Transforms and Partial Differential Equations

✍ Scribed by N. Subramaniam, K. S. Ramaswami

• Publisher: Pearson Education
• Year: 2018
• Tongue: English
• Leaves: 665
• Category: Library

✦ Table of Contents

Cover
About Pearson
Title Page
Copyright
Dedication
Roadmap to the Syllabus
Contents
Preface
Acknowledgements
About the Authors
Introduction
Chapter 1: Partial Differential Equations
1.1 Formation of P.D.E.
1.2 Integrals of Partial Differential Equations
1.3 Lagrange’s Linear Equation
1.4 Standard Types of First Order Equation
1.5 Equations Reducible to the Standard Forms
1.6 Homogeneous Linear Equations with constant coefficients
1.7 Non Homogeneous Linear P.D.E with Constant Coefficients
Short Questions and Answers
Chapter 2: Fourier Series
2.1 Fourier Series of a Function
2.2 Change of Interval
2.3 Half Range Series
2.4 Complex Form of Fourier Series
2.5 Root-Mean Square Value of a Function- Parseval’s Theorem
2.6 Practical Harmonic Analysis
Short Questions and Answers
Chapter 3: Applications of Partial Differential Equations
3. 1 Method of Sepa ration of Variables
3. 2 Classification of Second Order Quasi Linear Partial Differential Equations
3. 3 One Dimensional Wave Equation (ODWE) Vibrations of a Stretched String – Wave Equation
3. 4 One Dimensional Heat Flow Equation (ODHE)
3. 5 Two Dimensional Heat Flow Equation
Short Questions and Answers
Chapter 4: Fourier Transforms
4.1 Fourier Integral Theorem
4.2 Fourier Transforms
4.3 Fourier Sine and Cosine Transform
4.4 Finite Fourier Cosine and Sine Transform(Optional)
Short Questions and Answers
Chapter 5: Z-Transforms and Difference Equations
5.1 Z-Transform
5.2 Convolution Theorem
5.3 Inverse Z-Transform
5.4 Solution of Difference Equations
Short Questions and Answers