Transforms and Partial Differential Equations

Cover 1 About Pearson 2 Title Page 6 Copyright 7 Dedication 8 Roadmap to the Syllabus 10 Contents 12 Preface 14 Acknowledgements 15 About the Authors 16 Introduction 18 Chapter 1: Partial Differential Equations 18 1.1 Formation of P.D.E. 18 1.2 Integrals of Partial Differential Equations 40 1.3 Lagrange’s Linear Equation 46 1.4 Standard Types of First Order Equation 68 1.5 Equations Reducible to the Standard Forms 91 1.6 Homogeneous Linear Equations with constant coefficients 103 1.7 Non Homogeneous Linear P.D.E with Constant Coefficients 142 Short Questions and Answers 160 Chapter 2: Fourier Series 180 2.1 Fourier Series of a Function 180 2.2 Change of Interval 221 2.3 Half Range Series 240 2.4 Complex Form of Fourier Series 265 2.5 Root-Mean Square Value of a Function- Parseval’s Theorem 280 2.6 Practical Harmonic Analysis 292 Short Questions and Answers 305 Chapter 3: Applications of Partial Differential Equations 314 3. 1 Method of Sepa ration of Variables 314 3. 2 Classification of Second Order Quasi Linear Partial Differential Equations 320 3. 3 One Dimensional Wave Equation (ODWE) Vibrations of a Stretched String – Wave Equation 323 3. 4 One Dimensional Heat Flow Equation (ODHE) 363 3. 5 Two Dimensional Heat Flow Equation 392 Short Questions and Answers 432 Chapter 4: Fourier Transforms 446 4.1 Fourier Integral Theorem 446 4.2 Fourier Transforms 460 4.3 Fourier Sine and Cosine Transform 499 4.4 Finite Fourier Cosine and Sine Transform(Optional) 548 Short Questions and Answers 562 Chapter 5: Z-Transforms and Difference Equations 570 5.1 Z-Transform 570 5.2 Convolution Theorem 598 5.3 Inverse Z-Transform 601 5.4 Solution of Difference Equations 629 Short Questions and Answers 657 "Transforms and Partial Differential Equations comprises of five units, which present the important principles, methods and processes of obtaining results in an easy to understand and systematic manner. The text is supported by a large number of exercises and a variety of solved examples. Features: " Simple presentation with clarity and rigor " Step-by-step approach for problem solving " Comprehensive coverage of the required syllabus " Inclusion of short questions and answers."