Textbook on Differential Equations & Integral Transforms

This book has been specially written according to the latest Unified Syllabus to meet the requirements of the B.A. and B.Sc. Part-II Students of all Universities in Uttar Pradesh. The subject matter has been discussed in such a simple way that the students will find no difficulty to understand it. The proofs of various theorems and examples have been given with minute details. Each chapter of this book contains complete theory and a fairly large number of solved examples. Sufficient problems have also been selected from various university examination papers. At the end of each chapter an exercise containing objective questions has been given. Differential Equations & Integral Transforms 1 Dedication 2 Preface 3 Syllabus 4 Brief Contents 5 Section-A: Differential Equations (1) 6 Section-A: Differential Equations (2) 7 Chapter 1. Differential Equations of First Order and First Degree 8 Chapter 2. Differential Equations of the First Order but not of the First Degree 52 Chapter 3. Orthogonal Trajectories 78 Chapter 4. Linear Differential Equations with Constant Coefficients 88 Chapter 5. Homogeneous Linear Differential Equations 124 Chapter 6. Ordinary Simultaneous Differential Equations 136 Chapter 7. Linear Equations of Second Order with Variable Coefficients 158 Chapter 8. Partial Differential Equations of the First Order 200 Chapter 9. Linear Partial Differential Equations of Second and Higher Order with Constant Coeff. 252 Chapter 10. Partial Differential Equations of Second Order with Variable Coefficients 292 Chapter 11. Monge's Method 312 Chapter 12. Series Solutions of Differential Equations 330 Chapter 13. Legendre's Functions 354 Chapter 14. Bessel’s Functions 382 Section-B: Integral Transforms (1) 404 Section-B: Integral Transforms (2) 405 Chapter 1. The Laplace Transform 406 Chapter 2. The Inverse Laplace Transform 446 Chapter 3. Applications of Laplace Transform 480 Chapter 4. Fourier Transforms 508 Chapter 5. Finite Fourier Transforms 538 Chapter 6. Applications of Fourier Transforms in Initial and Boundary Value Problems 552 Chapter 7. Fourier Series 572