| Description |
1 online resource (ix, 374 pages) : illustrations |
| Contents |
Cover -- An Elementary Course on Partial Differential Equations -- Title -- Copyright -- Dedication -- Contents -- Preface -- Acknowledgements -- Symbols -- 1 Relevant Pre-requisites and Terminologies -- 1.1 Partial Derivatives and Allied Topics -- 1.2 Curves and Surfaces -- 1.3 Ordinary Differential Equations -- 1.4 Total Differential Equations -- 1.5 Simultaneous Total Differential Equations -- Exercises -- 2 Solution, Classification, and Formation of Partial Differential Equations -- 2.1 Order and Degree of a PDE -- 2.2 Solution of a PDE -- 2.3 PDEs Involving Two Independent Variables |
|
2.4 Classification of PDEs -- 2.5 Further Classification of PDEs -- 2.6 Linear Differential Operators -- 2.7 Auxiliary Conditions -- 2.8 Formation of Partial Differential Equations by Elimination of Arbitrary Constants -- 2.9 Formation of PDEs by Elimination of Arbitrary Functions -- 2.9.1 Formation of First-Order Quasilinear PDEs -- 2.9.2 Formation of Second-Order Linear PDEs -- 2.9.3 Formation of Second-Order Quasilinear PDEs -- 2.9.4 Formation of Second-Order Non-linear PDEs -- Exercises -- 3 Easily Solvable Partial Differential Equations -- 3.1 Direct Integration Method |
|
3.2 Linear Equations of Order One Containing Single Derivative -- 3.3 Linear PDEs Solvable as ODEs -- 3.4 Method of Separation of Variables -- Exercises -- 4 First-Order Partial Differential Equations -- 4.1 Linear PDEs: Reduction to Canonical Form -- 4.2 Semilinear PDEs: Geometry of Solutions -- 4.3 Quasilinear PDEs: Lagrange's Method -- 4.3.1 Geometric Interpretation of Lagrange's Method -- 4.3.2 An Application to Determine Surfaces Orthogonal to a Given Family of Surfaces -- 4.3.3 Quasilinear Equations in n Independent Variables -- 4.4 Certain Standard Forms of First-Order PDEs |
|
4.4.1 Standard Form I: Equations Containing Partial Derivatives Only -- 4.4.2 Standard Form II: Equations Containing None of the Independent Variables Explicitly -- 4.4.3 Standard Form III: Separable Equations -- 4.4.4 Standard Form IV: Clairaut's Equation -- 4.4.5 Equations Reducible to Standard Forms -- 4.5 Charpit's Method: A General Method of Finding the Complete Solution -- 4.6 Singular Solution of a Non-linear PDE -- 4.7 General Solution of a Non-linear PDE -- 4.8 Cauchy Problem and Particular Solution: Integral Surface through a Given Curve |
|
4.8.1 Cauchy Problems Solvable by Lagrange's Method: Particular Solution from General Solution -- 4.8.2 Cauchy Problems Solvable by Charpit's Method: Particular Solution from Complete Solution -- 4.9 Cauchy's Method of Characteristics: A General Method for Solving Cauchy Problems -- 4.9.1 Solution of a Cauchy Problem for Non-linear PDE -- 4.9.2 Standard Strategy for Quasilinear PDE -- 4.10 Simultaneous PDEs -- 4.11 PDEs in More Than Two Independent Variables: Jacobi's Method -- Exercises -- 5 Second-Order Partial Differential Equations -- 5.1 Linear PDEs: Standard Forms |
| Summary |
"Differential equations (DE) are important because of their applications in fields like pure and applied mathematics, physics, engineering, biology, and economics. DE are the base of mathematical modelling applied to solve real-life problems that may not be solved directly. The subject is introduced in the school curriculum of mathematics and taught at undergraduate and graduate levels across India. The differential equation is taught as two courses - ordinary differential equations and partial differential equations. This book is designed to serve as a textbook for the first course on partial differential equations which is known as partial differential equations (PDE) or differential equations II in most of the Indian universities. There are numerous books in this area but most do not give adequate emphasis on the basic requirements of undergraduate students. The authors have utilized their teaching experience of several years to fill this gap. Special attention is paid to elementary partial differential equations and this book covers important techniques like Monge's method, Monge-Ampere type non-linear equations, reduction of first-order linear equation in canonical form, derivation of second-order quasi-linear equations, higher-order PDE with constants coefficients and their reduction to variable coefficients and so on. In addition to topical coverage, a large pool of solved and unsolved problems sets for hands-on practice is also provided"-- Provided by publisher |
| Bibliography |
Includes bibliographical references and index |
| Notes |
Description based on online resource; title from digital title page (viewed on September 28, 2022) |
| Subject |
Differential equations, Partial.
|
|
MATHEMATICS / General.
|
|
Differential equations, Partial
|
| Form |
Electronic book
|
| Author |
Imdad, Mohammad, author.
|
| LC no. |
2022010317 |
| ISBN |
9781009201469 |
|
1009201468 |
|
