An Elementary Course on Partial Differential Equations

This book is designed to serve as a textbook for thefirst course on partial differential equations.After the introduction of the semester system invarious universities of India, normally there aretwo courses of differential equations atundergraduate levels, one is on ordinarydifferential equations (ODEs), whereas the other isexclusively on partial differential equations(PDEs). Generally, most of the books used at theundergraduate level include ODEs as well as PDEs,and all such books emphasise more on ODEs, which,consequently, affect the coverage of the PDEs. Onthe other hand, all the standard textbooks on PDEscover the contents of graduate as well aspostgraduate levels, wherein often undergraduatematerials are discussed in haste. Overall, it isnecessary to write a separate book exclusively forundergraduate students of Indian as well as foreignuniversities. With a view to have a detaileddiscussion on elementary topics of PDEs, weendeavour to write this book.

In fact, this book is based on our lecture notes, whichwe have given to our students at Aligarh MuslimUniversity (AMU) over the last several years. Wehope that this book will meet the requirement aswell as expectations of undergraduate students.While preparing this book, we have examined deeplythe syllabi of all such courses of B.Sc.(Mathematics) of all Indian universities. The coursecontents covered by this book can be described asthe union of all syllabi prescribed by variousIndian universities as well as UGC curriculum up toundergraduate level. The course contents arepresented in such a manner that they can be equallyuseful in various competitive examinations such asUPSC, UGC-CSIR NET, and GATE. On the other hand,from the application point of view, the book alsocontains the relevant contents of MathematicalPhysics/Engineering Mathematics/Applied Mathematics,which are the parts of course contents in B.Sc.(Physics) as well as B.E./B.Tech. We attempt tostrike a balance between theory and problems.Consequently, our book remains equally useful toboth pure as well as applied mathematicians. We havemade every attempt to have a simpler and lucidpresentation without scarifying theoretical rigour.The book provides different types of examples,updated references, and applications in diversefields. All methods of solution and necessaryconcepts are arranged in the form of theorems. Theproofs of theorems may be omitted for anundergraduate course or a course in otherdisciplines.