Applied Partial Differential Equations | Fourth Edition | By Pearson

This text emphasises the physical interpretation of mathematical solutions and introduces applied Mathematics while presenting differential equations. Coverage includes Fourier series, orthogonal functions, boundary value problems, green’s functions and transform methods. Features: 1.Step-by-step approach 2.Emphasis on examples and problem solving 3.Physical and mathematical derivations 4.Clear and lively writing style 5.1, 000 carefully prepared exercises 6.Learning aids 7.Pattern formation for reaction-diffusion equations and the Turing instability 8.Well done treatment of numerical methods for pde 9.Presentation of derivation of the diffusion of a pollutant 10.Discussion on Time dependent heat equations 11.Similarity solution for ht heat equation 12.Green’s functions for wave and Heat equations Chapter 13.Shock waves Chapter 14.Stability of systems of ordinary differential equation 15.Wave envelope equations table of Contents: 1. Heat equation 2. Method of separation of variables 3. Fourier series 4. Wave equation: vibrating strings and membranes 5. Sturm-liouville eigenvalue problems 6. Finite difference numerical methods for partial differential equations 7. Higher Dimensional partial differential equations 8. Nonhomogeneous problems 9. Green’s functions for Time-Independent problems 10. Infinite domain problems: Fourier transform solutions of partial differential equations 11. Green’s functions for wave and Heat equations 12. The method of characteristics for linear and Curvilinear wave equations 13. Laplace transform solution of partial differential equations 14. Dispersive waves: slow variations, stability, nonlinearity and perturbation methods bibliography answers to starred exercises index.