Advanced Differential Equations, 19/e

Advanced Differential Equations, 19/e

Authors : Dr. M.D. Raisinghania

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About the Author

Dr. M.D. Raisinghania :-
Former Reader and Head of the Mathematics Department, S.D. College, Muzaffarnagar. He obtained his Ph.D. in Mathematics on the thesis entitled "An Analytical Study of Some Non-Newtonian Fluid Flow Problems". He has 38 years of teaching experience. Dr. Raisinghania has published several research papers in the area of Fluid Mechanics in reputed journals.
 

About the Book

This book has been designed to acquaint the students with advanced concepts of differential equations. Comprehensively written, it covers topics such as Boundary Value Problems and their Separation of Variables, Laplace Transforms with Applications, Fourier Transforms and their Applications, the Hankel Transform and its Applications and Calculus of Variations. While the textbook lucidly explains the theoretical concepts, it also presents the various methods and applications related to differential equations. Students of mathematics would find this book extremely useful as well as the aspirants of various competitive examinations.
 

Key Features

• Follows a step-by-step approach to problem solving
• Numerous examples and solved problems with detailed explanations provided for effective understanding of the concepts
• Solutions to latest questions papers of various university examinations have also been provided
 

Table of Content

Part-I: Advanced Ordinary Differential Equations and Special Functions
• Picard's Iterative Method. Uniqueness and Existence Theorem • Simultaneous Differential Equations of the form (dx)/P = (dy)/Q = (dz)/R • Total (or Pfaffian) Differential Equations • Beta and Gamma Functions • Chebyshev Polynomials • Fourier Series • Power Series • Integration in Series • Legendre Polynomials • Legendre Functions of The Second Kind • Bessel Functions • Hermite Polynomials • Laguerre Polynomial • Hypergeometric Function • Orthogonal set of Functions and Strum-Liouville Problem

Part-II: Partial Differential Equations
• Origin of Partial Differential Equations • Linear Partial Differential Equations of Order One • Non-Linear Partial Differential Equations of Order One • Homogeneous Linear Partial Differential Equations with Constant Coefficients • Non-Homogeneous Linear Partial Differential Equations with Constant Coefficients • Partial Differential Equations Reducible to Equations with Constant Coefficients • Partial Differential Equations of Order two with Variables Coefficients • Classification of Partial Differential Equations Reduction to Cononial or Normal Form. Riemann Method • Monge's Method • Transport Equation • Cauchy Initial Value Problem for Linear First Order Partial Differential Equations

Part-III: Boundary Value Problems and Their Solutions by Separation of Variables
• Heat, Wave and Telegraph Equation. Method of Separation of Variables • Boundary Value Problems in Cartesian Coordinates • Boundary Value Problems in Polar Coordinates • Boundary Value Problems in Cylindrical Coordinates • Boundary Value Problems in Spherical Coordinates

Part-IV-A: Laplace Transforms with Applications
• The Laplace Transform • The Inverse Laplace Transform • Applications to Ordinary Differential Equations • Application to Integral Equations • Application to Boundary Value Problems

Part-IV-B: Fourier Transforms and Their Applications
• Fourier Integrals and Fourier Transforms • Finite Fourier Transforms

Part-IV-C: The Hankel Transforms and Their Applications
• The Hankel Transform and their Applications • The Finite Hankel Transform and its Applications

Part-V: Calculus of Variations
• Variational Problems with Fixed Boundaries • Variational Problems with Moving (or Free) Boundaries. One Sided Variations • Sufficient Conditions for an Extremum

• Additional Problems