An Applied and Computational Approach
Focusing on generalized functions and their integral transforms, this textbook utilizes the theory of functions of one complex variable to provide a comprehensive introduction. It features numerous concrete examples to illustrate concepts, making complex theories more accessible for readers.
A Computational Approach using a Mathematica Package
The theory of Laplace transformation is essential for engineers, physicists, and mathematicians, offering effective techniques for solving various scientific and engineering problems, particularly differential equations. Similarly, the z-transformation serves to address difference equations, establishing a parallel between the two theories. While both Laplace and z transformations are part of operational calculus, this book does not delve into Mikusinski's approach, which relies on abstract algebra and may not be easily accessible to practitioners. Instead, it focuses on practical applications. The capabilities of Mathematica are leveraged to enhance the use of Laplace and z-transformations. The author developed the Mathematica Package LaplaceAndzTransforms a decade ago, which computes both transformations and includes numerous routines across various application domains. Upon loading the Package, users gain access to around 150 new commands that complement Mathematica’s built-in functions for Laplace and z-transformations, ensuring that existing functionalities remain intact. This book is primarily aimed at readers engaged in practical applications, providing them with valuable tools to enhance their work in the field.