solution

In the subsequent chapter of the Engineering Mathematics course, the focus shifts to Partial Differential Equations (PDEs) and their solutions, which are fundamental in modeling physical phenomena across various engineering disciplines. The course covers methods for solving PDEs, including separation of variables, Fourier series methods, and numerical techniques such as finite difference methods. Applications range from heat conduction and fluid dynamics to electromagnetic theory and quantum mechanics. Understanding PDEs and their solutions equips students with the mathematical tools necessary to analyze and predict behavior in complex systems encountered in engineering practice.

4- Complex Analysis Part I. (The theory of functions of a complex variable)

4- Complex Analysis Part II

In the study of Complex Analysis within the Engineering Mathematics course, students explore foundational topics essential for understanding functions of a complex variable. The course begins with an introduction to analytical functions and their differentiability properties in the complex plane. Integral calculus in the complex plane is examined, focusing on techniques for integrating along paths in the complex plane. Series expansions in complex analysis are explored to approximate complex functions and study their behavior. The residue theorem and the computation of real integrals using complex analysis techniques are also covered, providing powerful tools for solving real-world engineering problems involving complex functions and integrals.