Introduction to Partial Differential Equations

This innovative book blends both the numerical simulation and the analysis of Partial Differential Equations. This approach is thoroughly modern, and yet includes the classical topics as they should appear in a PDE course. This is one of the first texts to take this modern approach. The large quantity of well-organized exercises and projects should help students with the correct way of approaching problems in PDE's. i

Inhalt
Setting the Scene.- Two-Point Boundary Value Problems.- The Heat Equation.- Finite Difference Schemes For The Heat Equation.- The Wave Equation.- Maximum Principles.- Poisson's Equation in Two Space Dimensions.- Orthogonality and General Fourier Series.- Convergence of Fourier Series.- The Heat Equation Revisited.- Reaction-Diffusion Equations.- Applications of the Fourier Transform.