This book presents comprehensive coverage of the fundamental concepts and applications of partial differential equations (PDEs). It is designed for the undergraduate [BA/BSc(Hons.)] and postgraduate (MA/MSc) students of mathematics, and conforms to the course curriculum prescribed by UGC.

**This book is recommended in Manipur University, Manipur, Gauhati University, Assam, D.M. College of Science, Manipur.**

The text is broadly organized into two parts. The first part (Lessons 1 to 15) mostly covers the first-order equations in two variables. In these lessons, the mathematical importance of PDEs of first order in physics and applied sciences has also been highlighted. The other part (Lessons 16 to 50) deals with the various properties of second-order and first-order PDEs.

The book emphasizes the applications of PDEs and covers various important topics such as the HamiltonJacobi equation, Conservation laws, Similarity solution, Asymptotics and Power series solution and many more. The graded problems, the techniques for solving them, and a large number of exercises with hints and answers help students gain the necessary skill and confidence in handling the subject.

**Key Features :**

**1.** Presents self-contained topics in a cohesive style.

**2.** Includes about 300 worked-out examples to enable students to understand the theory and inherent aspects of PDEs.

**3.** Provides around 450 unsolved problems with hints and answers to help students assess their comprehension of the subject.