This comprehensive textbook offers an in-depth exploration of transform techniques and partial differential equations, essential for students and professionals in mathematics, engineering, and applied sciences. Designed with academic rigor and practical clarity, the book presents fundamental concepts and advanced topics in a structured, accessible format.

Beginning with the formation and classification of partial differential equations, the text guides readers through various solution methods, including first-order and higher-order linear and non-linear PDEs. Emphasis is placed on conceptual understanding, with numerous examples illustrating applications in physical and engineering contexts.

The section on Fourier Series delves into periodic functions, even and odd function expansions, half-range series, and Parseval’s theorem. It bridges theory and application with harmonic analysis and the complex form of Fourier series, providing tools for analyzing time-based signals and functions.

Building on this foundation, the book introduces Fourier Transforms, covering integral transforms, properties, convolution theorem, and sine and cosine transforms. These tools are presented in the context of system modeling, data analysis, and wave propagation.

A dedicated chapter on the application of partial differential equations demonstrates the use of mathematical modeling to solve the wave, heat, and Laplace’s equations, equipping readers with skills for tackling real-world problems in physics and engineering.

The final segment focuses on Z-Transforms and difference equations, offering critical insight into discrete-time systems and digital signal processing. The theoretical framework is complemented by applications in system analysis and control engineering.

With clear explanations, step-by-step derivations, and well-structured exercises, this book supports both classroom instruction and self-study. Its blend of analytical techniques and practical applications makes it an indispensable resource for undergraduate and postgraduate studies in mathematical sciences and engineering disciplines.