An Elementary Course on Partial Differential Equations

This book will be useful for elementary courses in Partial Differential Equations for undergraduate programmes in pure and applied mathematics.

Aftab Alam (Author), Mohammad Imdad (Author)

9781009201445, Cambridge University Press

Paperback, published 5 January 2023

350 pages
24.1 x 18.3 x 1.6 cm, 0.53 kg

Partial differential equations are a vital part of any course in pure or applied mathematics. This book will be invaluable to anyone looking for a lucid but comprehensive introduction to PDEs. Designed to strike a balance between theory and practical problems, it covers all major methods as well as their historical backgrounds, theoretical rigour, and geometric significance. The book is divided into three parts. It starts with basic topics like ordinary differential equations, multivariable calculus, and geometry. This is followed by important techniques to solve certain types of partial differential equations. The last part is devoted to first, second, and higher-order PDEs. The chapters have been arranged to help students develop their knowledge gradually and systematically. Each method is discussed through theoretical descriptions in the form of theorems followed by illustrative problems to help the readers. Finally, numerous solved examples and practice problems helps the student learn to apply this knowledge.

1. Relevant Pre-requisites and Terminologies
2. Solution, Classification, and Formation of Partial Differential Equations
3. Easily Solvable Partial Differential Equations
4. First-Order Partial Differential Equations
5. Second-Order Partial Differential Equations
6. Higher Order Linear Partial Differential Equations.

Subject Areas: Differential calculus & equations [PBKJ]