# Advanced Differential Equations MD Raisinghania PDF: A Comprehensive Guide If you are looking for a book that covers advanced concepts of differential equations, such as boundary value problems, Laplace transforms, Fourier transforms, Hankel transforms, and calculus of variations, then you might want to check out Advanced Differential Equations by M.D. Raisinghania. This book is designed for students of mathematics, physics, and engineering, as well as aspirants of various competitive examinations. It provides lucid explanations, solved examples, and exercises based on the latest syllabus and papers of various universities and I.A.S. examination.

## Overview of Advanced Differential Equations by M.D. Raisinghania

Advanced Differential Equations by M.D. Raisinghania is divided into five parts:

• Part I: Advanced Ordinary Differential Equations and Special Functions: This part covers topics such as linear differential equations of higher order, power series solutions, Legendre polynomials, Bessel functions, hypergeometric functions, Hermite polynomials, Laguerre polynomials, Chebyshev polynomials, and orthogonal functions.
• Part II: Partial Differential Equations: This part covers topics such as formation and classification of partial differential equations, linear partial differential equations of first order, non-linear partial differential equations of first order, homogeneous linear partial differential equations with constant coefficients, non-homogeneous linear partial differential equations with constant coefficients, Monge’s method, and Cauchy’s method.
• Part III: Boundary Value Problems and their Solutions by Separation of Variables: This part covers topics such as boundary value problems in Cartesian coordinates, boundary value problems in polar coordinates, boundary value problems in cylindrical coordinates, boundary value problems in spherical coordinates, and boundary value problems in other coordinate systems.
• Part IV: Laplace Transforms with Applications: This part covers topics such as definition and properties of Laplace transforms, inverse Laplace transforms, convolution theorem, Heaviside’s unit step function, Dirac’s delta function, periodic functions, applications of Laplace transforms to ordinary differential equations, applications of Laplace transforms to partial differential equations, applications of Laplace transforms to integral equations, and applications of Laplace transforms to difference equations.
• Part V: Fourier Transforms and their Applications: This part covers topics such as definition and properties of Fourier transforms, inverse Fourier transforms, Fourier sine and cosine transforms, convolution theorem for Fourier transforms, Parseval’s identity for Fourier transforms,
applications of Fourier transforms to ordinary differential equations,
applications of Fourier transforms to partial differential equations,
applications of Fourier transforms to integral equations,
and applications of Fourier transforms to difference equations.
• Part VI: The Hankel Transforms and their Applications: This part covers topics such as definition and properties of Hankel transforms,
inverse Hankel transforms,
applications of Hankel transforms to ordinary differential equations,
applications of Hankel transforms to partial differential equations,
and applications of Hankel transforms to integral equations.
• Part VII: Calculus of Variations: This part covers topics such as variational problems with fixed boundaries,
Euler’s equation,
isoperimetric problems,
variational problems with moving boundaries,
Lagrange’s multiplier method,
and variational problems with subsidiary conditions.

The book also contains additional problems on the entire book at the end. 