The book explores a range of mathematical topics essential for application in engineering and applied sciences. It explores both the theoretical and practical aspects, providing a comprehensive foundation for the development of robust theories applicable to engineering and applied sciences. Mathematical Analysis for Engineering and Applied Sciences: Foundational and Fundamental Aspects discusses the essential mathematical principles that underpin the fields of applied science and engineering. This comprehensive book explores a blend of pure and applied mathematics, demonstrating how mathematical tools and techniques can be utilized to create a wide range of models for practical applications in these disciplines. It addresses the challenges of handling complex phenomena and provides algorithms, methods, and logical concepts that are invaluable for bioengineering, cryptosystems, surface modeling, and various other engineering applications. Individual researchers, educators, students, and department libraries will find this book of interest.