Introduction to Partial Differential Equations

This book serves as an accessible and comprehensive introduction to Partial Differential Equations (PDEs) for undergraduate students in the United States. It is designed to provide a solid foundation in the theory and applications of PDEs, catering to students studying mathematics, engineering, physics, and related fields.

Throughout the text, we present the fundamental concepts of PDEs in a clear and engaging manner, emphasizing both theoretical understanding and practical problem-solving skills. Starting with an overview of basic concepts such as classification of PDEs, boundary and initial conditions, and solution techniques, we gradually progress to more advanced topics including Fourier series, separation of variables, and method of characteristics.

Real-world applications of PDEs are woven throughout the book, demonstrating the relevance of this mathematical theory in fields such as heat conduction, fluid dynamics, quantum mechanics, and finance. Additionally, numerous examples, exercises, and applications are included to reinforce learning and encourage active engagement with the material.

Whether you’re preparing for further study in mathematics or seeking to apply PDEs in your chosen field, this book equips you with the knowledge and skills necessary to tackle a wide range of problems involving partial differential equations. It is our hope that this text will inspire curiosity and confidence in approaching the rich and diverse world of PDEs.