Updated throughout, this second edition of a bestseller illustrates the usefulness of PDEs through numerous applications and helps students appreciate the beauty of the underlying mathematics. It shows students how PDEs can model diverse problems, including the flow of heat, the propagation of sound waves, the spread of algae along the ocean¿s surface, the fluctuation in the price of a stock option, and the quantum mechanical behavior of a hydrogen atom. The text also contains many exercises, including standard ones and graphical problems using MATLAB®.