Generating Functions in Engineering and the Applied Sciences

This book provides a comprehensive introduction to generating functions, essential for beginners in engineering and applied sciences, covering various applications and techniques.

In the Generating Functions in Engineering and the Applied Sciences, readers are introduced to a variety of generating functions (GFs) that are essential in the fields of engineering and applied sciences. This Second Edition covers a range of topics, including probability GFs (PGF), moment and cumulant GFs (MGF, CGF), mean deviation GFs (MDGF), and survival function GFs (SFGF). Additionally, it explores rising and falling factorial GFs, factorial moments, and inverse factorial moment GFs, providing a comprehensive overview of the subject matter.

The book serves as a valuable resource for beginners, aiming to simplify complex concepts associated with single-variable GFs. It presents these functions in a clear and accessible manner, ensuring that readers can grasp the underlying principles without needing prior knowledge. The authors have included numerous examples and applications across various domains such as bioinformatics, combinatorics, economics, and structural engineering, demonstrating how GFs can be utilized to solve practical problems.

By introducing commonly encountered generating functions like ordinary GF (OGF), exponential GF (EGF), and others, Generating Functions in Engineering and the Applied Sciences equips readers with the tools necessary to apply these mathematical techniques effectively. The inclusion of applications in diverse fields further enhances the book's relevance, making it a must-read for anyone looking to deepen their understanding of generating functions and their applications in real-world scenarios.