Partial Differential Equations : Classical Theory with a Modern Touch (Hardcover)

List of illustrations; Preface; Acknowledgements; Notations; 1. Introduction; 2. Preliminaries; 3. First-order partial differential equations: method of characteristics; 4. Hamilton?Jacobi equation; 5. Conservation laws; 6. Classification of second-order equations; 7. Laplace and Poisson equations; 8. Heat equation; 9. One-dimensional wave equation; 10. Wave equation in higher dimensions; 11. Cauchy?Kovalevsky theorem and its generalization; 12. A peep into weak derivatives, Sobolev spaces and weak formulation; References; Index.