An introduction to partial differential equations
Publisher: Bookboon.com
Published: 2013
ISBN-13: 9788776819699
Table of contents: title: Content; title: 1. Part I First-order partial differential equations; title: 2. List of examples; title: 3. Preface; title: 4. Introduction; title: 4.1. Types of equation; title: 4.2. Exercises 1; title: 5. The quasi-linear equation; title: 5.1. Of surfaces and tangents; title: 5.2. The Cauchy (or initial value) problem; title: 5.3. The semi-linear and linear equations; title: 5.4. The quasi-linear equation in n independent variables; title: 5.5. Exercises 2; title: 6. The general equation; title: 6.1. Geometry again; title: 6.2. The method of solution; title: 6.3. The general PDE with Cauchy data; title: 6.4. The complete integral and the singular solution; title: 6.5. Exercises 3; title: 7. Answers; title: 8. Part II Partial differential equations: classification and canonical forms; title: 9. List of Equations; title: 10. Preface; title: 11. Introduction; title: 11.1. Types of equation; title: 12. First-order equations; title: 12.1. The linear equation; title: 12.2. The Cauchy problem; title: 12.3. The quasi-linear equation; title: 12.4. Exercises 2; title: 13. The wave equation; title: 13.1. Connection with first-order equations; title: 13.2. Initial data; title: 13.3. Exercises 3; title: 14. The general semi-linear partial differential equation in two independent variables; title: 14.1. Transformation of variables; title: 14.2. Characteristic lines and the classification; title: 14.3. Canonical form; title: 14.4. Initial and boundary conditions; title: 14.5. Exercises 4; title: 15. Three examples from fluid mechanics; title: 15.1. The Tricomi equation; title: 15.2. General compressible flow; title: 15.3. The shallow-water equations; title: 15.4. Appendix: The hodograph transformation; title: 15.5. Exercise 5; title: 16. Riemann invariants and simple waves; title: 16.1. Shallow-water equations: Riemann invariants; title: 16.2. Shallow-water equations: simple waves; title: 17. Answers; title: 18. Part III Partial differential equations: method of separation of variables and similarity & travelling-wave solutions; title: 19. List of Equations; title: 20. Preface; title: 21. Introduction; title: 21.1. The Laplacian and coordinate systems; title: 21.2. Overview of the methods; title: 22. The method of separation of variables; title: 22.1. Introducing the method; title: 22.2. Two independent variables: other coordinate systems; title: 22.3. Linear equations in more than two independent variables; title: 22.4. Nonlinear equations; title: 22.5. Exercises 2; title: 23. Travelling-wave solutions; title: 23.1. The classical, elementary partial differential equations; title: 23.2. Equations in higher dimensions; title: 23.3. Nonlinear equations; title: 23.4. Exercises 3; title: 24. Similarity solutions; title: 24.1. Introducing the method; title: 24.2. Continuous (Lie) groups; title: 24.3. Similarity solutions of other equations; title: 24.4. More general solutions from similarity solutions; title: 24.5. Exercises 4; title: 25. Answers; title: 26. Index