Advanced Differential Equations, 20/e

·         Total 43 chapters are divided in 5 parts to make to reading easy from one topic to another

·         More than 1100 examples aid in ease of understanding of the concepts  

·         More than 500 questions (as in-text and book-end exercises) to enhance and strengthen learning quotient

·         It will also be found useful by the students preparing for various competitive examinations

1. Miscellaneous Methods and Existence and Uniqueness Theorem for Solutions of First Order Initial Value Problems, 2. Picard's Iterative Method, Picard's Theorem and Existence And Uniqueness Of Solutions To First Order Initial Value Problems, 3. Beta and Gamma Functions, 4. Integration in Series, 5. Legendre Polynomials 6. Bessel Functions, 7. Hermite Polynomials, 8. Laguerre Polynomials, 9. Hypergeometric Function 10. The Error Function, Heaviside Unit Function or Unit Step Function) And Dirac Delta Function (Or Unit Impulse Function), 11. Systems of Linear Ordinary Differential Equations, 12. Orthogonal Sets of Functions and Strum Liouville Problem, 13. Simultaneous Equations of The Form (Dx)/P = (Dy)/Q = (Dz)/R, 14. Total Differential Equations, 15. Green's Function and Its Applications to Boundary Value Problems 

Part II: Partial Differential Equations

1. Origin of Partial Differential Equations, 2. Linear Partial Differential Equations of Order One , 3. Non-Linear Partial Differential Equations of Order One, 4. Homogeneous Linear Partial Differential Equations with Constant Coefficients, 5. Non-Homogeneous Linear Partial Differential Equations with Constant Coefficients, 6. Partial Differential Equations Reducible to Equations with Constant Coefficients, 7. Partial Differential Equations of Order Two with Variable Coefficients, 8. Classification of P.D.E. Reduction to Canonical Or Normal Forms Riemann Method, 9. Cauchy Initial Value Problem for Linear First Order Partial Differential Equations 

Part IIIA: Fourier Series

1. Fourier Series

Part IIIB: Boundary Value Problems and Their Solutions by Separation of Variables

1. Heat, Wave, Laplace, and Poisson Equations. Method Of Separation of Variables, 2. Boundary Value Problems in Cartesian Co-Ordinates,          Section I: Problems Based on One-Dimensional Heat (Or Diffusion) Equation, Section II: Problems Based on Two-Dimensional Heat (Or Diffusion) Equation,         Section III: Problems Based on Three-Dimensional Heat (Or Diffusion) Equation, Section IV: Problems Based on One-Dimensional Wave Equation, Section V: Problems Based on Two-Dimensional Wave Equation, Section VI: Problems Based on Three-Dimensions Wave Equation, Section VII: Problems Based on Two-Dimensional Laplace's Equation, Section VIII: Problems Based on Three-Dimensional Laplace' Equation, Section IX: Solution of Dirichlet Problem Involving the Poisson Equation, 3. Boundary Value Problems in Polar Coordinates, 4. Boundary Value Problems in Cylindrical Coordinates, 5. Boundary Value Problems in Spherical Coordinates

Part IVA: Laplace Transforms with Applications

1. The Laplace Transform, 2. The Inverse Laplace Transform, 3. Applications to Ordinary Differential Equations 4. Applications to Integral Equations, 5. Applications to Boundary Value Problems

Part IVB: Fourier Transforms and their Applications

1. Fourier Integrals and Fourier Transforms, 2. Finite Fourier Transforms

Part IVC: The Hankel Transforms and their Applications, 1. The Hankel Transform and Its Applications

2. The Finite Hankel Transform and Its Applications

Part V: Calculus of Variations with Applications

1. Variational Problems with Fixed Boundaries, 2. Variational Problems with Moving (or Free) Boundaries. One Sided Variation , 3. Sufficient Conditions for An Extremum, 4. Direct Methods in Variational Problems

This book is especially written for the students of B.A. (Mathematics), B.Sc., (Mathematics & Physics), M.A. (Mathematics), M.Sc. (Mathematics & Physics) and B.E./B.Tech. Besides, it will also be of immense value to the aspirants of AMIE, GATE, CSIR- UGC (NET) and other competitive examinations.