Partial Differential Equations : Methods and Applications

Introduction. 1. First-Order Equations. 2. Principles for Higher-Order Equations. 3. The Wave Equation. 4. The Laplace Equation. 5. The Heat Equation. 6. Linear Functional Analysis. 7. Differential Calculus Methods. 8. Linear Elliptic Theory. 9. Two Additional Methods. 10. Systems of Conservation Laws. 11. Linear and Nonlinear Diffusion. 12. Linear and Nonlinear Waves. 13. Nonlinear Elliptic Equations. Appendix on Physics. Hints and Solutions for Selected Exercises. References. Index. Index of Symbols.