The present book, consisting of two parts, is essentially a collection of Exercises and their Solutions in Ordinary Differential Equations (ODEs) and Partial Differential Equations (PDEs). Its special nature, which makes it different from the usual books on the subject, consists of providing sufficient theoretical materials at the beginning of each chapter, pertaining to that chapter. This certainly helps students straight way dwell into solving the exercises, referring to the relevant textbooks only for understanding the proofs of the important theorems and additional topics. The topics are at (senior) undergraduate and beginning graduate levels.

The importance of the subjects of ODE and PDE in the modern science and engineering curricula is well-known. Many interesting and important real-life problems are modelled using ODE and PDE. These include, but not limited to, physics, chemistry, biology, engineering, economics, sociology and psychology. These topics require extensive mathematical techniques, which are dealt with in many existing books on the subjects, with varying degrees of difficulty and contents. Many books, especially those used as textbooks, also contain a comprehensive list of exercises. Certain books also have Solutions Manuals, usually made available to teachers only. Many other books contain solutions to a selected list of exercises. In our experience, as teachers of these subjects for many years, we find that many students do not attempt to solve the exercises, except routine straightforward ones. This could be partially due to the fact that some exercises turn out to be tricky or difficult, often requiring some advanced knowledge in analysis and linear algebra for their solutions. Furthermore, those students who study the subjects on their own find solving exercises more difficult, thus missing out an important aspect of learning the subject.

This book is an outcome of our experience of teaching and research, not only in our respective institutions but also in many other institutions and universities across India. We have extensively given lectures on differential equations at these institutions, for more than three decades, as part of workshops, schools and series of lectures. After the successful publication of our two co-authored books, one on ODEs (2017) (Ref.[46]) and the other on PDEs (2020) (Ref.[45]), there was a constant inquiry about the Solutions Manuals of the problems in these books from the student and teacher community, as well as our well-wishers.