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Advanced Differential Equations by Raisinghania - Revised Edition

Product Code: 2840108
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This book is especially prepared for B.A., B.Sc. and Honours (Mathematics and Physics), M.A./M.Sc.(Mathematics and Physics), B.E. Students of Various Universities and for I.A.S., P.C.S., AMIE, GATE, CSIR, UGC, NET and Various Competitive Examinations. 2. References to the latest papers of various universities IAS and GATE etc. have been made at proper places. 3. Four new chapters, namely, `Chebyshev Polynomials`, `Beta & Gamma Functions`, `Power Series and Transport Equation` have been added in this edition. 4. A set of objective problems (including those asked in various Universities, GATE etc.) has been provided at the end of each chapter. 5. Almost each chapter of this book has been enlarged and rearranged so that in the present form, the reader will not find any difficulty in understanding the subject matter. 6. More solved examples have been added so that the reader may gain more confidence in the techniques of solving problems. 7. Errors and omissions of the previous edition have been corrected.

CONTENTS:

Part I : ADVANCED ORDINARY DIFFERENTAL EQAUATIONS AND SPECIAL FUNCTIONS : 1. Picard`s Iterative Methods Uniqueness and Existence Theorem 2. Simulataneous Differential Equations of the form(dx)/p=(dy)/Q=(dz)/R 3. Total (or Pfaffian) Differential Equations 4. Riccati`s Quation 5. Chebyshav Polynimials 6. Beta and Gamma Functions 7. Power Series 8. Integretion in Series 9. Legendre Polynomicals : Part I : Legendre Function of the First Kind Part II Associated Legendre Functions of the First Kind 10. Legendre Functions of the Second Kind 11. Bessel Functions 12. Hermite Polynomials 13. Lageurere polynomial 14. Hypergeometric Function 15. Orthogonal set of Function and Strum-Liouville Problems

Part II : PARTIAL DIFFERENTIAL EQUATIONS : 1. Orgin of Partial Differential Equations 2. Linear Partial Differential Equations of Order one 3. Non-linear Partial Differential Equations of Order one 4. Homegeneous Linear Partial Differential Equations with Constant Coefficients 5. Non-homogeneous Linear Partial Differential Equations with Constant Coefficients 6. Partial Differentials Equations Reducible to Equations with Constant Coefficients 8. Classifications of Partial Differential Equations Reductions to Cononial or Normal form. Riemann Method 9. Monge`s Method 10. Transport Equation Part III : BOUNDRY VALUE PROBLEMS AND THEIR SOLUTIONS BY SEPRATIONS OF VARIABLES : 1. Heat, Wave and Telegraph Equations. Methods of Separations of Variables 2. Boundary Value Problems in Certesian Coordinates : Part I : Problems Based on One-dimensional Heat (or Diffusion)Equations

Part II : Problems Based on Two-dimensional Heat (or Diffusion) Equations Part III : Problems Based on Three-dimensional Heat (or Diffusion) Equations

Part IV : Problem Based on One-dimensional Wave Equations

Part V : Problems Based on Two Dimensional Wave Equations

Part VI : Problems Based on Three Dimensional Wave Equation

Part VII : Problems Based on Two-dimensional Laplace`s Equation

Part VIII : Problems Based on Three-dimensional Laplace`s Equation

Part IX : Problem Based on Telegraph (or Translations) Line Equations 3. Boundary Value Problems in Polar Coordinates 4. Boundary Value Problems in Cylindrial Coordinates 5. Boudart Value Problem in Spherical Coordinates Part IV-A : LAPLACE TRANSFORM WITH APPLICATIONS : 1. The Laplace Transform 2. The Inverse Laplace Transform 3. Applications to Ordinary Differential Equations 4. Application to Integral Equations 5 Application to Boundary Value Problems Part IV-B : FOURIER TRANSFORMS AND THEIR APPLICATIONS : 1. Fourier Integrals and Fourier Transforms : Part I : Fourier Integrals and their Applications Part II : (Infinite) Fourier Transforms Part III : Application of Infinite Transforms to Boundary Value Problems 2. Finite Fourier Transforms : Part I : Finite Fourier Transforms Part II

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