Advanced Differential Equations, 19/e

• 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

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