Advanced Differential Equations Engelska 1995

This book has been designed to acquaint the students with the knowledge of advanced concepts of differential equations. This text covers topics such as Ordinary and Partial Differential Equations, Boundary Value Problems, Laplace Transforms, Fourier Transforms and Calculus. While the textbook lucidly presents the theoretical concepts, it also educates the students with the various methods and applications related to differential equations. Fetures : 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 TOC : PART-I: ADVANCED ORDINARY DIFFERNTIAL EQUATIONS AND SPECIAL FUNCTIONS 1. Picard's iterative method. Uniqueness and existence theorem 2. Simultaneous differential equations of the form (dx)/P = (dy)/Q = (dz)/R 3. Total (or Pfaffian) differential equations 4. Beta and Gamma function 5. Chebyshev polynomials 6. Fourier series 7. Power series 8. Integration in series 9. Legendre polynomials 10. Legendre functions of the second kind 11. Bessel functions 12 Hermite polynomials 13. Laguerre polynomial 14. Hypergeometric function 15. Orthogonal set of functions and Strum-Liouville problem 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 6. Partial differential equations reducible to equations with constant coefficients 7. Partial differential equations of order two with variables coefficients 8. Classifiation of partial differential equations Reduction to cononial 9. Monge's method 10. Transport equation 11. Cauchy initial value problem for linear first order partial differential equations PART-III: BOUNDARY VALUE PROBLEMS AND THEIR SOLUTIONS BY SEPARATION OF VARIABLES 1. Heat, wave and telegraph equation. Method of separation of variables 2. Boundary value problems in cartesian coordinates 3. Boundary value problems in polar coordinates 4. Boundary value problems in cylindrial coordinates 5. Boundary value problems in spherical coordinates PART-IV-A: LAPLACE TRANFORMS 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 2.Finite Fourier transforms PART-V: CALCULUS OF VARIATIONS 1. Variational problems with fixed boundaries 2. Variational problems with moving (or free) boundaries. One sided variations 3. Sufficient conditions for an extremum